1

Solutions Manual

FINANCIAL

MANAGEMENT

Principles and Practice

Fourth Edition

Timothy J. Gallagher

Colorado State University Joseph D. Andrew, Jr.

Webster University

2006 Freeload Press, Madison Wisconsin

i

(Insert publication data on this page)

ii

Solutions Manual

to accompany

Financial Management: Principles and Practice

4rd Edition

by Timothy J. Gallagher and Joseph D. Andrew, Jr.

This solutions manual provides the answers to all the review questions and end-of-chapter problems

in Financial Management: Principles and Practice, by Gallagher and Andrew. The answers and the steps

taken to obtain the answers are shown.

We remind our readers that in finance there is often more than one answer to a question or to a

problem, depending on one’s viewpoint and assumptions. We provide one answer to each question and show

one approach to solving each problem. Other answers and approaches may be equally valid, or judged even

better according to each individual’s preference.

iii

TABLE OF CONTENTS

Chapter 1 Solutions ................................................................................................................... 5

Chapter 2 Solutions ................................................................................................................... 9

Chapter 3 Solutions ................................................................................................................. 13







Chapter 10 Solutions ............................................................................................................... 67



Chapter 13 Solutions ............................................................................................................. 103









iv

5

Chapter 1 Solutions

Answers to Review Questions

1. How is finance related to the disciplines of accounting and economics?

Financial management is essentially a combination of accounting and economics. First, financial

managers use accounting information—balance sheets, income statements, and so on—to analyze,

plan, and allocate financial resources for business firms. Second, financial managers use economic

principles to guide them in making financial decisions that are in the best interest of the firm. In other

words, finance is an applied area of economics that relies on accounting for input.

2. List and describe the three career opportunities in the field of finance.

Finance has three main career paths: financial management, financial markets and institutions, and

investments.

Financial management involves managing the finances of a business. Financial managers—people

who manage a business firm's finances—perform a number of tasks. They analyze and forecast a

firm's finances; assess risk, evaluate investment opportunities, decide when and where to find money

sources and how much money to raise, and decide how much money to return to the firm's investors.

Bankers, stockbrokers, and others who work in financial markets and institutions focus on the flow of

money through financial institutions and the markets in which financial assets are exchanged. They

track the impact of interest rates on the flow of that money.

People who work in the field of investments locate, select, and manage income-producing assets. For

instance, security analysts and mutual fund managers both operate in the investment field.

3. Describe the duties of the financial manager in a business firm.

Financial managers measure the firm's performance, determine what the financial consequences will

be if the firm maintains its present course or changes it, and recommend how the firm should use its

assets. Financial managers also locate external financing sources and recommend the most beneficial

mix of financing sources, and they determine the financial expectations of the firm's owners.

All financial managers must be able to communicate, analyze, and make decisions based on

information from many sources. To do this, they need to be able to analyze financial statements,

forecast and plan, and determine the effect of size, risk, and timing of cash flows.

4. What is the basic goal of a business?

The primary financial goal of the business firm is to maximize the wealth of the firm's owners.

Wealth, in turn, refers to value. If a group of people owns a business firm, the contribution that firm

makes to that group's wealth is determined by the market value of that firm.

6

5. List and explain the three financial factors that influence the value of a business.

The three factors that affect the value of a firm's stock price are cash flow, timing, and risk.

The Importance of Cash Flow: In business, cash is what pays the bills. It is also what the firm

receives in exchange for its products and services. Cash is therefore of ultimate importance, and the

expectation that the firm will generate cash in the future is one of the factors that gives the firm its

value.

The Effect of Timing on Cash Flows: Owners and potential investors look at when firms can expect

to receive cash and when they can expect to pay out cash. All other factors being equal, the sooner

companies expect to receive cash and the later they expect to pay out cash, the more valuable the

firm and the higher its stock price will be.

The Influence of Risk: Risk affects value because the less certain owners and investors are about a

firm's expected future cash flows, the lower they will value the company. The more certain owners

and investors are about a firm's expected future cash flows, the higher they will value the company.

In short, companies whose expected future cash flows are doubtful will have lower values than

companies whose expected future cash flows are virtually certain.

6. Explain why accounting profits and cash flows are not the same thing.

Stock value depends on future cash flows, their timing, and their riskiness. Profit calculations do not

consider these three factors. Profit, as defined in accounting, is simply the difference between sales

revenue and expenses. It is true that more profits are generally better than less profits, but when the

pursuit of short-term profits adversely affects the size of future cash flows, their timing, or their

riskiness, then these profit maximization efforts are detrimental to the firm.

7. What is an agent? What are the responsibilities of an agent?

An agent is a person who has the implied or actual authority to act on behalf of another. The owners

whom the agents represent are the principals. Agents have a legal and ethical responsibility to make

decisions that further the interests of the principals.

8. Describe how society's interests can influence financial managers.

Sometimes the interests of a business firm's owners are not the same as the interests of society. For

instance, the cost of properly disposing of toxic waste can be so high that companies may be tempted

to simply dump their waste in nearby rivers. In so doing, the companies can keep costs low and

profits high, and drive their stock prices higher (if they are not caught). However, many people

suffer from the polluted environment. This is why we have environmental and other similar laws:

So that society's best interests take precedence over the interests of individual company owners.

When businesses take a long-term view, the interests of the owners and society often (but not always)

coincide. When companies encourage recycling, sponsor programs for disadvantaged young people,

7

run media campaigns promoting the responsible use of alcohol, and contribute money to worthwhile

civic causes, the goodwill generated as a result of these activities causes long-term increases in the

firm's sales and cash flows, which translate into additional wealth for the firm's owners.

9. Briefly define the terms proprietorship, partnership, and corporation.

A proprietorship is a business owned by one person.

Two or more people who join together to form a business make up a partnership. This can be done on

an informal basis without a written partnership agreement, or a contract can spell out the rights and

responsibilities of each partner.

A limited liability company is a hybrid between a partnership and a corporation. Profits and losses

pass through to the members. Members generally enjoy limited liability.

Corporations are legal entities separate from their owners. To form a corporation, the owners specify

the governing rules for the running of the business in a contract known as the articles of

incorporation. They submit the articles to the government of the state in which the corporation is

formed, and the state issues a charter that creates the separate legal entity.

10. Compare and contrast the potential liability of owners of proprietorships, partnerships (general

partners), and corporations.

The sole proprietor has unlimited liability for matters relating to the business. This means that the

sole proprietor is responsible for all the obligations of the business, even if those obligations exceed

the amount the proprietor has invested in the business.

Each partner in a partnership is usually liable for the activities of the partnership as a whole. Even if

there are a hundred partners, each one is technically responsible for all the debts of the partnership.

If ninety-nine partners declare personal bankruptcy, the hundredth partner still is responsible for all

the partnership's debts.

A corporation is a legal entity that is liable for its own activities. Stockholders, the corporation's

owners, have limited liability for the corporation's activities. They cannot lose more than the amount

they paid to buy the corporation’s stock.

Answers to End-of-Chapter Problems

1. An accountant prepares financial statements while a financial analyst interprets them.

2. A financial manager’s role in a publicly traded company is to make financial decisions so as to

best serve the principal stockholders.

8

3. a. The value of the firm would go down due to the increase in the amount of time it takes to

receive the cash inflows.

b. The value of the firm would go up due to the increase in expected cash inflows.

c. If expected future cash flows do not change the value of the firm would go down due to the

increased riskiness of the firm.

4. This practice obviously takes advantage of people who are in a difficult financial situation. This

transaction is voluntary, however, and high risk loans have high interest rates.

5. LLCs have a small number of members like partnerships and each of these members is likely to

have an active voice in the company like a partnership. The LLC is taxed like a partnership.

Unlike a partnership, and more like a corporation, the owners generally enjoy limited liability.

9

Chapter 2 Solutions


1. What are financial markets? Why do they exist?

Financial markets are where financial securities are bought and sold. They exist primarily to bring

deficit economic units (those needing money) and surplus economic units (those having extra money)

together.

2. What is a security?

Securities are claims on financial assets. They can be described as “claim checks” that give their

owners the right to receive funds in the future. Securities are traded in both the money and capital

markets. Money market securities include Treasury bills, negotiable certificates of deposit,

commercial paper, and banker’s acceptances. Capital market securities include bonds and stock.

3. What are the characteristics of an efficient market?

The term market efficiency refers to the ease, speed, and cost of trading securities. In an efficient

market, securities can be traded easily, quickly, and at low cost. Markets lacking these qualities are

considered to be inefficient.

4. How are financial trades made on an organized exchange?

Each exchange-listed security is traded at a specified location on the trading floor called the post. The

trading is supervised by specialists who act either as brokers (bringing together buyers and sellers) or

as dealers (buying or selling the stock themselves). Prominent international securities exchanges

include the New York Stock Exchange (NYSE) and major exchanges in Tokyo, London,

Amsterdam, Frankfurt, Paris, Hong Kong, and Mexico.

5. How are financial trades made in an over-the-counter market? Discuss the role of a dealer in the OTC

market.

In contrast to the organized exchanges, which have physical locations, the over-the-counter market

has no fixed location,or more correctly, it is everywhere. The over-the-counter market, or OTC, is a

network of dealers around the world who maintain inventories of securities for sale. If you wanted to

buy a security that is traded OTC, you would call your broker, who would then shop among

competing dealers who have the security in their inventory. After locating the dealer with the best

price, your broker would buy the security on your behalf.

10

The role of dealers: Dealers make their living buying securities and reselling them to others. They

operate just like car dealers who buy cars from manufacturers for resale to others. Dealers make

money by buying securities for one price (called the bid price) and selling them for a higher price,

(called the ask price). The difference, or spread, between the bid price and the ask price represents

the dealer’s fee.

6. What is the role of a broker in security transactions? How are brokers compensated?

Brokers handle orders to buy or sell securities. Brokers are agents who work on behalf of an investor.

When investors call with an order, brokers work on their behalf to find someone to take the other side

of the proposed trade. If investors want to buy, brokers find sellers. If investors want to sell, brokers

find buyers. Brokers are compensated for their services when the person whom they represent, the

investor, pays them a commission on the sale or purchase of securities.

7. What is a Treasury bill? How risky is it?

Treasury bills are short-term debt instruments issued by the U.S. Treasury that are sold at a discount

and pay face value at maturity. They are very nearly risk-free as they are backed by the U.S.

Government which could, if need by, print money to pay their holders at maturity.

8. Would there be positive interest rates on bonds in a world with absolutely no risk (no default risk,

maturity risk, and so on)? Why would a lender demand, and a borrower be willing to pay, a positive

interest rate in such a no-risk world?

Yes, there would be a positive rate of interest in a risk-free world. This is because regardless of risk,

lenders of money must postpone spending during the time the money is loaned. Lenders, then, lose

the opportunity to invest their money for that period of time. To compensate for the cost of losing

investment opportunities while they postpone their spending, lenders demand, and borrowers pay, a

basic rate of return, the real rate of interest.

Answers to End of Chapter Problems

2-1. a. Surplus economic units have income that exceeds their expenditures. Wealthy families in the

household sector and most states (which have balanced budget requirements) are surplus economic

units.

b. Deficit economic units have expenditures that exceed their incomes. Home buyers and college

students are likely to be deficit economic units.

2.2. a. false

b. false

c. false

d. false

11

2-3. a. 2 3 4 1

b. The money market is dominated by large institutional traders and there is much competition. The

New York Stock Exchange tends to have larger more actively traded stocks. The over-the-counter

market tends to have smaller less actively traded securities. The real estate market has very high

transaction costs and trades take months.

2.4. a. A money market security is short term and actively traded.

b. Treasury bills and commercial paper are both traded in the money market.

2-5. $66.25/$1,000 = 6 5/8 % coupon rate

2-6. The yield on a Bonds-R-Us bond:

Real rate of interest...................... 2%

Inflation premium........................ 3%

Default risk premium................... 1%

Liquidity risk premium................ 1%

Maturity risk premium................. 1%

Total yield on Bonds-R-Us Bond: 8%

(reference figure 2-2)

2-7. Treasury Yield Curve:

Given:

Treasury Security Yields:

Maturity in Years (for Chart)

Three-month T-bills 4.50% 0.25

Six-month T-bills 4.75% 0.5

One-year T-notes 5.00% 1

Two-year T-notes 5.25% 2

Three-year T-bonds 5.50% 3

Five-year T-bonds 5.75% 5

Ten-year T-bonds 6.00% 10

Thirty-year T-bonds 6.50% 30

Chart: (see next page)

12

Implications:

a. For borrowers: Borrowers tend to look for the low point of the curve, which indicates the least

expensive loan maturity. In this case the low point is 3 months, leading the borrower to seek a short-

term loan. However, if a firm borrows long-term and obtains the higher interest rate, that rate is

locked in for the life of the loan (30 years in this case). If interest rates rise the borrower may be glad

he/she locked in the long-term rate.

b. Lenders face the opposite situation. Granting short-term-term loans at relatively low interest rates

may look unattractive now; but if short-term rates rise, the lenders will be able to roll over

investments at higher and higher rates.

13

Chapter 3 Solutions


1. Define intermediation.

The financial system makes it possible for surplus and deficit economic units to come together,

exchanging funds for securities, to their mutual benefit. When funds flow from surplus economic

units to a financial institution to a deficit economic unit, the process is known as intermediation. The

financial institution acts as an intermediary between the two economic units.

2. What can a financial institution often do for a surplus economic unit that it would have difficulty

doing for itself if the surplus economic unit (SEU) were to deal directly with a deficit economic unit

(DEU)?

Surplus economic units do not usually have the expertise to determine whether deficit economic units

can and will make good on their obligations, so it is difficult for them to predict when a would-be

deficit economic unit will fail to pay what it owes. Such a failure is likely to be devastating to a

surplus economic unit that has lent a proportionately large amount of money. In contrast, a financial

institution is in a better position to predict who will pay and who won't. It is also in a better position,

having greater financial resources, to occasionally absorb a loss when someone fails to pay. (This is

just one example of the beneficial things financial institutions do for SEUs)

3. What can a financial institution often do for a deficit economic unit (DEU)that it would have

difficulty doing for itself if the DEU were to deal directly with an SEU?

SEUs typically want to supply a small amount of funds, while DEUs typically want to obtain a large

amount of funds. Thus it is often difficult for surplus and deficit economic units to come together on

their own to arrange a mutually beneficial exchange of funds for securities. A financial institution

can step in and save the day. A bank, savings and loan, or insurance company can take in small

amounts of funds from many individuals, form a large pool of funds, and then use that large pool to

purchase securities from individual businesses and governments. (This is just one example of the

beneficial things financial institutions do for DEUs)

4. What are a bank's primary reserves? When the Fed sets reserve requirements, what is its primary

goal?

Vault cash and deposits in the bank's account at the Fed are used to satisfy these reserve

requirements; they are called primary reserves. These primary reserves are non-interest-earning

assets held by financial institutions.

The Federal Reserve requires all commercial banks to keep a minimum amount of reserves on hand

to meet the withdrawal demands of its depositors and to pay other obligations as they come due.

14

Many would argue, however, that the reserve requirement is set more with monetary policy in mind

than to ensure that banks meet their depositors' withdrawal requests.

5. Compare and contrast mutual and stockholder-owned savings and loan associations.

Some savings and loan associations are owned by stockholders, just as commercial banks and other

corporations are owned by their stockholders. Other S&Ls, called mutuals, are owned by their

depositors. When a person deposits money in an account at a mutual S&L, that person becomes a

part owner of the firm. The mutual S&L's profits (if any) are put into a special reserve account from

which dividends are paid from time to time to the owner/depositors.

6. Who owns a credit union? Explain.

Credit unions are owned by their members. When credit union members put money in their credit

union, they are not technically "depositing" the money. Instead, they are purchasing shares of the

credit union. In general, credit unions exist to pay interest on shares bought by, and collect interest

on loans made to, the members.

7. Which type of insurance company generally takes on the greater risks: a life insurance company or a

property and casualty insurance company?

The risks protected against by property and casualty companies are much less predictable than are the

risks insured by life insurance companies. Hurricanes, fires, floods, and trial judgments are all much

more difficult to predict than the number of sixty-year-old females who will die this year among a

large number in this risk class. This means that property and casualty insurance companies must

keep more liquid assets than do life insurance companies.

8. Compare and contrast a defined benefit and a defined contribution pension plan.

In a defined benefit plan, retirement benefits are determined by a formula that usually considers the

worker's age, salary, and years of service. The employee and/or the firm contribute the amounts

necessary to reach the goal. In a defined contribution plan, the contributions to be made by the

employee and/or employer are spelled out, but retirement benefits depend on the total accumulation

in the individual's account at the retirement date.

9. Special security software is used such that customers who enter their identification and password

information can keep sensitive information out of the hands of hackers.

15


3-1. a) If there were no financial institutions the SEUs and the DEUs would find that the amount of

money needed by a given DEU did not match the amount of money available by a given SEU. The

money available would not be put to work and the economic activity that would have otherwise taken

place would not.

b) If financial institutions were available in this society they could position themselves between the

SEUs and DEUs. The financial institution could pool the $1,000 available (100 SEUs times $10

each) and pass that money along in $100 increments to the DEUs. This could be done via either a

debt or equity claim that the financial institution would accept from the DEU in return for the money.

3-2. a) .10 rate on loans made - .05 rate paid to depositors = .05 = 5% interest rate spread

b) (.5 x .10) + (.5 x .12) = .11 = 11% weighted average loan rate

(.5 x .05) + (.5 x .07) = .06 = 6% weighted average deposit rate

11% - 6% = 5% interest rate spread

3-3. ($48,300,000 - $7,800,000) x .03) + (($60,000,000 - $48,300,000) x .10) + ($20,000,000 x 0) +

($10,000,000 x 0) = $6,732,000

3-4. a) The FOMC should buy government securities in the open market. This would increase the

reserves of the banking system and would put downward pressure on the federal funds rate.

b) The Fed’s trader at the New York Federal Reserve Bank would contact various government

securities dealers and would buy the Treasury securities from them. Payment would be made by

crediting the accounts at the Fed of these dealers. This would make more funds available and would

tend to put downward pressure on the cost of these funds, the federal funds rate.

3-5. a) ($1,000,000 x .08) – ($1,000,000 x .07) = $10,000 a profit of $10,000

b) ($1,000,000 x .08) – ($1,000,000 x .09) = -$10,000 a loss of $10,000

16

Chapter 4 Solutions


1. Why do total assets equal the sum of total liabilities and equity? Explain.

Assets = Liabilities + Equity

Assets are the items of value a business owns. Liabilities are claims on the business by non-owners,

and equity is the owners' claim on the business. The sum of the liabilities and equity is the total

capital contributed to the business, which, by definition, equals the total value of the assets.

2. What are the time dimensions of the income statement, the balance sheet, and the statement of cash

flows? Hint: Are they videos or still pictures? Explain.

The income statement is like a video: It measures a firm's profitability over a period of time (which

can be a week, a month, a year, or any other time period).

The balance sheet is like a still photograph. The balance sheet shows the firm's assets, liabilities, and

equity at a given point in time.

This cash flow statement like the income statement, can be compared to a video: It shows how cash

flows into and out of a company over a given period of time.

3. Define depreciation expense as it appears on the income statement. How does depreciation affect

cash flow?

Accounting depreciation is the allocation of an asset's initial cost over time. Depreciation expense on

an income statement is the amount of the asset=s initial cost allocated to the period covered by the

income statement.

Depreciation expense is not a cash flow. Depreciation as an expense category affects cash flow,

however, because it is tax-deductible. Depreciation expense lowers a company’s taxable income

and, therefore its income tax liability. In this way depreciation reduces cash outflows..

4. What are retained earnings? Why are they important?

Retained earnings represents the sum of all the earnings available to common stockholders of a

business during its entire history, minus the sum of all the common stock dividends which it has ever

paid. Those earnings that were not paid out were, by definition, retained.

Retained earnings are important because they represent amounts reinvested in a company on behalf

of the company’s owners instead of being paid out in the form of dividends.

17

5. Explain how earnings available to common stockholders and common stock dividends paid from the

current income statement affect the balance sheet item retained earnings.

The change in the retained earnings account from one balance sheet to the next equals net income

less preferred stock dividends (which is the amount of earnings available to common stockholders)

less common stock dividends.

6. What is accumulated depreciation?

Depreciation is the allocation of an asset's initial cost over time. Accumulated depreciation is the

total of all the depreciation expense that has been recognized to date.

7. What are the three major sections of the statement of cash flows?

Cash flows from Operations

Cash flows from investing activities

Cash flows from financing activities

Net change in cash balance

Cash balance at beginning of period

Cash balance at end of period

8. How do financial managers calculate the average tax rate?

Average tax rates are calculated by dividing tax dollars paid by earnings before taxes (EBT).

9. Why do financial managers calculate the marginal tax rate?

Financial managers use marginal tax rates to estimate the future after-tax cash flows from

investments. Since they are interested in how much of the next dollar earned from new investments

will have to be paid in taxes, they use the marginal tax rate (rather than the average tax rate) to

calculate the tax liability.

10. Identify whether the following items belong on the income statement or the balance sheet.

a. Interest Expense IS l. Cash BS

b. Preferred Stock Dividends Paid IS m. Capital in Excess of Par BS

c. Plant and Equipment BS n. Operating Income IS

d. Sales IS o. Depreciation Expense IS

e. Notes Payable BS p. Marketable Securities BS

f. Common Stock BS q. Accounts Payable BS

g. Accounts Receivable BS r. Prepaid Expenses BS

h. Accrued Expenses BS s. Inventory BS

i. Cost of Goods Sold IS t. Net Income IS

j. Preferred Stock BS u. Retained Earnings BS

k. Long-Term Debt BS

18

11. Indicate in which section the following balance items belong (current assets, fixed assets, current

liabilities, long-term liabilities, or equity).

a. Cash CA h. Capital in Excess of Par EQ

b. Notes Payable CL i. Marketable Securities CA

c. Common Stock EQ j. Accounts Payable CL

d. Accounts Receivable CA k. Prepaid Expenses CA

e. Accrued Expenses CL l. Inventory CA

f. Preferred Stock EQ m. Retained Earnings EQ

g. Plant and Equipment FA


4-1.

CASE A CASE B

Revenues 200,000 110,000

Expenses 160,000 70,000

Net Income 40,000 40,000

Retained Earnings, Jan 1 300,000 100,000

Dividends Declared 70,000 30,000

Retained Earnings, Dec 31 270,000 110,000

Current Assets, Dec 31 80,000 230,000

Non-current Assets, Dec 31 850,000 180,000

Total Assets, Dec 31 930,000 410,000

Current Liabilities, Dec 31 40,000 60,000

Non-current Liabilities, Dec 31 100,000 140,000

Total Liabilities, Dec 31 140,000 200,000

CS & Cap. in Excess of Par, Dec 31 520,000 100,000

Total Stockholders’ Equity, Dec 31 790,000 210,000

4-2.

CASE A CASE B

Sales 500,000 250,000

COGS 200,000 100,000

Gross Profit 300,000 150,000

Operating Expenses 60,000 60,000

Operating Income (EBIT) 240,000 90,000

Interest Expense 10,000 10,000

Earnings Before Taxes (EBT) 230,000 80,000

Tax Expense (40%) 92,000 32,000

Net Income 138,000 48,000

4-3. a) 15%; $48,000 X 0.15 = $7,200

b) $7,200/$48,000 = 0.15 or 15%

19

4-4. a) Tax = $50,000 X 0.15 + $25,000 X 0.25 + $25,000 X 0.34 + $50,000 X 0.39

= $41,750

b) Effective tax rate = $41,750/$150,000 = 0.2783 or 27.83%

4-5. The marginal tax rate is the tax rate applied to the next dollar of income. Therefore, the marginal tax

rate is 34%.

The average tax rate is 34%

50,000 * .15 = 7,500

25,000 * .25 = 6,250

25,000 * .34 = 8,500

235,000 * .39 = 91,650

2,865,000 * .34 = 974,100

$1,088,000

$1,088,000/$3,200,000 = 34%

4-6. $1 + $400,000/200,000 = $3.00 per share

4-7. Sales $10,000,000

- Operating Costs 5,200,000

- Interest Expense 200,000

= EBT $4,600,000

- Taxes (40%) 1,840,000

Net after-tax income $2,760,000

Simon’s net after-tax income was $2,760,000 for the year.

4-8. Depreciation expense in 2006 = $70,000 - $60,000 = $10,000.

4-9

a) Cash + Marketable Securities + Inventory + Accounts Receivable + Prepaid expenses.

(11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) = 35,000,000

Current Assets = $35,000,000

b) Fixed assets – depreciation

30,000,000 – 8,000,000 = 22,000,000

Net Fixed Assets = $22,000,000

c) Notes Payable + Accrued Expenses

4,000,000 + 2,000,000 = 6,000,000

Current Liabilities = $6,000,000

20

d) Current Assets – Current Liabilities

(11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) – (4,000,000 + 2,000,000)

35,000,000 – 6,000,000 = 29,000,000

Net Working Capital = $29,000,000

4-10. a ) Gross Profit $440,000 - $200,000 = $240,000

b ) Operating Income (EBIT) $240,000 - $40,000 - 85,000 = $115,000

c ) Earning Before Taxes (EBT) $ 115,000 - $40,000 = $75,000

d ) Income Taxes $ 75,000 X 0.4 = $30,000

e ) Net Income $75,000 - $30,000 = $45,000

4-11 $1,500,000 – $200,000 = $1,300,000

Simon and Pieman had a net worth of $1,300,000 at the end of the year.

4-12 a ) 2006 Depreciation Expense for this process line

($131,000 + $12,000) X (0.245) = $35,035

b ) Amount of tax savings due to this investment.

$35,035 X 0.4 = $14,014

4-13. Operating Income (EBIT) = $768,000

+ Depreciation = $42,000

+ Amortization = $15,000

$825,000

Target Telecom’s EBITDA = $825,000.

4-14 a ) The company's 2006 taxable income = ($400,000 - $130,000 X 0.2)

= $374,000

b ) Income tax = $374,000 X 0.34 = $127,160

4-15. a) Earnings = [($600,000 - 50,000) X (1 - .34) - $63,000] = $300,000

Earnings per share = $300,000 / 100,000 = $3 per share

b) Addition to Retained Earnings = $300,000 - 100,000 = $200,000

21

4-16. a ) Current Assets: 2005: $5,534 + 14,745 + 10,733 + 952 + 3,234 = $35,198

2006: $9,037 + 15,943 + 11,574 + 1,801 + 2,357=$40,712

b ) Total Assets: 2005: $35,198+(57,340 - 29,080)+1,010+2,503 = $66,971

2006: $40,712+(60,374 - 32,478)+1,007+4,743 = $74,358

c ) Current Liabilities: 2005: $3,253 + 6,821 = $10,074

2006: $2,450 + 7,330 = $9,780

d ) Total Liabilities: 2005: $10,074 + 2,389 = $12,463

2006: $9,780 + 2,112 = $11,892

e ) Total Stockholders' Equity: 2005: $8,549 + 45,959 = $54,508

2006: $10,879 + 51,587 = $62,466

4-17. 2005: $12,463 TL + $54,508 EQ = $66,971 TA

2006: $11,892 TL + $62,466 EQ = $74,358 TA

4-18. (Dollars)

a ) Accumulated Depreciation 3,398 Inflow

b ) Accounts Receivable (net) 1,198 Outflow

c ) Inventories 841 Outflow

d ) Prepaid Expenses 877 Inflow

e ) Accounts Payable 803 Outflow

f ) Accrued Expenses 509 Inflow

g ) Plant and Equipment (gross) 3,034 Outflow

h ) Marketable Securities 849 Outflow

i ) Land 3 Inflow

j ) Long Term Investments 2,240 Outflow

k ) Common Stock 2,330 Inflow

l ) Bonds Payable 277 Outflow

4-19. Pinewood Company and Subsidiaries

Statement of Cash Flows For the year 2006

Operations: Net Income 10,628

Add: Depreciation Exp. 3,398

Decrease in Prepaid Expenses 877

Increase in Accrued Expenses 509

Less: Increase in A/C Receivable (1,198)

Increase in Marketable Securities ( 849)

Increase in Inventories ( 841)

Decrease in A/C Payable ( 803)

Total Cash Flow from Operations $11,721

Investments:

Add: Decrease in Land 3

Less: Increase in Plant and Equipment (3,034)

Increase in Long Term Investment (2,240)

Total Cash Flow from Investments ($5,271)

22

Financing:

Add: Increase in Common Stock 2,330

Less: Common Stock Dividends (5,000)

Decrease in Bonds Payable ( 277)

Cash Flow from Financing ($2,947)

Net Cash Flow $3,503

4-20. $3,503 = $9,037 end of ‘02 cash - $5,534 end of ‘01 cash Yes, the net cash flow figure from

problem #16 gives the same answer as calculating the change in the cash figures from the end of 2005 to the

end of 2006 balance sheets.

4-21. Sales 900,000

COGS 300,000

Gross Profit 600,000

Operating Expenses 200,000

Operating Income (EBIT) 400,000

Interest Expense 100,000

Income before taxes (EBT) 300,000

Tax Expense (30%) 90,000

Net Income $210,000

4-22. Retained Earnings end of 2006 $8,700,000

Retained Earnings end of 2005 8,000,000

Addition to retained earnings 2006 700,000

Earnings Available to Common Stockholders $1,500,000

-Addition to Retained Earnings -700,000

Dividends paid to Common Stockholders 2006 = $ 800,000

4-23. Year Deprec. % * Depreciable Base = Depreciation

1 10% $385,000 $38,500

2 18% $385,000 $69,300

3 14.4% $385,000 $55,440

4 11.5% $385,000 $44,275

5 9.2% $385,000 $35,420

6 7.4% $385,000 $28,490

7 6.6% $385,000 $25,410

8 6.6% $385,000 $25,410

9 6.5% $385,000 $25,025

10 6.5% $385,000 $25,025

11 3.3% $385,000 $12,705

4-24. Basis = $1,000,000 + $100,000 + $50,000 = $1,150,000

Year 3 depreciation = $1,150,000 * .148 = $170,200

23

4-25. Year 1 $7,000,000 * .1 = $700,000

Year 2 $7,000,000 * .18 = $1,260,000

Year 3 $7,000,000 * .144 = $1,008,000

Year 4 $7,000,000 * .115 = $805,000

Year 5 $7,000,000 * .092 = $644,000

Year 6 $7,000,000 *.074 = $518,000

Year 7 $7,000,000 * .066 = $462,000

Year 8 $7,000,000 * .066 = $462,000

Year 9 $7,000,000 * .065 = $455,000

Year 10 $7,000,000 * .065 = $455,000

Year 11 $7,000,000 * .033 = $231,000

24

Chapter 5 Solutions


1. What is a financial ratio?

A financial ratio is a number that expresses the value of one financial variable relative to another.

Put more simply, a financial ratio is the result you get when you divide one financial number by

another. Calculating an individual ratio is simple, but each ratio must be analyzed carefully to

effectively measure a firm's performance.

2. Why do analysts calculate financial ratios?

Ratios are comparative measures. Because the ratios show relative value, they allow financial

analysts to compare information that could not be compared in its raw form. For example, ratios may

be used to compare one ratio to a related ratio, a firm's performance to management's goals, a firm's

past and present performance, or a firm's performance to similar firms

3. Which ratios would a banker be most interested in when considering whether to approve an

application for a short-term business loan? Explain.

Bankers and other lenders use liquidity ratios to see whether to extend short-term credit to a firm.

Liquidity ratios measure the ability of a firm to meet its short-term obligations. These ratios are

important because failure to pay such obligations can lead to bankruptcy. Generally, the higher the

liquidity ratio, the more able a firm is to pay its short-term obligations.

4. Which ratios would a potential long-term bond investor be most interested in? Explain.

Current and potential lenders of long-term funds, such as banks and bondholders, are interested in

debt ratios. When a business's debt ratios increase significantly, bondholder and lender risk increases

because more creditors compete for that firm's resources if the company runs into financial trouble.

5. Under what circumstances would market to book value ratios be misleading? Explain.

The Market to Book ratio is useful, but it is only a rough approximation of how liquidation and going

concern values compare. This is because the Market to Book ratio uses accounting-based book

values. The actual liquidation value of a firm is likely to be different than the book value. For

instance, the assets of a firm may be worth more or less than the value at which they are currently

carried on the company's balance sheet. In addition, the current market price of the company's bonds

and preferred stock may also differ from the accounting value of these claims.

25

6. Why would an analyst use the Modified Du Pont system to calculate ROE when ROE may be

calculated more simply? Explain.

Actually, an analyst would not use the Modified Du Pont equation to calculate ROE for precisely the

reason stated above. What an analyst would use the Modified Du Pont equation for is to help analyze

the factors that contribute to a firm's ROE. In other words, analysts use the Modified Du Pont system

to “take apart” ROE to see what factors are influencing it.

7. Why are trend analysis and industry comparison important to financial ratio analysis?

Trend analysis helps financial managers and analysts see whether a company's current financial

situation is improving or deteriorating.

Cross-sectional analysis, or industry comparison, allows analysts to put the value of a firm's ratios in

the context of its industry.


5-1. a) Gross Profit Margin = Gross Profit/Sales

20,000,000/35,000,000 = .5714

Gross Profit margin = 57.14%

b) Operating Profit Margin = EBIT/Sales

16,000,000/35,000,000 = .4571

Operating Profit Margin = 45.71%

c) Net Profit Margin = Net Income/Sales

8,100,000/35,000,000 = .2314

Net Profit Margin = 23.14%

5-2. Current Ratio = Total Current Assets/Total Current Liabilities

(5,000) / (500 +850 + 600) = 2.56

Current Ratio = 2.56

Quick Ratio = (Total Current Assets - Inventory)/Total Current Liabilities

(5,000 – 900)/(500 + 850 + 600) = 2.10

Quick Ratio = 2.10

5-3. Average Daily Credit Sales = Annual credit sales/365

5,000,000/365 = $13,698.63

Average Collection Period = Accounts Receivable/Average Daily Credit Sales

$500,000/13,698.63 = 36.5

Average Collection Period = 36.5 days

26

5-4. Inventory Turnover = Sales/Inventory

35,000,000/2,400,000 = 14.58

Inventory Turnover = 14.58 X

Total Asset Turnover = Sales/Total Assets

35,000,000/(15,000,000 + 20,000,000) = 1

Total Asset Turnover = 1 X

5-5. a) Book value per share

Book price per share = Common Stock Equity/Number of shares Outstanding

$4,500,000/650,000 =$6.92

BPS = $6.92

b) Market to book value ratio

Market to book value ratio = Market price per share/Book value per share

$25.00/$6.92 = 3.61

Market to book value ratio = 3.61

5-6. a) Gross profit margin: $47,378/$94,001 = 50.40%

b) Operating profit margin $12,941/$94,001 = 13.77%

c) Net profit margin $8,620/$94,001 = 9.17%

d) Return on assets $8,620/$66,971 = 12.87%

e) Return on equity $8,620/$54,508 = 15.81%

While the Net profit margin is higher than the industry average, the Return on assets is lower. Pinewood

may consider increasing its debt to leverage profits.

5-7. a) Current assets = $5,534 + $14,745 + $10,733 + $952 + $3,234 = $35,198

Current ratio = $35,198/$10,074 = 3.494

b) Quick ratio = ($35,198 - $10,733)/$10,074 = 2.429

Pinewood seems highly capable of paying off short-term debts.

5-8. a) Total debt = $3,253 + $6,821 + $2,389 = $12,463

Debt to total assets = $12,463/$66,971 = 18.61%

b) Times interest earned = $12,941/$48 = 270 times

Yes. The Pinewood has very low debt and its earnings are extremely high compared to its interest

expense.

5-9. a. Average collection period $14,745/($94,001 / 365) = 57.25 days

b. Inventory turnover $94,001/$10,733 = 8.76

c. Total asset turnover $94,001/$66,971 = 1.404

We would need to know the industry averages for these figures, and also know about Pinewood’s

credit and inventory management practices to comment meaningfully on the above figures.

27

5-10. Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity

= 0.0917 X 1.404 X $66,971/$54,508 = 15.82%

5-11. a) EVA = EBIT (1- tax rate) – (invested capital * investor’s required rate of return)

EVA = $12,941,000 * (1 - 0.35) – ($77,389,000 * 0.10) = $672,750

b) Pinewood has a true economic profit of $672,750. This is the amount by which its

earnings exceed the returned expected by the firm’s investors.

c) MVA = Total market value – invested capital

MVA = ($75,000,000 + $2,389,000) – ($54,508,000 + $2,389,000) = $20,492,000

d) Pinewood has a total market value that is $20,492,000 greater that the amount of capital

invested in the firm.

5-12. a) EVA = EBIT (1 – Tax Rate) – (invested capital * investors required rate of return)

EVA = $8,000 (.65) – ($33,000 * .12)

= $5,200 – $3,960

EVA = $1,240

b) The economic value is positive; therefore, Eversharp earned a sufficient amount during the

year to provide more than the expected rate of return from the investors and lenders who

contributed to the capital of the company.

c) MVA = Total market value – invested capital

MVA = $33,000 - $21,000 = $12,000

d) Eversharp’s total market value exceeds its invested capital by $12,000.

5-13. EVA & MVA Calculation:

Income tax rate 35%

Cost of Capital 12% Ka

Stock Price (ref) $9

Number of shares outstanding (ref) 3,000

Market Value of Common Equity (ref) $27,000

Book Value of Common Equity $15,210

Debt Capital (ref) $6,630 (Notes payable + Long-Term Debt )

Total Invested Capital (ref) $33,630 (Debt + Common)

EVA

MVA

a. EVA $189 EBIT(1-Tr) - (Invested Capital * Ka)

b. Comment on EVA: This year T & J earned enough to exceed the return expected by the

contributors of the firm's capital by $189.

28

5-14. a. Du Pont: ROA = Net Profit Margin X Total Asset Turnover

= (80/1,000) X (1,000/500) = 16%

Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over

Equity

= ($80/$1,000) X ($1,000/$500) X (1/(1-0.5) = 32%

b. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.7) = 53.3%

c. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.9) = 160%

d. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.1) = 17.78%

5-15.

Assets Liabilities + Equity

Cash $6,000 Accounts Payable $6,000

Accounts Receivable 15,068 Notes Payable 2,739

Inventory 6,667 Accrued Expenses 600

Prepaid Expenses 282 Total Current Liabilities 9,339

Total Current Assets 28,017 Bonds Payable 15,661

Fixed Assets 34,483 Common Stock 16,000

Retained Earnings 21,500

Total Assets $62,500 Total Liabilities + Equity $62,500

Total Assets = Sales / Total Asset Turnover = $100,000/1.6 = $62,500

Fixed Assets = Sales / Fixed Asset Turnover = $100,000/2.9 = $34,483

Total Current Assets = $62,500 - $34,483 = $28,017

Accounts Receivable = Sales/day X Ave. Collection Period = ($100,000/365) X 55 = $15,068

Inventory = Sales / Inventory Turnover = $100,000/15 = $6,667

Prepaid Expenses = $28,017 - ($15,068 + $6,667 + $6,000) = $282

Total Debt = Total Assets X Debt to Asset Ratio = $62,500 X 0.4 = $25,000

Total Current Liabilities = Total Current Assets / Current Ratio = $28,017/3 = $9,339

Bonds Payable = Total Debt - Total Current Liabilities = $25,000 - $9,339 = $15,661

Retained Earnings = $62,500 - ($16,000 + $25,000) = $21,500

Notes Payable = $9,339 - ($600 + $6,000) = $2,739

5-16. NI/$5,000 = 0.10

NI = $500

TE = TA - TL = $10,000 - $6,000 = $4,000

ROE = $500/$4,000 = .125 = 12.5%

5-17. Current Liability = $20,000 - $18,000 = $2,000

Current Ratio = $5,000/$2,000 = 2.5 times

5-18. Return on Assets = Net Profit Margin X Total Asset Turnover

0.12 = 0.04 X Total Asset Turnover

Total Asset Turnover = 0.12/0.04 = 3

29

5-19. Gross Profit = 0.50 X $5,000,000 = $2,500,000

5-20. EBIT = $2,500,000 - $200,000 - $50,000 = $2,250,000

Operating Profit Margin = $2,250,000/$5,000,000 = .45 = 45%

5-21. Net Income = 0.20 X $5,000,000 = $1,000,000

5-22. Net Income = 0.20 X $5,000,000 = $1,000,000

ROA = $1,000,000/$20,000,000 = .05 = 5%

5-23. Net Income = 0.10 X $15,000,000 = $1,500,000

5-24. Current Ratio = (20,000,000 - 2,000,000)/4,000,000 = 4.5

5-25. Quick Ratio = ($20,000,000 - $2,000,000 - $3,000,000)/$4,000,000 = 3.75 times

5-26. Total Debt = 0.30 X $20,000,000 = $6,000,000

Debt to Equity ratio = $6,000,000/$14,000,000 = 0.43

5-27. Inventory Turnover = 5,000,000/3,000,000 = 1.67

5-28. Return on Assets = 0.20 X 0.25 = 0.05 = 5%

5-29. a) Du Pont: ROA = Net Profit Margin X Total Asset Turnover

= ($200/$2,000) X ($2,000/$1,000) = .20 = 20%

Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity

= ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.6)) = .50 = 50%

b) ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.8)) = 100%

c) ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.2)) = 25%

5-30. Notoriously Niagara Niagara’s Notions

a) NPM = $100,000/$500,000 = 0.20 NPM = $10,000/$500,000 = 0.02

b) TATO = $500,000/$500,0000 = 0.10 TATO = $500,000/$500,000 = 1.0

c) ROA = 0.20 X 0.10 = 0.02 ROA = 0.02 X 1.0 = 0.02

30

d) Notoriously Niagara must have a higher net profit margin because their asset turnover is low

compared to that of Niagara’s Notions even though they have the same ROA. Niagra’s Notions has a high

asset turnover but a low net profit margin.

5-31. a ) $2,250,000/1,750,000=$1.29

b ) $40/$1.29 = 31

c ) $15,000,000/1,750,000 = $8.57

d ) $40/$8.57 = 4.67

e ) Yes, the market seems to believe that the company has going-concern value as evidenced by

the market to book ratio greater than 1.

5-32. Net Profit Margin Current Ratio Total Asset Turnover

Year NI/Sales CA/CL Sales/TA

2004 10.00% .94 1.05

2005 9.44% 1.02 1.15

2006 9.36% 1.08 1.18

Golden Products

Industry averages: 9.42% 1.13 2.00

The NPM is about average, although it is deteriorating. The liquidity, as measured by the current

ratio, is below average but improving. Asset utilization, as measured by the total asset turnover is way below

average.

5-33. The Industry averages are:

Fixed Asset Turnover Return on Assets Debt to Assets Ratio Return on equity

1.33 11.00% 0.60 26%

YEAR PM CR TATO FATO ROA D/A ROE

2004 10.00% 0.94 1.05 1.21 10.53% 0.68 33.33%

2005 9.44% 1.02 1.15 1.33 10.90% 0.64 30.36%

2006 9.36% 1.08 1.18 1.36 11.00% 0.60 27.50%

Golden Products has an improving ROA that now equals that of the industry norm. The ROE has

slipped a little, but is still above the industry norm in spite of the fact that Golden has a little less debt

in its capital structure in 2006. Overall, Johnny should be pleased.

5-34. ( Figures in $ '000) Mining Smelting Rolling Extrusion Whole Company

NPM 3.3% 8.7% 11.7% 10.0% 9.7%

ROA 4.2% 10.4% 17.9% 13.9% 13.4%

31

5-35. National Glass Company

Income Statement (in $ 000's) Ratios:

2006

ACP 48.7 days

Sales $45,000 Inventory Turnover 9 X Cost of Goods Sold 23,000 Debt to Assets 40%

Gross Profit 22,000 Current Ratio 1.6250

Selling and Admin Expenses 13,000 Total Asset turnover 1.50

Depreciation 3,000 Fixed Asset Turnover 2.6471

Operating Income 6,000 Return on Equity 19.33%

Interest Expense 200 Return on Assets 11.6%

Earnings Before Tax 5,800 Operating Profit Margin 13.33%

Income Taxes 2,320 Gross Profit Margin 48.89%

Net Income $3,480

Preferred Dividends $0

Earnings Available to Common $3,480

Balance Sheet (in $ 000's)

As of Dec 31

2006

Assets

Current Assets:

Cash $2,000

Accounts Receivable 6,000

Inventory 5,000

Total Current Assets 13,000

Plant & Equipment, Net 16,000

Land 1,000 Total Assets $30,000

Liabilities & Equity Current Liabilities: Accounts Payable $2,000 Notes Payable 3,000

Accrued Expenses 3,000 Total Current Liabilities 8,000 Bonds Payable 4,000

Total Liabilities 12,000 Common Stock 4,000 Retained Earnings 14,000

Total Stockholders' Equity 18,000 Total Liabilities & Equity $30,000

5-36.

a.) (Industry) Kingston, 2006 Kingston, 2007

i. Gross Profit Margin (50%) 48.9% 48.9%

ii. Operating Profit Margin (15%) 15.1% 13.3%

iii. Net Profit Margin (8%) 8.5% 7.5%

iv. Return on Assets (10%) 11.56% 9.97%

v. Return on Equity (20%) 19.3% 16.3%

vi. Current Ratio (1.5) 1.63 1.62

vii. Quick Ratio (1.0) 1.00 1.04

viii. Debt to Total Asset (0.5) .4 .39

ix. Times Interest Earned (25) 15.5X 14.6X

32

x. Average Collection Period (45 days) 53.5days 61.6days

xi. Inventory Turnover (8) 8.18X 8.62X

xii. Total Asset Turnover (1.6) 1.4X 1.3X

b.) Kingston has about the same net profit margin and return on equity as the industry norm. The return on

assets ratio for Kingston is about the same as than the industry norm.

c.) Determine the sources and uses of funds and prepare a statement of cash flows for 2007.

(1) Sources and Uses of Funds: Change, 2006 to 2007 Balance Sheet Sources Uses Net Income $3,353

Dividends paid $733

Depreciation $3,000

Cash ($200) $200

Accounts Receivable, Net $1,600 $1,600

Inventory $220 $220

Property, Plant & Equipment, Gross $5,000 $5,000

Land $0

Accounts Payable $600 $600

Notes Payable $300 $300

Accrued expenses $100 $100

Bonds Payable $0

Common Stock $0

Totals $7,553 $7,553

(2) Statement of Cash Flows:

Kingston Tool Company

Statement of Cash Flows for the year 2007

( in $ 000s)

Cash Flows from Operations:

Net Income $3,353

Depreciation 3,000

Decrease(Increase) in Accounts Receivable (1,600)

Decrease(Increase) in Inventory (220)

Increase(Decrease) in Accounts Payable 600

Increase(Decrease) in Notes Payable 300

Increase(Decrease) in Accrued Expenses 100

Total Cash Flows from Operations $5,533

Cash Flows from Investments:

New Property, Plant, & Equipment ($5,000)

Total Cash Flows from Investments ($5,000)

Cash Flows from Financing:

Dividends Paid ($733)

Total Cash Flows from Financing (733)

-

Net Cash Flow ($200)

Beginning Cash Balance $2,000

Ending Cash Balance $1,800

33

d.) Profit margins are eroding and generally a little below the industry norm. Liquidity is about average.

Debt is low, but interest coverage is below the industry norm in spite of the low debt load. Inventory

turnover is way below average. The negative cash flow of $200,000 came mainly from the buildup of

accounts receivable and plant & equipment.

e.) The current ratio, quick ratio, and times interest earned would get the most scrutiny from loan officers.

5-36b. EVA = EBIT * (1 – tax rate) – (invested capital * investor’s required rate of return)

EVA = ($4,000 * 0.60) – ($60,000 * 0.10) = -$3,600

EVA = -$3,600

MVA = Total market value – invested capital

MVA = $50,000 - $60,000 = -$10,000

MVA = -$10,000

5.37. a) Accounts Receivable/Average Daily Credit Sales

$564,000.00 / ($3,814,000 / 365)= 53.71 = 54 days

b) Super Dot Com was more profitable in 2006 than it was in 2004.

2004 2006_________

$519,000/$2,100,000 $1,115,000/$3,814,000

Net Profit Margin 24.71% 29.23%

$519,000/$2,859,000 $1,115,000/$5,316,000

Return on Assets 18.15% 20.97%

Both the NPM and ROA ratios were better in 2006.

c) Super Dot Com was less liquid at the end of 2006 than it was at the end of 2004.

2004 2006_________

$981,000/$245,000 $1,720,000/$623,000

Current Ratio 4.00 2.76

($981,000 - $307,000)/$245,000 ($1,720,000 - $960,000)/$623,000

Quick Ratio 2.75 1.22

34

Chapter 6 Solutions


1. Why do businesses spend time, effort, and money to produce forecasts? Explain.

Businesses succeed or fail depending on how well prepared they are to deal with the situations they

confront in the future. Therefore they expend considerable sums making estimates (forecasts) of

what the future situation is likely to be. Businesses develop new products, set production quotas, and

select financing sources based on forecasts about the future economic environment and the firm's

condition. If economists predict interest rates will be relatively high, for example, firms may plan to

limit borrowing and defer expansion plans.

2. What is the primary assumption behind the experience approach to forecasting?

The experience approach to forecasting is based on the assumption that things will happen a certain

way in the future because they happened that way in the past. For instance, if it has always taken you

fifteen minutes to drive to the grocery store, then you will probably assume that it will take you about

fifteen minutes the next time you drive to the store. Similarly, financial managers often assume sales,

expenses, or earnings will grow at certain rates in the future because they grew at that rate in the past.

3. Describe the sales forecasting process.

Sales forecasting is a group effort. Sales and marketing personnel usually provide assessments of

demand and the competition. Production personnel usually provide estimates of manufacturing

capacity and other production constraints. Top management will make strategic decisions affecting

the firm as a whole. Financial managers coordinate, collect, and analyze the sales forecasting

information. Figure 6-1 in the text shows a diagram of the process.

4. Explain how the cash budget and the capital budget relate to pro forma financial statements.

The cash budget shows the projected flow of cash in and out of the firm for specified time periods.

The capital budget shows planned expenditures for major asset acquisitions. Forecasters incorporate

data from these budgets into pro forma financial statements under the assumption that the budget

figures will, in fact, occur.

5. Explain how management goals are incorporated into pro forma financial statements.

Management sets a target goal, and forecasters produce pro forma financial statements under the

assumption that the goal will be reached. For example, if management’s goal is to pay off all short-

term notes during the coming year, forecasters would incorporate this into the pro forma balance

sheet by setting Notes Payable to zero.

35

6. Explain the significance of the term additional funds needed.

When the pro forma balance sheet is completed, total assets and total liabilities and equity will rarely

match. The discrepancy between forecasted assets and forecasted liabilities and equity results when

either too little or too much financing is projected for the amount of asset growth expected. The

discrepancy is called additional funds needed (AFN) when forecast assets exceed forecast liabilities

and equity, and excess financing when forecast liabilities and equity exceed forecast assets.

7. What do financial managers look for when they analyze pro forma financial statements?

After the pro forma financial statements are complete, financial managers analyze the forecast to

determine (1) what current trends suggest what will happen to the firm in the future, (2) what effect

management's current plans and budgets will have on the firm, and (3) what actions to take to avoid

problems revealed in the pro forma statements

8. What action(s) should be taken if analysis of pro forma financial statements reveals positive trends?

Negative trends?

When analyzing the pro forma statements, managers often see signs of emerging positive or negative

conditions. If forecasters discover positive indicators, they will recommend that current plans be

continued. If forecasters see negative indicators, they will recommend corrective action.


6-1.

Sales Record for The Miniver Corporation

Sales in 2007 is expected to be approximately $215,000 following the trend of the last six years as shown

above.

$0

$50,000

$100,000

$150,000

$200,000

$250,000

1997 1998 1999 2000 2001 2002 2003

36

6-2.

This year Next Year Forecasting Assumption

Sales 100 120 Sales will grow 20%(100 X 1.2)

- Variable Costs 50 60 Constant % of sales(120 X 0.5)

- Fixed Costs 40 40 Remains same

= Net Income 10 20 (120 - 60 - 40)

Dividends 5 10 Keep 50% Payout Ratio(20 X 0.5)

Current Assets 60 72 Constant % of sales(120 X 0.6)

Fixed Assets 100 100 Remains same

Total Assets 160 172 (100 + 72)

Current Liabs. 20 24 Constant % of sales (120 X 0.2)

Long-term Debt 20 20 Remains same

Common Stock 20 20 Remains same

Retained Earns. 100 110 (100+20-10)

Tot Liabs & Eq 160 174

AFN = 172-174= -2 (Negative AFN means there are excess funds.)

6-3. Jolly Joe's Pizza, Inc.

Financial Status and Forecast

2006 Est. for 2007

Sales $10,000 20,000

COGS 4,000 8,000

Gross Profit 6,000 12,000

Fixed Expenses 3,000 3,000

Before-Tax Profit 3,000 9,000

Tax @ 33.33% 1,000 3,000

Net Profit $2,000 6,000

Dividends $0 0

Current Assets $25,000 50,000

Net Fixed Assets 15,000 15,000

Total Assets $40,000 65,000

Current Liabilities $17,000 34,000

Long-term debt 3,000 3,000

Common Stock 7,000 7,000

Retained Earnings 13,000 19,000

Total Liabs & Eq $40,000 63,000

Joe will need $2,000 in additional funds in 2007 ($65,000 - $63,000).

37

6-4. Sugar Cane Alley

Financial Status and Forecast

2006 Est. for 2007

Sales $90,000 110,000

COGS 48,000 58,667


Selling and

marketing expenses 13,000 15,889

General and admini-

strative expenses 5,000 5,000

Depreciation Expense 2,000 2,000

Operating Income 22,000 28,444

Interest Expense 800

EBT 27,644

Tax @ 30% 8,293

Net Profit 19,351

Dividends 10,000

Addition to RE 9,351

6-5. a ) Cash .111111 X $110,000 = $12,222

Accounts Receivable .024667 X $110,000 = $2,713

Inventory .088889 X $110,000 = $9,778

b ) Property and Equipment, gross $25,000

Accumulated Depreciation $6,000

Property and Equipment, net $19,000

Total Assets $19,000 + $12,222 + $2,713 + $9,778 = $43,713

c ) Accounts Payable .015333 X $110,000 = $1,687

d ) Total Liabilities = $8,000 + $1,687 = $9,687

e ) Total Liabilities and Equity = $9,687 + $9,351 + $5,000 + $26,840

= $50,878

f ) Total Assets = $12,222 + $2,713 + $9,778 + $19,000 = $43,713

AFN = $43,713 - $50,878 = -$7,165

There are excess funds of $7,165.

g ) 2006: Net Profit Margin = $14,840/$90,000 = 16.49%

2007: Net Profit Margin = $19,351/$110,000 = 17.6%

38

6-6.

Assets 2006 2007 Liabilities 2006 2007

Cash $10,000 $12,500 Accounts Payable $10,500 $13,125

Acct Rec. 25,000 31,250 Notes Payable 10,000 12,500

Inventory 20,000 25,000 Accrued Expenses 11,000 13,750

Prepaid Exp 2,000 2,500 Long Term Debt 15,000 15,000

Total Current Common Equity 38,500 38,500

Assets 57,000 71,250 Total Liabilities

Fixed Assets 32,000 32,000 Equity 85,000 $92,875

Depreciation 4,000 4,000

Total Assets 85,000 $99,250

*Net Sales for 2007 = $150 million * 1.25 = $187.5 million

Additional funds needed = $99,250 - $92,875 = $6,375

6-7.

2006 2007

Sales 1,000 1,250

Variable Costs 500 562.50

Fixed Costs 160 160

Net Income 340 527.50

Dividends 136 290.13

6-8. Pro Forma Balance Sheets

End of Year

Assets 2006 2007 Liabilities + Equity 2006 2007

Cash $4,000 4,400 Accounts Payable $4,400 4,840

Accounts Rec 10,000 11,000 Notes Payable 4,000 4,400

Inventory 13,000 14,300 Accrued Expenses 5,000 5,500

Prepaid Exp 400 440 Tot.Current Liabilities13,400 14,740

Current Assets27,400 30,140 Bonds Payable 6,000 6,000

Fixed Assets 11,000 11,000 Common Equity 19,000 21,468

Total Assets $38,400 $41,140 Tot.Liab. + Equity $38,400 $42,208

In 2007 there would be $1,068 ($42,208-$41,140) in excess funds. This assumes, as the problem states, that

notes payable would increase by 10% along with other current liabilities. Notes payable usually does not

increase with sales.

Year Total Sales PBT NI Addition to RE

2007 $85,000 X 1.1 $93,500 X .11 $10,285 X .6 $6,171 X .40

= $93,500 = $10,285 = $6,171 = $2,468

39

6-9.

Compute the following ratios for 2006 and 2007:

2006 2007

Current Ratio 3 3

Debt to Assets Ratio 25% 25.3%

Sales to Assets Ratio 62.5% 66.27%

Net Profit Margin 10% 13.64%

Return on Assets 6.25% 9.04%

Return on Equity 8.33% 12.10%

Liquidity seems strong and stable. Debt is modest and stable. Asset utilization is improving slightly while

all the profit margins calculated show marked improvement.

6-10. BRIGHT FUTURE CORPORATION

Historical and Projected Income Statements

Historical Projected 2006 2007 Sales $10,000,000 $12,000,000 Cost of goods Sold $4,000,000 $4,800,000 Gross Profit $6,000,000 $7,200,000 Selling & Admin. Expenses $800,000 $960,000 Depreciation Expense $2,000,000 $2,000,000 Operating Income (EBIT) $3,200,000 $4,240,000 Interest Expenses $1,350,000 $1,350,000 Earnings Before Tax (EBT) $1,850,000 $2,890,000 Income Tax (40%) $740,000 $1,156,000 Net Income (NI) $1,110,000 $1,734,000 Common Stock Dividends paid $400,000 $400,000 Addition to Retained earnings $710,000 $1,334,000 Earnings per Share (1,000,000 shares) $1.11 $1.73 BRIGHT FUTURE CORPORATION Historical and Projected Balance Sheets Projection with AFN Historical Projected Excess Financing Dec 31, 2006 Dec 31, 2007 Incorporated ASSETS Current Assets: Cash $9,000,000 $10,800,000 $10,800,000 Marketable Securities $8,000,000 $9,600,000 $9,600,000 Accounts Receivable (gross) $1,200,000 $1,440,000 $1,440,000 Less: Allowance for bad Debts $200,000 $240,000 $240,000 Accounts Receivable (Net) $1,000,000 $1,200,000 $1,200,000 Inventory $20,000,000 $24,000,000 $24,000,000 Prepaid Expenses $1,000,000 $1,200,000 $1,200,000 Total Current Assets $39,000,000 $46,800,000 $46,800,000 Plant and Equipment (gross) $20,000,000 $20,000,000 $20,000,000 Less: Accumulated Depreciation $9,000,000 $11,000,000 $11,000,000 Plant and equipment (net) $11,000,000 $9,000,000 $9,000,000 TOTAL ASSETS $50,000,000 $55,800,000 $55,800,000 LIABILITIES AND EQUITY Current Liabilities: Accounts payable $12,000,000 $14,400,000 $14,400,000 Notes Payable $5,000,000 $5,000,000 $5,000,000

40

Accrued Expenses $3,000,000 $3,600,000 $3,600,000 Total Current Liabilities $20,000,000 $23,000,000 $23,000,000 L-T Debt (Bonds Payable, 5%, due 2015) $20,000,000 $20,000,000 $21,466,000

Total Liabilities $40,000,000 $43,000,000 $44,576,000 Common Stock (1,000,000 shares, $1 par) $1,000,000 $1,000,000 $1,000,000 Capital in Excess of Par $4,000,000 $4,000,000 $4,000,000 Retained Earnings $5,000,000 $6,334,000 $6,334,000 Total Equity $10,000,000 $11,224,000 $11,224,000 TOTAL LIABILITIES AND EQUITY $50,000,000 $54,224,000 $55,800,000 Question 2a. Excess Financing (Additional Funds Needed) $1,466,000

AFN is incorporated in L-T debt. If $1,466,000 of new L-T debt is issued the financing need will be met.

Other financing sources could be used but we chose new L-T debt in this illustration.

Question 2, Ratios:

2006 2007 b. Current Ratio 1.95 2.03 c. Total Asset Turnover 0.20 0.22 Inventory Turnover 0.50 0.50 d. Total Debt to Assets 0.80 0.77 e. Net Profit Margin 11.10% 14.45% Return on Assets 2.22% 3.11% Return on Equity 11.10% 15.30%

Question 3, Comments on liquidity, asset productivity, debt management, and profitability:

Liquidity is improving. Debt is high but stable. Inventory and overall asset utilization are stable. The net

profit margin appears healthy. The return on assets ratio is much lower than the net profit margin because of

the low asset turnover. The return on equity ratio is much higher than the return on assets because of the

high debt load.

Question 4, Recommendations:

A 20% projected increase in sales is quite impressive. Management should prepare now, however, to raise

the $1,466,000 that will be needed in 2007 to support the necessary new investments if the projected sales

increase is to be achieved.

41

Chapter 7 Solutions


1. What is risk aversion? If common stockholders are risk averse, how do you explain the fact that they

often invest in very risky companies?

Risk aversion is the tendency to avoid additional risk. Risk-averse people will avoid risk if they can,

unless they receive additional compensation for assuming that risk. In finance, the added

compensation is a higher expected rate of return.

People are not all are equally risk averse. For example, some people are willing to buy risky stocks,

while others are not. The ones that do, however, almost always demand an appropriately high

expected rate of return for taking on the additional risk.

2. Explain the risk–return relationship.

The relationship between risk and required rate of return is known as the risk–return relationship. It

is a positive relationship because the more risk assumed, the higher the required rate of return most

people will demand.

Risk aversion explains the positive risk–return relationship. It explains why risky junk bonds carry a

higher market interest rate than essentially risk-free U.S. Treasury bonds.

3. Why is the coefficient of variation often a better risk measure when comparing different projects than

the standard deviation?

Whenever we want to compare the risk of investments that have different means, we use the

coefficient of variation (CV). The CV represents the standard deviation's percentage of the mean.

Because the CV is a ratio, it adjusts for differences in means, while the standard deviation does not.

therefore the CV provides a standardized measure of the degree of risk that can be used to compare

alternatives.

4. What is the difference between business risk and financial risk?

Business risk refers to the uncertainty a company has with regard to its operating income (also

known as earnings before interest and taxes or EBIT). Business risk is brought on by sales volatility

and intensified by the presence of fixed operating costs.

Financial risk is the additional volatility of net income caused by the presence of interest expense.

Firms that have only equity financing have no financial risk because they have no debt on which to

make fixed interest payments. Conversely, firms that operate primarily on borrowed money are

exposed to a high degree of financial risk.

42

5. Why does the riskiness of portfolios have to be looked at differently than the riskiness of individual

assets?

The riskiness of portfolios has to be looked at differently than the riskiness of individual assets

because the weighted average of the standard deviations of returns of individual assets does not result

in the standard deviation of a portfolio containing the assets. There is a reduction in the fluctuations

of the returns of portfolios which is called the diversification effect.

6. What happens to the riskiness of a portfolio if assets with very low correlations (even negative

correlations) are combined?

How successfully diversification reduces risk depends on the degree of correlation between the two

variables in question. When assets with very low or negative correlations are combined in portfolios,

the riskiness of the portfolios (as measured by the coefficient of variation) is greatly reduced.

7. What does it mean when we say that the correlation coefficient for two variables is -1? What does it

mean if this value were zero? What does it mean if it were +1?

Correlation is measured by the correlation coefficient, represented by the letter r. The correlation

coefficient can take on values between +1.0 (perfect positive correlation) to -1.0 (perfect negative

correlation). The closer r is to +1.0, the more the two variables will tend to move with each other at

the same time. The closer r is to -1.0, the more the two variables will tend to move opposite each

other at the same time. An r value of zero indicates that the variables’ values aren't related at all.

This is known as statistical independence.

8. What is nondiversifiable risk? How is it measured?

Unless the returns of one-half the assets in a portfolio are perfectly negatively correlated with the

other half—which is extremely unlikely—some risk will remain after assets are combined into a

portfolio. The degree of risk that remains is nondiversifiable risk, the part of a portfolio's total risk

that can't be eliminated by diversifying.

Nondiversifiable risk is measured by a term called beta (). The ultimate group of diversified assets,

the market, has a beta of 1.0. The betas of portfolios, and individual assets, relate their returns to

those of the overall stock market. Portfolios with betas higher than 1.0 are relatively more risky than

the market. Portfolios with betas less than 1.0 are relatively less risky than the market. (Risk-free

portfolios have a beta of zero.)

9. Compare diversifiable and nondiversifiable risk. Which do you think is more important to financial

managers in business firms?

Diversifiable risk can be dealt with by, of course, diversifying. Nondiversifiable risk is generally

compensated for by raising one’s required rate of return. Both types of risk are important to financial

managers.

43

10. How do risk-averse investors compensate for risk when they take on investment projects?

Because of risk aversion, people demand higher rates of return for taking on higher-risk projects.

11. Given that risk-averse investors demand more return for taking on more risk when they invest, how

much more return is appropriate for, say, a share of common stock, than is appropriate for a Treasury

bill?

Although we know that the risk–return relationship is positive, the question of much return is

appropriate for a given degree of risk is especially difficult. Unfortunately, no one knows the answer

for sure. One well-known model used to calculate the required rate of return of an investment, given

its degree of risk, is the Capital Asset Pricing Model (CAPM).

12. Discuss risk from the perspective of the Capital Asset Pricing Model (CAPM).

The Capital Asset Pricing Model, or CAPM, can be used to calculate the appropriate required rate of

return for an investment project given its degree of risk as measured by beta (). A project's beta

represents its degree of risk relative to the overall stock market. In the CAPM, when the beta term is

multiplied by the market risk premium term, the result is the additional return over the risk-free rate

that investors demand from that individual project. High-risk (high-beta) projects have high required

rates of return, and low-risk (low-beta) projects have low required rates of return.


7-1. Cash Flow

Probability

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

P x (CF - mean)2

$10,000

5.00%

$500

($9,000)

$81,000,000

$4,050,000

$13,000

10.00%

$1,300

($6,000)

$36,000,000

$3,600,000

$16,000

20.00%

$3,200

($3,000)

$9,000,000

$1,800,000

$19,000

30.00%

$5,700

$0

$0

$0

$22,000

20.00%

$4,400

$3,000

$9,000,000

$1,800,000

$25,000

10.00%

$2,500

$6,000

$36,000,000

$3,600,000

$28,000

5.00%

$1,400

$9,000

$81,000,000

$4,050,000

Sum of (R x P) = mean:

$19,000

Sum of P x (CF- mean)2 = variance:

$18,900,000

Square root of variance = standard deviation of the variance:

$4,347

Coefficient of Variation = std.dev./mean =

22.88%

44

7-2. EXPECTED VALUE, STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF OPERATING INCOME

Operating

Sales

Variable

Fixed

Income

Prob.

Estimate

Expenses

Expenses

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

Px(CF - mean2

$500

$250

$250

$0

2.00%

$0

($350)

$122,500

$2,450

$700

$350

$250

$100

8.00%

$8

($250)

$62,500

$5,000

$1,200

$600

$250

$350

80.00%

$280

$0

$0

$0

$1,700

$850

$250

$600

8.00%

$48

$250

$62,500

$5,000

$1,900

$950

$250

$700

2.00%

$14

$350

$122,500

$2,450

a.


$350

Sum of (CF- mean)2 x P= variance

$14,900

b.

Square root of variance = standard deviation:

$122

c.

Coeff. of Variation = std.dev/mean:

34.88%

d. New expected value, standard deviation, and coefficient of variation based on revised sales forecast:

Operating

Sales

Variable

Fixed

Income

Probability

Estimate

Expenses

Expenses

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

Px(CF - mean)2

$500

$250

$250

$0

10.00%

$0

($350)

$122,500

$12,250

$700

$350

$250

$100

15.00%

$15

($250)

$62,500

$9,375

$1,200

$600

$250

$350

50.00%

$175

$0

$0

$0

$1,700

$850

$250

$600

15.00%

$90

$250

$62,500

$9,375

$1,900

$950

$250

$700

10.00%

$70

$350

$122,500

$12,250

a.


$350

Sum of P x (CF - mean)2 = variance:

$43,250

b.


$208

c.

Coeff. of Variation = std. dev./mean:

59.43%

e. Comments:

Note how the increased possibilities that sales will be other than $1,200 caused the standard deviation and coefficient of variation of operating income to nearly double.

7-3. Mean:

.10(1,000) + .2(5,000) + .45(10,000) + .15(15,000) + .10(20,000) =

100 + 1,000 + 4,500 + 2,250 + 2,000

Mean = $9,850

Standard Deviation:

ơ 2 = .1(1,000 – 9,850)2 + .2(5,000 – 9,850)2 + .45(10,000 – 9,850)2 + .15(15,000 – 9,850)2 +

.1(20,000 – 9,850)2

ơ 2 = 7,832,250 + 4,704,500 + 10,125 + 3,978,375 + 10,302,250

ơ 2 = 26,827,500

ơ = √ 26,827,500

ơ = 5,179.53

Standard deviation = 5,179.53

45

7-4. I. EQUITY EDDIE'S COMPANY:

Operating

Income

Interest

Before-Tax

Net

Probability

Estimate

Expense

Income

Taxes

Income

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

Px(CF - mean)2

$100

$0

$100

$28

$72

5.00%

$4

($216)

$46,656

$2,333

$200

$0

$200

$56

$144

10.00%

$14

($144)

$20,736

$2,074

$400

$0

$400

$112

$288

70.00%

$202

$0

$0

$0

$600

$0

$600

$168

$432

10.00%

$43

$144

$20,736

$2,074

$700

$0

$700

$196

$504

5.00%

$25

$216

$46,656

$2,333

a.


$288


$8,813

b.


$94

c.

Coeff. of Variation = std. dev./mean:

32.60%

II. BARRY BORROWER'S COMPANY:

Operating

Income

Interest

Before-Tax

Net

Probability

Estimate

Expense

Income

Taxes

Income

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

Px(CF - mean)2

$110

$40

$70

$19.6

$50.4

5.00%

$2.52

($237.60)

$56,453.76

$2,822.69

$220

$40

$180

$50.4

$129.6

10.00%

$12.96

($158.40)

$25,090.56

$2,509.06

$440

$40

$400

$112.0

$288.0

70.00%

$201.60

$0.00

$0.00

$0.00

$660

$40

$620

$173.6

$446.4

10.00%

$44.64

$158.40

$25,090.56

$2,509.06

$770

$40

$730

$204.4

$525.6

5.00%

$26.28

$237.60

$56,453.76

$2,822.69

a.


$288.00


$10,663.49

b.

Square root of variance = standard deviation=

$103.26

c.

Coeff. of Variation = std. dev./ mean:

35.86%

e. Comments: Note how Barry Borrower's use of debt financing causes his company to have a higher

standard deviation and coefficient of variation of net income than Equity Eddie's.

7-5.

STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF CASH FLOWS FOR THE GO-RILLA PROJECT

Cash Flow

Probability

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

P x (CF - mean)2

$20,000

1.00%

$200

($6,000)

$36,000,000

$360,000

$22,000

12.00%

$2,640

($4,000)

$16,000,000

$1,920,000

$24,000

23.00%

$5,520

($2,000)

$4,000,000

$920,000

$26,000

28.00%

$7,280

$0

$0

$0

$28,000

23.00%

$6,440

$2,000

$4,000,000

$920,000

46

$30,000 12.00% $3,600 $4,000 $16,000,000 $1,920,000

$32,000

1.00%

$320

$6,000

$36,000,000

$360,000


$26,000


$6,400,000

a.


$2,530

b. Coefficient of Variation = std. dev./mean:

9.73%

c.

Comment:

Given that the average coefficient of variation of George's other product lines is 12%, we would say that the Go-Rilla project is LESS risky than average

7-6.

Effect of Adding Asset B to Existing Portfolio A

Correlation coefficient r between existing portfolio A and new asset B:

0

Amount invested in Portfolio A:

$700,000

Amount invested in Asset B:

$200,000

Total value of combined portfolio:

$900,000

Weight of existing assets in combined portfolio:

77.8%

Weight of new asset B in combined portfolio:

22.2%

Expected Return of existing portfolio A:

9.00%

Standard deviation of existing portfolio A:

3.00%

Coefficient of variation of existing portfolio A:

33.33%

Expected Return of new asset B:

12.00%

Standard deviation of new asset B:

4.00%

Coefficient of variation of new asset B:

33.33%

Expected Return of combined portfolio per equation 7-1:

9.67%

Standard deviation of combined portfolio per equation 7-5:

2.50%

Coefficient of Variation of combined portfolio:

25.83%

a. Comparison of standard deviations of existing portfolio A and the new combined portfolio:

Standard deviation of existing portfolio A:

3.00%

Standard deviation of combined portfolio:

2.50%

a. Comparison of coefficients of variation of existing portfolio A and the new combined portfolio:

Coefficient of variation of existing portfolio A:

33.33%

Coefficient of variation of combined portfolio:

25.83%

47

7-7. Coefficient of variation (CV) = Standard Deviation/Mean

288/1,200 = .24

CVzazzle = 24%

7-8. Total Portfolio = $10,000

Weights: Stock A: 4,000/10,000 = .4

Stock B: 6,000/10,000 = .6

.4(13) + .6(9) = 10.6%

Expected Rate of Return = 10.6%

7-9. ơp = √ (0.3)2 * (0.05)2 + (0.7)2 * (0.02)2 + ( 2 * 0.3 * 0.7 * 0.6 * 0.05 * 0.02)

ơp = √0.000673

ơp = 0.0259

ơp = 2.59%

7-10.

Effect of Adding PROJ1 to Existing Portfolio

Expected Return of existing portfolio:

11.00%

Standard deviation of existing portfolio:

4.00%

a.

Coefficient of variation of existing portfolio:

36.36%

Expected Return of new PROJ1:

13.00%

Standard deviation of new PROJ1:

5.00%

b.

Coefficient of variation of new PROJ1:

38.46%

Amount invested in existing portfolio:

$820,000

Amount invested in PROJ1:

$194,000

Total value of combined portfolio:

$1,014,000

c. Weight of existing assets in combined portfolio:

80.9%

d.

Weight of new PROJ1 in combined portfolio:

19.1%

Correlation coefficient r between existing portfolio and new PROJ1:

0

e.

Standard deviation of combined portfolio:

3.37%

(lower than existing portfolio)

: Expected Return of combined portfolio per equation 7-1

11.38%

f.: Coefficient of Variation of combined portfolio

29.63%

(lower than existing portfolio)

g.

Firm's risk decreases with the addition of PROJ1 to the portfolio

48

7-11. Required Rate of Return per the CAPM

Risk free rate (kRF)

5.0%

Expected rate of return on the market (km)

15.0%

Beta

1.2

Required rate of return on stock per the CAPM:

17.0%

(equation 7-6)

7-12. kl = 4.5 + .5(12.5) = 10.75%

ka = 4.5 + 1.0(12.5) = 17%

kh = 4.5 + 1.6(12.5) = 24.5%

7-13. Effect on CAPM Required Rate of Return of Adding a New Project

Risk free rate (kRF)

5.0%

Expected rate of return on the market (km)

15.0%

Existing firm's Beta

1.5

New Project's Beta

0.8

a. Required rate of return on company per the CAPM:

20.0%

b. Required rate of return on new project per the CAPM:

13.0%

Weight of new project in firm's portfolio:

20.0%

Weight of firm's other assets:

80.0%

c. Beta of firm with new project

1.36

7-14. STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF PSC SALES REVENUE

Sales

Probability

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

P x (CF - mean)2

$800

2.00%

$16

($1,200)

$1,440,000

$28,800

$1,000

8.00%

$80

($1,000)

$1,000,000

$80,000

$1,400

20.00%

$280

($600)

$360,000

$72,000

$2,000

40.00%

$800

$0

$0

$0

$2,600

20.00%

$520

$600

$360,000

$72,000

$3,000

8.00%

$240

$1,000

$1,000,000

$80,000

$3,200

2.00%

$64

$1,200

$1,440,000

$28,800

Sum of (R x P) = exp val:

$2,000

49


$361,600


$601

Coefficient of Variation = std. dev./mean:

30.07%

7-15. COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME

Operating

Sales

Variable

Fixed

Income

Probability

Estimate

Expenses

Expenses

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

Px(CF - mean)2

$800

$480

$0

$320

2.00%

$6

($480)

$230,400

$4,608

$1,000

$600

$0

$400

8.00%

$32

($400)

$160,000

$12,800

$1,400

$840

$0

$560

20.00%

$112

($240)

$57,600

$11,520

$2,000

$1,200

$0

$800

40.00%

$320

$0

$0

$0

$2,600

$1,560

$0

$1,040

20.00%

$208

$240

$57,600

$11,520

$3,000

$1,800

$0

$1,200

8.00%

$96

$400

$160,000

$12,800

$3,200

$1,920

$0

$1,280

2.00%

$26

$480

$230,400

$4,608


$800


$57,856


$241


30.07%

7-16.

COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME

Operating

Sales

Variable

Fixed

Income

Probability

Estimate

Expenses

Expenses

Estimate

of Occurrence

CF

P

CF x P

CF - mean

(CF - mean)2

Px(CF - mean)2

$800

$480

$400

($80)

2.00%

($2)

($480)

$230,400

$4,608

$1,000

$600

$400

$0

8.00%

$0

($400)

$160,000

$12,800

$1,400

$840

$400

$160

20.00%

$32

($240)

$57,600

$11,520

$2,000

$1,200

$400

$400

40.00%

$160

$0

$0

$0

$2,600

$1,560

$400

$640

20.00%

$128

$240

$57,600

$11,520

$3,000

$1,800

$400

$800

8.00%

$64

$400

$160,000

$12,800

$3,200

$1,920

$400

$880

2.00%

$18

$480

$230,400

$4,608


$400

50


$57,856


$241


60.13%

Comment:

Note how the addition of fixed costs caused the coefficient of variation of PSC's operating income to double from what it was in problem 7-10

7-17. MEASURING PSC'S FINANCIAL RISK

I. Expected value, standard deviation, and coefficient of variation of PSC's net income when no interest expense is present

Sales Variable Fixed Operating Interest Before-Tax

Probability of

Estimate Expenses Expenses Income Expense Income Taxes Net Income

Occurrence

NI P NI X P NI - mean (NI - mean)2

P X (NI - mean)2

$800 $480 $400 -$80 $0 -$80 -$56 -$24 2% $0 -$144 $20,736 $415

$1,000 $600 $400 $0 $0 $0 $0 $0 8% $0 -$120 $14,400 $1,152

$1,400 $840 $400 $160 $0 $160 $112 $48 20% $10 -$72 $5,184 $1,037

$2,000 $1,200 $400 $400 $0 $400 $280 $120 40% $48 $0 $0 $0

$2,600 $1,560 $400 $640 $0 $640 $448 $192 20% $38 $72 $5,184 $1,037

$3,000 $1,800 $400 $800 $0 $800 $560 $240 8% $19 $120 $14,400 $1,152

$3,200 $1,920 $400 $880 $0 $880 $616 $264 2% $5 $144 $20,736 $415

Sum of (NI X P) = mean $ 120

Sum of P X (CF - mean)2 = variance: $5,207

Square root of variance = standard deviation: $72

Coefficient of Variation = std. dev./mean: 60.1%

II. Expected value, standard deviation, and coefficient of variation of PSC's net income when interest expense is present


Probability of

Estimate Expenses Expenses Income Expense Income Taxes Net Income

Occurrence

NI P NI X P NI - mean (NI - mean)2

P X (NI - mean)2

$800 $480 $400 ($80) $60 ($140) ($42) ($98) 2% ($2) ($336) $112,896 $2,258

$1,000 $600 $400 $0 $60 ($60) ($18) ($42) 8% ($3) ($280) $78,400 $6,272

$1,400 $840 $400 $160 $60 $100 $30 $70 20% $14 ($168) $28,224 $5,645

$2,000 $1,200 $400 $400 $60 $340 $102 $238 40% $95 $0 $0 $0

$2,600 $1,560 $400 $640 $60 $580 $174 $406 20% $81 $168 $28,224 $5,645

$3,000 $1,800 $400 $800 $60 $740 $222 $518 8% $41 $280 $78,400 $6,272

$3,200 $1,920 $400 $880 $60 $820 $246 $574 2% $11 $336 $112,896 $2,258

Sum of (R X P) = mean = $ 238

Sum of P X (CF - mean)2 = variance = $28,349

Square root of variance = standard deviation = $168

Coefficient of variation equals std. dev./mean = 70.7%

51

7-18. I. New coefficient of variation of PSC's operating income:

Operating

Sales Variable Fixed Income Probability of

Estimate Expenses Expenses Estimate Occurrence

EBIT P EBIT X P

EBIT - mean

(EBIT - mean)2

P X (EBIT - mean)2

$800 $480 $250 $70 1% $0.70 ($480) $230,400 $2,304

$1,000 $600 $250 $150 6% $9.00 ($400) $160,000 $9,600

$1,400 $840 $250 $310 13% $40.30 ($240) $57,600 $7,488

$2,000 $1,200 $250 $550 60% $330.00 $0 $0 $0

$2,600 $1,560 $250 $790 13% $102.70 $240 $57,600 $7,488

$3,000 $1,800 $250 $950 6% $57.00 $400 $160,000 $9,600

$3,200 $1,920 $250 $1,030 1% $10.30 $480 $230,400 $2,304

Sum of (EBIT X P) = mean = $550.00



Coefficient of Variation = std. dev./mean = 35.8%

II. New coefficient of variation of PSC's net income when no interest expense is present


Net Probability of

Estimate Expenses Expenses Income Expense Income Taxes Income Occurrence

NI P NI X P

(NI - mean)2

P X (NI - mean)2

$800 $480 $250 $70 $0 $70 $21 $49 1% $0 $112,896 $1,129

$1,000 $600 $250 $150 $0 $150 $45 $105 6% $6 $78,400 $4,704

$1,400 $840 $250 $310 $0 $310 $93 $217 13% $28 $28,224 $3,669

$2,000 $1,200 $250 $550 $0 $550 $165 $385 60% $231 $0 $0

$2,600 $1,560 $250 $790 $0 $790 $237 $553 13% $72 $28,224 $3,669

$3,000 $1,800 $250 $950 $0 $950 $285 $665 6% $40 $78,400 $4,704

$3,200 $1,920 $250 $1,030 $0 $1,030 $309 $721 1% $7 $112,896 $1,129

Sum of (NI X P) = mean = $385




III. New coefficient of variation of PSC's net income when interest expense is present

Sales Variable Fixed Operating Interest B-T Net Probability of

Estimate Expenses Expenses Income Expense Income Taxes Income Occurrence

NI P NI X P

(NI - mean)2

P X (NI - mean)2

$800 $480 $250 $70 $40 $30 $9 $21 1% $0 $112,896 $1,129

$1,000 $600 $250 $150 $40 $110 $33 $77 6% $5 $78,400 $4,704

$1,400 $840 $250 $310 $40 $270 $81 $189 13% $25 $28,224 $3,669

$2,000 $1,200 $250 $550 $40 $510 $153 $357 60% $214 $0 $0

$2,600 $1,560 $250 $790 $40 $750 $225 $525 13% $68 $28,224 $3,669

$3,000 $1,800 $250 $950 $40 $910 $273 $637 6% $38 $78,400 $4,704

$3,200 $1,920 $250 $1,030 $40 $990 $297 $693 1% $7 $112,896 $1,129

Sum of (NI X P) = mean = $357

52




Summary:

Old Coefficient of variation of operating income (business risk) 60.13%

New coefficient of variation of operating income (business risk) 35.81%

Old difference between the coefficient of variation of net income with and without interest expense (financial risk)

-10.6%

New difference between the coefficient of variation of net income with and without interest expense (financial risk)

-2.8%

Comments: The effect of PSC's risk reduction measures was to lower business risk substantially, but

financial risk increased slightly. Managers must evaluate this trade-off and proceed accordingly.

53

Chapter 8 Solutions


1. What is the time value of money?

The time value of money means that money you hold in your hand today is worth more than money

you expect to receive in the future. Similarly, money you must pay out today is a greater burden than

the same amount paid in the future.

2. Why does money have time value?

Positive interest rates indicate that money has time value. When one person lets another borrow

money, the first person requires compensation in exchange for reducing current consumption. The

person who borrows the money is willing to pay to increase current consumption. The required rate

of return on an investment reflects the pure time value of money, an adjustment for expected

inflation, and any risk premiums present.

3. What is compound interest? Compare compound interest to discounting.

Compound interest occurs when interest is earned on interest and on the original principal of an

investment. Discounting is the inverse of compounding. Compound interest causes the value of a

beginning amount to increase at an increasing rate. Discounting causes the present value of a future

amount to decrease at an increasing rate.

4. How is present value affected by a change in the discount rate?

Present value is inversely related to the discount rate. In other words, present value moves in the

opposite direction of the discount rate. If the discount rate increases, present value decreases. If the

discount rate decreases, present value increases.

5. What is an annuity?

An annuity is a series of equal cash flows, spaced evenly over time.

6. Suppose you are planning to make regular contributions in equal payments to an investment fund for

your retirement. Which formula would you use to figure out how much your investments will be

worth at retirement time, given an assumed rate of return on your investments?

To figure out how much your investments will be worth at retirement time, given an assumed rate of

return on your investments, you would use the future value of an annuity formula:

54

Future Value of an Annuity Formula

k

kPMTFVA

n 1)1(

where: FVA = Future Value of an Annuity

PMT = Amount of each annuity payment

k = Interest rate per time period

n = Number of annuity payments

7. How does continuous compounding benefit an investor?

The effect of increasing the number of compounding periods per year is to increase the future value

of the investment. The more frequently interest is compounded, the greater the future value. The

smallest compounding period is used when we do continuous compounding--compounding that

occurs every tiny unit of time (the smallest unit of time imaginable).

8. If you are doing PVA and FVA problems, what difference does it make if the annuities are "ordinary

annuities" or "annuities due"?

In FVA or a PVA of annuity due problems, annuity payments earning interest one period sooner than

in ordinary annuity problems. So, higher FVA and PVA values result with an annuity due. The first

payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due

problems, each annuity payment occurs one period sooner, so the payments are discounted less

severely.

9. Which formula would you use to solve for the payment required for a car loan if you know the

interest rate, length of the loan, and the borrowed amount? Explain.

To solve for k when the known values are PVA, n, and PMT, start with the present value of an

annuity formula, Equation 8-3b, as follows:

Present Value of an Annuity Formula, Table Method

PVA = PMT(PVIFA k, n)

Next, rearrange terms and solve for (PVIFA k, n) as follows

PVA / PMT = (PVIFA k, n)

Now refer to the PVIFA values in the text, Table IV. You know n, so find the n row corresponding

to the number of periods in your problem on the left hand side of the table. You have also determined

the PVIFA, so move across the n row until you find (or come close to) the value of PVIFA that you

have solved for. The percent column in which the value is located is the interest rate.

55


8-1. $1,000 X (1 + 0.07)5 = $1,402.55

8-2. a) 0% $50,000 X (1 + 0.00)10 = $50,000.00

b) 5% $50,000 X (1 + 0.05)10 = $81,444.73

c) 10% $50,000 X (1 + 0.10)10 = $129,687.12

d) 20% $50,000 X (1 + 0.20)10 = $309,586.82

8-3. $5,000 * (1 + 0.08)10 = $10,794.62

8-4. a) 3% $100,000 * (1 + 0.03)15 = $155,796.74

b) 6% $100,000 * (1 + 0.06)15 = $239,655.82

c) 9% $100,000 * (1 + 0.09)15 = $364,248.25

d) 12% $100,000 * (1 + 0.12)15 = $547,356.58

8-5 a) 50,000 $50,000 * (1 + 0.10)25 = $541,735.30

b) 75,000 $75,000 * (1 + 0.10)25 = $812,602.95

c) 100,000 $100,000 * (1 + 0.10)25 = $1,083,470.59

d) 125,000 $125,000 * (1 + 0.10)25 = $1,354,338.24

8-6 a) 5 years $60,000 * (1 + 0.12)5 = $105,740.50

b) 10 years $60,000 * (1 + 0.12)10 = $186,350.89

c) 15 years $60,000 * (1 + 0.12)15 = $328,413.95

d) 20 years $60,000 * (1 + 0.12)20 = $578,777.59

8-7. PV = $20,000 X [1/(1 + .12)10] = $6,439.46

8-8. a) 0% $60,000 X [1/(1+0.00)20] = $60,000.00

b) 5% $60,000 X [1/(1+0.05)20] = $22,613.37

c) 10% $60,000 X [1/(1+0.10)20] = $8,918.62

d) 20% $60,000 X [1/(1+0.20)20] = $1,565.04

8-9 $9,000 * [1/(1+0.08)4] = $6,615.27

8-10 a) 3% $25,000 * [1/(1 + 0.03)10] = $18,602.35

b) 6% $25,000 * [1/(1 + 0.06)10] = $13,959.87

c) 9% $25,000 * [1/(1 + 0.09)10] = $10,560.27

d) 12% $25,000 * [1/(1 + 0.12)10] = $8,049.33

56

8-11. a)$50,000 $50,000 * [1/(1 + 0.06)15 = $20,863.25

b)$75,000 $75,000 * [1/(1 + 0.06)15 = $31,294.88

c)$100,000 $100,000 * [1/(1 + 0.06)15 = $41,726.51

d)$125,000 $125,000 * [1/(1 + 0.06)15 = $52,158.13

8-12. a) 5 years $80,000 * [1/(1 + 0.09)5] = $51,994.51

b) 10 years $80,000 * [1/(1 + 0.09)10] = $33,792.86

c) 15 years $80,000 * [1/(1 + 0.09)15] = $21,963.04

d) 20 years $80,000 * [1/(1 + 0.09)20] = $14,274.47

8-13. PVA = $500 X [(1-1/1.0610)/0.06] = $3,680.04

8-14. a) 0% $10,000 X 30 = $300,000

b) 10% $10,000 X [(1-1/1.1030)/0.10] = $94,269.14

c) 20% $10,000 X [(1-1/1.2030)/0.20] = $49,789.36

d) 50% $10,000 X [(1-1/1.5030)/0.50] = $19,999.90

8-15. $20,000 * [(1-1/1.0710)/0.07] = $140,471.63

8-16. a) 9 % $10,000 * [(1-1/1.095)/0.09] = $38,896.51

b) 13% $10,000 * [(1-1/1.135)/0.13] = $35,173.31

c) 15% $10,000 * [(1-1/1.155)/0.15] = $33,521.55

d) 21% $10,000 * [(1-1/1.215)/0.21] = $29,259.84

8-17. FVA = $500 X [(1.095-1)/.09] = $2,992.36

8-18. a) 0% $6,000 X 12 = $72,000.00

b) 2% $6,000 X [(1.0212-1)/0.02] = $80,472.54

c) 10% $6,000 X [(1.1012-1)/0.10] = $128,305.70

d) 20% $6,000 X [(1.2012-1)/0.20] = $237,483.01

8-19. $5,000 * [(1.0610 – 1)/0.06] = $65,903.97

8-20. $5,000 * [(1.118 – 1)/0.11] = $59,297.17

8-21. a) $1,000 $1,000 * [(1.105 – 1)/0.10] = $6,105.10

b) $10,000 $10,000 * [(1.105 – 1)/0.10] = $61,051.00

c) $75,000 $75,000 * [(1.105 – 1)/0.10] = $457,882.50

d) $125,000 $125,000 * [(1.105 – 1)/0.10] = $763,137.50

57

8-22. $1,200 X [(1.1240 – 1)/.12] X 1.12 = $1,030,970.87

8-23. $500 * [(1.085 – 1)/0.08] * 1.08 = $3,167.96

8-24. $56,370.93 * 1.06 = $59,753.19

8-25. $80 X [(1-1/1.1220)/.12] X 1.12 = $669.26

8-26. $30,000 * [1-1/1.0925)/0.09] * 1.09 = $321,198.35

8-27. $1,300 * [1-1/1.00583333180)/0.00583333] * 1.00583 = $144,632.74

8-28. $185,361 = FVIF10,k% X $50,000

FVIF10,k% = 3.7072; from Table I, k = 14%

8-29. $1,000 X (1 + k)5 = $773.78

(1 + k)5 = $773.78/$1,000

(1 + k)5 = .77378

1 + k = .95

k = -.05 = -5%

8-30. $50,000 * (1 + k)10 = $246,795

(1 + k)10 = $246,795/$50,000

(1 + k)10 = 4.9359

1 + k = 1.173104

k = .1731 = 17.31%

8-31. PV = $50/0.08 = $625

8-32. $80/0.09 = $888.89

8-33. $65/0.085 = $764.71

8-34. FV = $10 X (1.08)200 = $48,389,496

8-35. PVA = PMT X PVIFA k,n

$24,000 = $4,247.62 X PVIFA k,10

58

5.6502 = PVIFA k,10

k = 12%

8-36 PVA = PMT X PVIFA k,n

$200,000 = $1,330.61 X PVIFA k,360

150.3070 = PVIFA k,360

k = .5833% per month X 12 = 7% annual rate

8-37. a ) 5 years? 10,000/(1+.07)5 = 7130

b ) 10 years? 10,000/(1+.07)10 = 5083

c ) 20 years? 10,000/(1+.07)20 = 2584

8-38. PV = $16,850.58 X [1/(1+.11)5]

PV = $10,000

8-39. a ) FV = $20,000 X (1 + .05)7 = $28,142.01

b ) FV = $20,000 X (1 + .07)10 = $39,343.03

8-40. $55.00 = $67.73 X [PVIFk%, 12 years ]

.8120 = PVIFk%, 12 years; k = 1.75%

8-41. 1,000 = 2653.3 X [PVIF5%, ?];

.3769 = PVIF5%,?; ? = 20 semi-annual periods, so it will take 10 years.

8-42. PV = 20,000 X [(1-1/1.0615)/0.06] = $194,244.98

8-43. $4,000 * [(1.0920 –1)/0.09] * 1.09 = $223,058.12

8-44. $100 * [(1.0220 –1)/0.02] = $2,429.74

8-45. $2,000 X [((1+.08)10 - 1)/.08] = $2,000 X 14.4866 = $28,973

8-46. a ) $300 X [((1+.02)120 - 1)/.02] = $146,477

b ) $146,477 = $6,000 X [PVIFA2%, n quarters ]

PVIFA2%, n quarters = 24.4128; n = 34 quarters or 8.5 years

59

8-47. $30,000 = PMT X [(1-1/(1+0.1)7)/0.1];

$30,000 = PMT X 4.86841882; PMT = $6,162.16

8-48. $10,000/.12 = $83,333.33

8-49. FV = $500 X e.05 x 23 = $1,579.10

8-50. FVIF k=8%, n=? = 2

n = 9 years

8-51. PVA = PMT X PVIFA k,n

$4,000 = $200 X PVIFA k=.195/12, n=?

20 = PVIFA k=.01625, n=?

n = 24.39 months

8-52. $14,568.50 = $5,000 X [PVIFAk%,4 years], assuming payments start one year from the date of

borrowing

[PVIFAk%,4 years] = 2.9137; k = 14%

8-53. a) FVA = $1,000 X [[(1+.02)60 - 1]/.02] = $114,051.54

b) $114,051.54 = $6,000 X PVIFA.02, n quarters

PVIFA.02, n quarters = 19.00859; n = 24 quarters = 6 years

8-54. Option 1) PV = $5,650

Option 2) PV = $6,750 X [1/1.028] = $5,761.06

Option 3) PV = $800 X [(1-(1/(1+.02)8)/.02] = $5,860.39

Option 4) PV = $1,000 + $5,250 X (1/(1+.02)8) = $5,480.82

Option 4) is the one with lowest cost to Jack.

8-55. n = 30 X 12 = 360

k = .09/12 =0 .0075 or 0.75%

$120,000 = PMT X [(1-1/1.0075360)/0.0075]

PMT = $120,000/124.28186568 = $965.55

8-56. PVA = PMT [(1-1/1.005 180)/.005]

$250,000 = PMT X 118.5035147

PMT = $2,109.64

8-57. a) n = 4 X 12 = 48

k = .06/12 =0 .005 or 0.5%

60

$18,000 = PMT X [(1-1/1.00548)/0.005]

PMT = $18,000/42.58031778 = $422.73

b) n = 6 X 12 = 72

k = .06/12 =0 .005 or 0.5%

$18,000 = PMT X [(1-1/1.00572)/0.005]

PMT = $18,000/60.33951394 = $298.31

8-58, Missing Cash Flow Problem

I. Given Information: Discount Rate 10%

Known Cash Flows Time 0 Time 1 $100 Time 2 $150 Time 3 Time 4 $100

Total Present Value of all Cash Flows, including the missing cash flow $320.74

II. Solution: The value of the missing cash flow at Time 3:

Known Cash Flows Present Value of Known Cash Flows Time 0 Time 1 $100 $90.9091 Time 2 $150 $123.9669 Time 3 Time 4 $100 $68.3013

Total Present Value of all Cash Flows, including the missing cash flow $320.74 (given) Total present value of known cash flows only $283.1774

Difference (Present Value of missing cash flow) $37.5657

Future Value of Missing Cash Flow at Time 3 $50

8-59. a) n = 5*12 = 60

k = .08/12 = .0066666

$22,000 = PMT * [1-1/1.00666666760)/0.006666667]

PMT = $22,000/118.5035147 = $446.0806 = $446.08

61

Chapter 9 Solutions


1. Which is lower for a given company: the cost of debt or the cost of equity? Explain. Ignore taxes in

your answer.

The cost of debt is always less than the cost of equity for a given firm. This is because the debt

investor is taking a lower risk than the equity investor and therefore the required rate of return is

lower.

2. When a company issues new securities, how do flotation costs affect the cost of raising that capital?

When a company issues new securities flotation costs increase the cost of raising the capital. The

company receives a smaller amount of the proceeds from the new issues, the greater the flotation

costs.

3. What does the “weight” refer to in the weighted average cost of capital?

The weight referred to in weighted average cost of capital refers to the portion of the total capital

raised by the firm that comes from a given source such as debt, preferred stock or equity.

4. How do tax considerations affect the cost of debt and the cost of equity?

Because interest on debt is tax deductible to the issuing firm, the higher the tax rate the lower the

after tax cost of debt financing. Tax considerations do not enter into the cost of equity calculation

since dividends paid to stockholders are not tax deductible to the firm.

5. If dividends paid to common stockholders are not legal obligations of a corporation, is the cost of

equity zero? Explain your answer.

Although common stockholders do not have a contractual claim on dividends the funds supplied by

stockholders definitely have a cost. Equity investors are paid last and so they are taking the greatest

risk among all the suppliers of capital. If the company does not earn a higher rate of return on equity

funds to compensate for the higher risk taken by equity investors, the price of the stock will fall and

therefore the value of the firm.

6. What is the investment opportunity schedule (IOS)? How does it help financial managers make

business decisions?

62

The investment opportunity schedule shows graphically proposed capital budgeting projects

depicting the IRR and dollar amount of investment for each project. This helps the financial manager

make business decisions since the investment opportunity schedule and the marginal cost of capital

schedule can be plotted together, with those projects on the IOS schedule above the MCC being

acceptable.

7. What is a marginal cost of capital schedule (MCC)? Is the schedule always a horizontal line?

Explain.

The marginal cost of capital schedule is a graphic depiction of the weighted average cost of capital at

different levels of financing. The MCC schedule is not always a horizontal line. For many firms the

MCC schedule increases, usually at discreet intervals, as the amount of funds to be raised increases.

8. For a given IOS and MCC, how do financial managers decide which proposed capital budgeting

projects to accept, and which to reject?

For a given IOS and MCC, all independent projects that plot on the IOS above the MCC are

accepted. Those projects on the IOS below the MCC are rejected.


9-1. a) (i) YTM = 7% AT kd = .07(1-.40) = 4.2%

(ii) YTM = 11% AT kd = .11(1-.40) = 6.6%

(iii) YTM = 13% AT kd = .13(1-.40) = 7.8%

b) (i) YTM = 7% AT kd = .07(1-.34) = 4.62%

(ii) YTM = 11% AT kd = .11(1-.34) = 7.26%

(iii) YTM = 13% AT kd = .13(1-.34) = 8.58%

9-2. a ) AT kd = .10(1-.00) = 10.0%

b ) AT kd = .10(1-.22) = 7.8%

c ) AT kd = .10(1-.34) = 6.6%

9-3. Company YTM Tax Rate(%) AT kd

A 8% 34% 0.8(1-.34) = 5.28%

B 11% 40% 0.11(1-.40) = 6.60%

C 14% 30% 0.14(1-.30) = 9.80%

63

9-4. YTM AT kd AT kd

T=40% T=34%

8% 0.08(1-.40) = 4.80% 0.08(1-.34) = 5.28%

14% 0.14(1-.40) = 8.40% 0.14(1-.34) = 9.24%

16% 0.16(1-.40) = 9.60% 0.16(1-.34) = 10.56%

9-5. a ) kd = 13%

b ) AT kd = .13(1-.40) = 7.8%

9-6. kd = .095 * (1 - .35) = .06175 = 6.2%

9-7. kp = $2/($26 - $0.75) = $2/$25.25 = 7.92%

9-8. kp = $8.00/($61.00 - $1.00) = 13.3%

AT kd = .11(1-.40) = 6.6%

Leo is correct. The cost of debt is lower.

9-9. a) kp = $6/$50 = 12%

b) kp = $6/($50 - $2.25) = 12.57%

9-10. kp = $100 X 0.12/($89 - ($89 X 0.05))

= $12/($89 - $4.45) = 14.19%

9-11. kp = $0.75/($27 - $1) = 2.88%

9-12. a) ks = ($7/$143) + 0. 13 = 17.90%

b) kn = ($7/($143 - $4) + 0. 13 = 18.04%

9-13. AT kd = 0.14(1-.30) = 9.80%

ks = ($1.50/$39.00) + 0.04 = 7.85%

The cost of the company's retained earnings is lower. This would lead you to reevaluate the

estimated numbers, or question the applicability of the valuation models used here, since ks cannot be

lower than AT kd for a given company.

9-14. ks = .045 + 1.4(.12 - .045) = 15%

64

9-15. a) ks = ($7/$65) + 0.10 = 20.77%

b) kn = ($7/($65 - $3)) + 0.10 =21.29%

Yes. Floatation costs make cost of capital from new common stock higher.

9-16. ks = kRF + (kM - kRF) X

= .03 + (.11 - .03) X 1.6 = 15.8%

9-17. a ) ks = ($2 X 1.05)/$30 + .05 = 12.0%

b ) kn = ($2 X 1.05)/($30-$2) + .05 = 12.5%

c ) ks = .03 + (.12 - .03) x 1.4 = 15.6%

9-18. AT kd = 0.10(1-0.4) = 6%

kp = $2/($31 - $1) = 6.67%

kn = $4/($100 -$4) + .06 = 10.17%

ka = (0.3)(6) + (0.15)(6.67) + (0.55)(10.17) = 8.394%

9-19. AT kd = 0.11(1-0.4) = 6.60%

kp = $2/($26 - $0.75) = 7.92%

kn = $7/($143 - $4) + .13 = 18.04%

ka = (300,000/600,000)(0.066) + (100,000/600,000)(0.0792) +

(200,000/600,000)(0.1804) = 10.63%

9-20. ka = (600/1250)(0.12(1-0.04)) + (250/1250)(0.14) + (400/1250)(0.16)

= (.48 X .072) + (.20 X .14) + (.32 X .16)

= .03456 + .028 + .0512 = 11.38%

9-21. AT kd = .10(1-.35) = 6.5%

kp = $2/($25 - $1.00) = $2/$24 = 8.33%

kn = ($5/($140 - $4) + 0.10 = 13.68%

ka = (300,000/1,000,000)(0.065) + (100,000/1,000,000)(0.0833) +(600,000/1,000,000)(0.1368) =

10.99%

= minimum expected rate of return needed to satisfy the suppliers of capital.

9-22. 0.60(0.05) + 0.10(0.08) + 0.30(0.12) = 0.074 = 7.4%

9-23. kd = .095(1 - 0.35) = .06175 = 6.2%

kp = $10/$50 = 0.20 = 20%

ks = 0.04 + 1.1(0.12 – 0.04) = 12.8%

65

Weight:

Debt = 230,000/430,000 = 0.54

Preferred Stock = 100,000/430,000 = 0.23

Common Equity = 100,000/430,000 = 0.23

WACC = .54(0.062) + .23(0.20) + .23(0.128) = .10892 = 10.892%

9-24. a ) $200,000/0.40 = $500,000 equity break-point

b ) $500,000/0.60 = $833,333 debt break-point

9-25. $1,000,000/.4 = $2,500,000 total capital raised before BPd1 is reached.

$2,000,000/.4 = $5,000,000 total capital raised before BPd2 is reached.

$2,750,000/.5 = $5,500,000 total capital raised before BPe is reached.

a ) ka = (0.40)(0.11(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 10.34%

b ) ka = (0.40)(0.13(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 10.82%

c ) ka = (0.40)(0.15(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 11.30%

9-26. INVESTMENT OPPORTUNITIES PROJECT INVESTMENT RETURN OPTIMAL CAPITAL STRUCTURE: DEBT 35.00% EQUITY 65.00% A $500,000 0.16 TAX RATE 40.00% B $1,600,000 0.12 NET INCOME NEXT YEAR: $1,200,000 C $600,000 0.15 ADDITION TO RETAINED EARNINGS $1,000,000 D $1,500,000 0.18 LOAN INTEREST RATE 10.00% FOR LOAN UPTO $750,000 $4,200,000 12.00% FOR LOAN ABOVE $750,000 COMMON STOCK PRICE PER SHARE $50 DIVIDEND PER SHARE $5 GROWTH RATE 9.00% FLOATATION COST 8.00%

a. COST OF NEW EQUITY 19.87% COST OF RETAINED EARNINGS 19.00% AT COST OF DEBT 6.00% FOR LOAN UPTO $750,000 7.20% FOR LOAN ABOVE $750,000

b. EQUITY BREAK POINT $1,538,462 DEBT $538,462 DEBT BREAK POINT $2,142,857 DEBT $750,000 TOTAL EQUITY $1,392,857

c. MCC UPTO TOTAL CAPITAL OF $1,538,462 = 14.45% MCC BETWEEN $1,538,462 AND $2,142,857 15.02% MCC ABOVE $2,142,857 15.44%

66

d. INVESTMENT OPPORTUNITY SCHEDULE

PROJECT INVESTMENT RETURN

D $1,500,000 0.18

A $500,000 0.16

C $600,000 0.15

B $1,600,000 0.12 e.

f. Only Projects D and A would be chosen. They are the ones with IRR values on the IOS schedule that

plot above the MCC schedule.

MCC/IOS ScheduleStone Wood Products

11.00%

12.00%

13.00%

14.00%

15.00%

16.00%

17.00%

18.00%

19.00%

$0 $500 $1,000 $1,500 $2,000 $2,500 $3,000 $3,500 $4,000 $4,500

Capital Budget Size ($000s)

Costs

of C

apital and IR

Rs

MCC IOS

Project D

AC

B

67

Chapter 10 Solutions


1. How do we calculate the payback period for a proposed capital budgeting project? What are the

main criticisms of the payback method?

We calculate the payback period for a proposed project by adding a project’s positive cash flows, one

period at a time, until the sum equals the initial investment. The number of time periods it takes to

cover this investment is the payback period. The main criticisms of the payback method are that cash

flows after the payback period are ignored and the time value of money is not considered.

2. How does the net present value relate to the value of the firm?

The net present value is the dollar amount of the change to the value of the firm if the project under

consideration is accepted.

3. What are the advantages and disadvantages of the internal rate of return method?

The internal rate of return method is a discounted cash flow method and a number expressed as a

percentage. These are typically seen as advantages. The main disadvantage of the internal rate of

return is that it is somewhat more difficult to calculate, although this is less true with the ready

availability of financial calculators.

4. Provide three examples of mutually exclusive projects.

Mutually exclusive projects are projects that compete against each other for our selection. If a firm

were considering the purchase of a new computer, needing only one computer, then the proposals

made by the sales reps from Hewlett-Packard, Compaq, and Toshiba would be mutually exclusive

projects vying for our selection.

5. What is the decision rule for accepting or rejecting proposed projects when using net present value?

When using the net present value decision rule any project with a net present value greater than or

equal to zero would be acceptable. Any project with a negative net present value would be rejected.

6. What is the decision rule for accepting or rejecting proposed projects when using internal rate of

return?

68

Whenever the internal rate of return is greater than or equal to the required rate of return, the hurdle

rate, the project is accepted. When the internal rate of return is less than this required rate of return,

the project is rejected.

7. What is capital rationing? Should a firm practice capital rationing? Why?

Capital rationing is the practice of setting dollar limits on what will be invested in new capital

budgeting projects. Proprietorships, partnerships and private corporations are in a position to do

whatever the owners wish. It can be argued, however, that for a publicly traded corporation capital

rationing may not be consistent with maximizing the value of the firm. This is because some value

adding projects may be rejected if they would cause the firm to exceed its self imposed capital

rationing limit.

8. Explain how to resolve a “ranking conflict” between the net present value and the internal rate of

return. Why should the conflict be resolved as you explained?

Whenever there is a ranking conflict between net present value and internal rate of return we

generally suggest that the project with the highest net present value be chosen. This is because the

net present value method ties more directly with the primary financial goal of the firm, to maximize

firm value.

9. Explain how to measure the firm risk of a capital budgeting project.

The firm risk of a capital budgeting project measures the impact of adding a new project to the

existing projects of the firm.

10. Why is the coefficient of variation a better risk measure to use than the standard deviation when

evaluating the risk of capital budgeting projects?

The coefficient of variation is a better risk measure than the standard deviation alone because the CV

adjusts for the size of the project. The CV measures the standard deviation divided by the mean and

therefore puts the standard deviation into context. For example, a standard deviation of .05 may be

considered large relative to a mean of .02 but would be considered a small value relative to a mean

value of 8.

11. Explain why we measure a project’s risk as the change in the CV.

We measure a project’s risk as the change in the coefficient of variation because this focuses on the

change in the riskiness of the firm’s existing portfolio.

12. Explain how using a risk-adjusted discount rate improves capital budgeting decision making

compared to using a single discount rate for all projects?

69

The risk-adjusted discount rate improves capital budgeting decision making compared to the single

discount rate approach because the RADR allows us to set a higher hurdle for the high risk project

and a lower hurdle for the low risk project thus aligning our capital budgeting decision making

process more closely with the goal of maximizing the value of the firm.


10-1. a ) Peter: (10,000) + 4,000 + 4,000 + 4,000 ----> 2.5 years

Paul: (10,000) + 2,000 +8,000 + 2,000 ----> 2.0 years

Mary: (10,000) + 10,000 + 1,000 + 1,000 ----> 1 year

b ) Mary's project is most liquid using payback as the liquidity measure.

10-2. CF0 = -20,000,000

CF1-25 = $2,000,000

I = 8%

NPV = $1,349,552

10-3. IRR = 8.78%

10-4. CF0 = -20,000,000

CF25 = 146, 211,879.90

MIRR = 8.28%

10-5. Expected Cash Flows

Year Weights Cum. CF Waters Cum. CF

0 -$200,000 (200,000) -$300,000 (300,000)

1 100,000 (100,000) 200,000 (100,000)

2 75,000 (25,000) 150,000 50,000

3 50,000 25,000 150,000 200,000

4 100,000 125,000 150,000 350,000

Project Weights: 2.5 years

Project Waters: 1.67 years

Project Waters is the better project according to payback because it recoups its investment in a shorter time.

70


Year Weights Waters

0 -$200,000 -$300,000

1 100,000 200,000

2 75,000 150,000

3 50,000 150,000

4 100,000 150,000

k= 10%

NPVweights (k = 10%) = $58,759.65

NPVwaters (k= 10%) = $220,934.36

10-7. a ) NPV = (17,291.42) + 5,000[1/1.121] + 8,000[1/1.122] + 10,000[1/1.123] =

$668.22

b ) NPV = (17,291.42) + 5,000[1/(1+k)1] + 8,000[1/(1+k)2] + 10,000[1/(1+k)3] = $0

IRR = k = 14%

c ) Yes. NPV is positive and IRR > Cost of capital

10-8. a ) Rifle Stock: NPV = -9,000 + 2,000 X .8850 + 5,000 X .7831 + 1,000 X .6931 + 4,000 X

.6133 = -168.20

Fork Lift: NPV = -12,000 +5,000 X .8850 + 4,000 X .7831 +6,000 X .6931 + 2,000 X .6133

= +942.60

Packaging Equip. NPV = -18,200 + 5,000 X .7831 + 10,000 X .6931 + 12,000 X .6133 =

+6.10

b ) Fork Lift and Packaging; both have positive NPVs.

10-9. a ) Cal's Project: NPV = -100,000 + 22,611 X (4.5638) = $3,192.08

Aron's Project:NPV = -300,000 + 63,655 X (4.5638) = -$9,491.31

b ) Cal's Project: 100,000/22,611 = PVIFAk,7 year; k = 13% = IRR

Aron's Project:300,000/63,655 = PVIFAk,7 year; k = 11% = IRR

c ) Cal's Project; NPV is positive and IRR > Cost of Capital.

d ) No.

71

10-10.

Time Cash Flow

FV of Cash Flow at T-10 if reinvested @ 15%

cost of capital (per Equation 8-1a)

Years to go

Initial investment ($10,000)

T- 1 $4,000 $14,072 9

T- 2 $4,000 $12,236 8

T- 3 $4,000 $10,640 7

T- 4 $4,000 $9,252 6

T- 5 $4,000 $8,045 5

T- 6 $4,000 $6,996 4

T- 7 $4,000 $6,084 3

T- 8 $4,000 $5,290 2

T- 9 $4,000 $4,600 1

T- 10 $4,000 $4,000 0

Terminal Value $81,215

a.) IRR 38%

b.) MIRR 23.3%

10-11. a ) Printer #1: Payback = 2 years

Printer #2: Payback = 1.77 years

b ) Printer #1: NPV = -2,000 +900 X .9091 + 1,100 X .8264 + 1,300 X .7513 = +703.92

Printer #2: NPV = -2,500 + 1,500 X .9091 + 1,300 X .8264 + 800 X .7513 = +539.01

c ) Printer #1: NPV = 0 = -2,000 + 900 X [1/(1+k)1] + 1,100 X [1/(1+k)2] + 1,300 X

[1/(1+k)3]

IRR = k = .2782 = 27.82%

Printer #2: NPV = 0 = -2,500 + 1,500 X [1/(1+k)1] + 1,300 X [1/(1+k)2] + 800 X

[1/(1+k)3]

IRR = k = .2325 = 23.25%

d ) Printer #1 with higher NPV and higher IRR

e ) Printer #1: NPV = -2,000 + 900 X .8621 + 1,100 X .7432 + 1,300 X .6407 = +426.32

Printer #2: NPV = -2,500 + 1,500 X .8621 + 1,300 X .7,432 + 800 X .6407

= +271.87

No. NPV of Printer #1 is still higher.

72


Year Program

0 -20,000,000

1 1,000,000

2 2,000,000

3 5,000,000

4 6,000,000

5 6,000,000

6 6,000,000

7 6,000,000

8 6,000,000

9 6,000,000

10 6,000,000

I = 15%

NPV = $2,082,694.77

IRR = 17.14%

MIRR = 16.14%

TV = $89,336,820

10-13. a ) Project A: NPV = -11,000 + 4,000 X (3.9975) = $4,990.00

Project B: NPV = -17,000 + 4,500 X (3.9975) = $988.75

Project A. Project A should be selected because it has the higher NPV

b) Both. Both the NPVs are positive.

c ) Project A: IRR : 11000/4000 = PVIFAk,6 year; k =28.16 %

Project B: IRR : 17000/4500 = PVIFAk,6 year; k = 15.07%

d ) Mutually exclusive: Project A has the higher IRR and would be selected.

Independent: Select both. (IRR > Cost of Capital for both the projects)

e ) Project C: NPV = -17,000 + 37,500X(PVIF13%,6 year)

= -17,000 + 37,500 X .4803 = $1,011.25

Project C. NPV of Project C > NPV of Project B Project C would be chosen

of Project B if these projects were mutually exclusive.

f ) Project C: IRR: 17,000/37,500 = .4533 = PVIFk,6 year; k = 14.09 %

IRR of Project C < IRR of Project B Project B would be chosen because it

has the higher IRR value.

g) Selections based on NPV and IRR method contradict each other. Since NPV method is

generally preferred, select Project C.

73

10-14. a ) NPV = -5M + 1.85M(2.7982) -.25M(.4761) = $57,645

b ) Multiple IRRs are possible because of two sign changes in the cash flow series. In this case

there is only one IRR, however. Do an NPV profile if you don’t believe us. The IRR is 16.59%.

TI BAII PLUS Financial Calculator Solution IRR

Keystrokes

Display

[CF]

CF0 = old contents

[2nd][CLR Work]

CF0 = 0.00

5000000[+/-][ENTER]

CF0 = -5,000,000.00

C01 = 1,850,000.00 F01 = 4.00

[ -][ENTER]

C02 = -250,000.00 F02 = 1.00

[IRR]

IRR = 0.00

[CPT]

IRR = 16.59

c ) The IRR of 16.59% is greater than the required rate of return of 16%, so the project would get a

positive recommendation.

10-15. a) Hydroelectric Project Geothermal Project

CF0 = ($100,000) CF0 = ($100,000)

CF1 = $20,000 CF1 = $60,000

CF2 = $30,000 CF2 = $40,000

CF3 = $40,000 CF3 = $20,000

CF4 = $90,000 CF4 = $10,000

b) NPVhydro (k = 6%) = $50,441.02

NPVgeo (k = 6%) = $44,181.07

Accept the Geothermal Upgrade project.

c) NPVhydro (k = 15%) = $17,834.06

NPVgeo (k = 15%) = $25,253.98

Neither project would be accepted because the NPV for each is negative.

d) Approximately 9.58%. This is where the NPV profiles cross.

e) Greater than 21.66%

f) Greater then 31.92%

74

10-16. The Chalk Line Machine, Gel Padded Glove, Insect Repellant, and Recycled Base Cover projects

collectively have initial cash outlays of $90,000 (under the budget limit) and have NPVs that sum to

$12,950. No other combination of projects gives a higher total NPV and stays under the budget

limit.

10-17. Given Information:

Initial investment $5,669.62 Yearly net cash flows:

Year 1 $2,200 Year 2 $2,200 Year 3 $2,200

Required rate of return 12% a. NPV of the investment:

Year: 0 1 2 3 Annual cash flows ($5,670) $2,200 $2,200 $2,200

PV of cash flows ($5,670) $1,964 $1,754 $1,566

NPV ($386)

b. Comment on the acceptability of the investment:

c. NPV Profile:

Discount rate 0% 5% 10% NPV 930 322 (199)

Comment:

d. Comment:

10-18. STD(IRR) = [(.05x(0%-6%)2 + .1x(1%-6%)2 + .2x(3%-6%)2 + .3x(6%-6%)2 + .2x(9%-6%)2 +

.1x(11%-6%)2 + .05x(12%-6%)2].5 = 3.49%

Comment: The project is unacceptable because it has a negative NPV. You would not accept it even if you had cash available.

Comment: According to the NPV profile, the discount rate would have to be less than about 8% in order for the project's NPV to be positive.

Comment: The IRR is that discount rate which produces an NPV of zero. Therefore, the IRR could be calculated to determine the "hurdle rate" below which the project's NPV would be positive (8% in this case).

NPV PROFILE

930

322

(199)

($500)

($300)

($100)

$100

$300

$500

$700

$900

0% 5% 10%

DISCOUNT RATE

NP

V

75

COEFF. OF VARIATION (CV) = 3.49%/6% = .5817

10-19. PORT. STD. WITH A = [(.22x.022)+(.82x.032)+(.82x.032)+(2x.2x.8x.5x.02x.03)].5

= .0262 = 2.62%

E(IRR) of portfolio with A = (.2x14%)+(.8x13%) = 13.2%

CV of portfolio with A = 2.62%/13.2% = .1985

PORT. STD. WITH B = [(.22x.062)+(.82x.032)+(2x.2x.8x.5x.02x.03)].5 = .0317 = 3.17%

E(IRR) of portfolio with B = (.2x16%)+(.8x13%) = 13.6%

CV of portfolio with B = .0317/.136 = .2331

PORT. STD. WITH C = [(.22x.052)+(.82x.032)+(2x.2x.8x.5x.05x.03)].5 = .0303 = 3.03%

E(IRR) of portfolio with C = (.2x11%)+(.8x13%) = 12.6%

CV of portfolio with C = .0303/.126 = .2405

PORT. STD. WITH D = [(.22x.042)+(.82x.032)+(2x.2x.8x.5x.04x.03)].5 = .0288 = 2.88%

E(IRR) of portfolio with D = (.2x14%)+(.8x13%) = 12.6%

CV of portfolio with B = .0288/.132 = .2182

Project A has the lowest risk and Project C the highest as measured by the CV.

10-20. a) 1. CVA = 2%/10% = .2

2. E(IRR) of new combined portfolio = (700,000/900,000 x 10%) + (200,000/900,000 x 11%

= 10.22%

3. STD. Of new combined portfolio = [(.7782x.022)+(.2222x.03)+(2x.222x.778x.9x.02x.03)].5

= .0218 = 2.18%

4. CV of new combined portfolio = .0218/.1022 = .2133

b) .2133 - .20 = .0133 change in CV

c) average risk

d) 1. Ave. Risk: NPV = $55,000/1.131 + 55,000/1.132 + 55,000/1.133 + 100,000/1.134 - 200,000

= ($8,805)

2. High Risk: NPV = $55,000/1.161 + 55,000/1.162 + 55,000/1.163 + 100,000/1.164 - 200,000

= ($21,247)

3. Low Risk: NPV = $55,000/1.101 + 55,000/1.102 + 55,000/1.103 + 100,000/1.104 - 200,000

= $5,078

10-21. a) (.125x2%)+(.20x5%)+(.35x9%)+(.20x13%)+(.125x16%) = 9.00%

b) .125(.02-.09)2 + .2(.05-.09)2 + .35(.09-.09)2 + .2(.13-.09)2 + .125(.16-.09)2 = .001865

= .1865%

square root of .001865 = .0432 = 4.32% standard deviation

c) CV of existing portfolio = .02/.08 = .25

d) E(IRR) of new combined portfolio = (.8x8%)+(.2x9%) = 8.20%

76

e) STD. DEV. of the combined portfolio = [(.22x.04322)+(.82x.022)+(2x.2x.8x1x.0432x.02)].5 = .0246

= 2.46%

f) CV of combined portfolio = .0246/.0820 = .3005

g) .3005 - .25 = .0505 increase in CV

10-22. Proj. A Proj. B Proj.C Proj. D

Standard deviation of existing portfolio: 4.00% 4.00% 4.00% 4.00%

Standard deviation of new project: 9.00% 5.00% 3.00% 1.00%

Standard deviation of combined portfolio 3.71% 3.63% 3.61% 3.60%

expected return E(R) of new project: 18.00% 15.00% 11.00% 8.00%

expected return E(R) of existing portfolio: 12.00% 12.00% 12.00% 12.00%

expected return E(R) of combined portfolio: 12.60% 12.30% 11.90% 11.60%

a. Coefficient of variation of existing portfolio: 33.33%

b.&c. Coefficient of variation of combined portfolio: 29.45% 29.55% 30.36% 31.05%

d. A IS THE D IS THE

LOWEST HIGHEST

RISK RISK

PROJECT PROJECT

10-23. a. CV of existing portfolio = 5%/15% = 33.33%

b. WT of existing portfolio of PROJ1 is added = $820,000/($820,000+$194,000) = .809

= 8.09%

c. WT of PROJ1 if added to existing portfolio = 1 - .809 = .191 = 19.1%

d. STD. DEV. of combined portfolio = [(.8092x.052)+(.1912x.09)+(2x.809x.191x1x.05x.09)].5 =

.0577 = 5.77%

The combined portfolio standard deviation is higher than that of the existing portfolio (5.77% versus

5.00%).

e. CV of the combined portfolio = 5.77%/[(.809x15%)+(.191x18%)] = 5.77%/15.57%

= .3706

10-24.

= $298,500 x 6.7100814 - $2,000,000

= $2,002,959.30 - $2,000,000

= $2,959.30

a) $2,000,000 -

.08

)(1.08

1 - 1

x $298,500 = NPV10

77

= $298,500 x 6.14456711 - $2,000,000

= $1,834,153.28 - $2,000,000

= ($165,846.72)

c) The project should not be adopted.

d)

NPV = $0 = CF x 6.14456711 - $2,000,000

$2,000,000 = CF x 6.14456711

CF = $325,490.79

10-25 (Comprehensive Problem) Given Information:

Project 1 Project 2

Yearly net cash flows:

Initial investment ($200,000) ($200,000)

Year 1 $0 $90,000

Year 2 $0 $70,000

Year 3 $20,000 $50,000

Year 4 $30,000 $30,000

Year 5 $40,000 $10,000

Year 6 $60,000 $10,000

Year 7 $90,000 $10,000

Year 8 $100,000 $10,000

Weighted average cost of capital 7.2%

a. NPVs of the projects:

Project 1 Project 2

NPV $19,398 $33,705

b. IRRs of the projects:

Project 1 Project 2

b) $2,000,000 - .10

)(1.10

1 - 1

x $298,500 = NPV10

$2,000,000 - .10

)(1.10

1 - 1

x CF = $0 = NPV10

78

IRR 8.8% 14.4%

c. NPV Profiles:

Discount rate 2% 4% 6% 8% 10% 12% 14% 16%

NPV Project 1 99,769 65,182 35,340 9,502 (12,943) (32,504) (49,605) (64,600)

NPV Project 2 65,526 52,380 40,396 29,435 19,376 10,118 1,573 (6,337)

Comment: Both projects have the same NPV at a discount rate of approximately 5.5%. At that discount rate the NPV

of both projects is about $45,000.

d. Project selection at other WACCs:

Select Reason

i. WACC > 5.4% Project 2 Project 2's NPV is higher

ii. WACC > 8.81% Project 2 Project 1's NPV is negative

iii. WACC > 14.39%

Neither project The NPV for both projects is negative

e) Look at the NPV profile. If the discount rate is 5%, this is to the left of the crossover point. Project 1

would have a higher NPV than Project 2. This would create a ranking conflict if the projects were mutually

exclusive. Project 2 has a higher IRR (14.3% for Project 2 versus 8.81 percent for Project 1).

At a discount rate below 5.4%, NPV and IRR give conflicting ranking signals. At a discount rate of

5.4% or more, the ranking of the two projects is the same.

f) a. Both projects would be accepted at a 7.2% cost of capital.

NPV PROFILES

($80,000)

($60,000)

($40,000)

($20,000)

$0

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

2% 4% 6% 8% 10% 12% 14% 16%

DISCOUNT RATE

NP

V Project 1

Project 2

79



1. Why do we focus on cash flows instead of profits when evaluating proposed capital budgeting

projects?

We focus on cash flows instead of profits when evaluating proposed capital budgeting projects

because it is cash flow that changes the value of a firm. You can spend cash but you can not spend

profit.

2. What is a sunk cost? Is it relevant when evaluating a proposed capital budgeting project? Explain.

A sunk cost is a cash flow that has already occurred, or that will occur, whether a project is accepted

or rejected. It is irrelevant when evaluating a proposed project.

3. How do we estimate expected incremental cash flows for a proposed capital budgeting project?

We estimate expected incremental cash flows for a proposed project by estimating the changes in

sales and expenses that are incremental to the project, adding back the incremental depreciation

expense since depreciation expense is a non-cash expense.

4. What role does depreciation play in estimating incremental cash flows?

Depreciation expense is a tax deductible expense and therefore affects cash flow through its effect on

taxes. Depreciation expense that is incremental to a proposed project therefore affects incremental

cash flows.

5. How and why does working capital affect the incremental cash flow estimation for a proposed large

capital budgeting project? Explain.

Many large projects require additional working capital. This investment in additional working

capital becomes part of the initial investment. This investment is recovered at the end of the

project’s life. There may be some spontaneous increase in current liabilities associated with a

project, but the change in net working capital, if any, is likely to be a positive value requiring an

increase in the initial investment of that amount.

6. How do opportunity costs affect the capital budgeting decision-making process?

Opportunity costs reflect the foregone benefits of the alternative not chosen when a capital budgeting

project is selected. Any decrease in the cash flows of the firm directly tied to the selection of a new

project could be part of the opportunity cost value and included in our capital budgeting analysis.

80

7. How are financing costs generally incorporated into the capital budgeting analysis process?

Financing costs are usually captured in the discount or hurdle rate when doing NPV or IRR analysis.

The operating cash flows usually do not include financing costs because this would be double

counting.

Answers to End-of—Chapter Problems

11-1. Price of Selected Model $6,000

Attachments 5,000

Paint Name 300

Garage and Maint. Facility 12,000

$23,300

Cash Flow t0 = ($23,300)

11-2. (a) Resale Price: $60,000

Price of Equipment: $200,000

Resale Value: $60,000

Years Used: 3

MACRS Classification: 5 years

Income Tax: 40%

Accumulated Depreciation: 20% + 32% + 19.2% = 71.2% or,

0.712 X $200,000 = $142,400

Book Value: $200,000 - $142,400 = $57,600

Taxable Gain (Loss): $60,000 - $57,600 = $2,400

Tax (Refund): $2,400 X 0.40 = $960

Net Cash Flow: $60,000 - $960 = $59,040

(b) Resale Price: $80,000

Price of Equipment: $200,000

Resale Value: $80,000

Years Used: 3

MACRS Classification: 5 years

Income Tax: 40%

Accumulated Depreciation: 20% + 32% + 19.2% = 71.2% or,

0.712 X $200,000 = $142,400

Book Value: $200,000 - $142,400 = $57,600

Taxable Gain (Loss): $80,000 - $57,600 = $22,400

Tax (Refund): $22,400 X 0.40 = $8,960

Net Cash Flow: $80,000 - $8,960 = $71,040

81

11-3. a) $10,000 - $3,000 - $2,000 = $5,000

b ) $5,000 X .35 = $1,750

c ) $5,000 - $1,750 = $3,250

d ) $3,250 + $2,000 depr. add back = $5,250

e ) Interest Expense. It is included in the cost of funds when calculating NPV and when setting the

IRR hurdle rate.

11-4. Mower $20,000

Annual Revenues (increase) 100,000

Operating Costs (increase) 30,000

Year 1

$100,000

- 30,000

70,000

Depreciation (20%) - 4,000

EBIT 66,000

Taxes (35%) - 23,100

42,900

Depreciation + 4,000

Net operating CF $46,900

The net operating incremental cash flow for year 1 is $46,900

11-5. $2,000 * (1 – 0.35) = $1,300

11-6. Initial Cost of new Equipment $375,000

End of year: 1 2 3 4 5 6

Earnings Before Depreciation

and Taxes (EBDT) $120,000 $90,000 $70,000 $70,000 $70,000 $70,000

Discount rate 13%

Tax rate 40%

Year 1 2 3 4 5 6

MACRS depreciation

percentages for five-year class 20.00% 32.00% 19.20% 11.50% 11.50% 5.80%

life equipment

Calculations:

Incremental Cash Flows:

Year 1 2 3 4 5 6

EBDT $120,000 $90,000 $70,000 $70,000 $70,000 $70,000

New depreciation expense (75,000) (120,000) (72,000) (43,125) (43,125) (21,750)

82

Change in Operating Income 45,000 (30,000) (2,000) 26,875 26,875 48,250

Income tax on new income (18,000) 12,000 800 (10,750) (10,750) (19,300)

Change in earnings after tax 27,000 (18,000) (1,200) 16,125 16,125 28,950

Add back depreciation 75,000 120,000 72,000 43,125 43,125 21,750

Net incremental

operating cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $50,700

Present value of cash flows $90,265 $79,881 $49,068 $36,339 $32,159 $24,352

Total present value

of cash flows $312,064

Less initial cost ($375,000)

= NPV ($62,936)

The NPV is negative so the project should be rejected.

11-7. Rhodes Manufacturing Corporation (with salvage value)

Given:

Initial Cost of new Equipment $375,000

End of year: 1 2 3 4 5 6

Earnings Before Depreciation

and Taxes (EBDT) $120,000 $90,000 $70,000 $70,000 $70,000 $70,000

Discount rate 13%

Tax rate 40%

Year 1 2 3 4 5 6

MACRS depreciation

percentages for five-year class 20.00% 32.00% 19.20% 11.50% 11.50% 5.80%

life equipment

Resale value of equipment $50,000 at the end of the sixth year

Calculations:

Incremental Cash Flows:

Year 1 2 3 4 5 6

EBDT $120,000 $90,000 $70,000 $70,000 $70,000 $70,000

New depreciation expense (75,000) (120,000) (72,000) (43,125) (43,125) (21,750)

Change in Operating Income 45,000 (30,000) (2,000) 26,875 26,875 48,250

Income tax on new income (18,000) 12,000 800 (10,750) (10,750) (19,300)

Change in earnings after tax 27,000 (18,000) (1,200) 16,125 16,125 28,950

Add back depreciation 75,000 120,000 72,000 43,125 43,125 21,750

Net incremental

operating cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $50,700

Resale value of equipment 50,000

Less income tax on sale (20,000)

Net cash flow from equipment sale 30,000

Total Net cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $80,700

83

Present value of cash flows $90,265 $79,881 $49,068 $36,339 $32,159 $38,762

Total present value



= NPV ($48,526)

The NPV is negative so the project should be rejected.

11-8. a ) $85,000 + $20,000 = $105,000

b ) $125,000 X .10 = $12,500

Oper. Exp. -20,000

Depr. Exp. -10,500

-18,000

Tax Saving@40% 7,200

-10,800

Add back Depr. 10,500

Net Incremental Oper. Cash flow -300

c ) End of year 5 at the time of the sale

11-9. GHOST SQUADRON HISTORICAL AIRCRAFT, INC.

ASSUMPTIONS:

Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 Yr 7 Yr 8

MACRS Depreciation 14.3% 24.5% 17.5% 12.5% 8.9% 8.9% 8.9% 4.5%

Tax rate 35%

Cost of capital 12%

ESTIMATED INCREMENTAL CASH FLOWS:

Initial Investment at t=0:

Crew transport & wreckage collection ($100,000)

Transport to restoration facility ($35,000)

Plane restoration ($600,000)

Total Initial Investment ($735,000)

Year: 1 2 3 4 5 6 7

New Revenues $70,000 $70,000 $70,000 $70,000 $70,000

Additional operating expenses ($40,000) ($40,000) ($40,000) ($40,000) ($40,000) ($40,000) ($40,000)

Depreciation on plane ($105,105) ($180,075) ($128,625) ($91,875) ($65,415) ($65,415) ($65,415)

Change in Operating Income ($145,105) ($220,075) ($98,625) ($61,875) ($35,415) ($35,415) ($35,415)

Tax on new income $50,787 $77,026 $34,519 $21,656 $12,395 $12,395 $12,395

Change in Earnings after tax ($94,318) ($143,049) ($64,106) ($40,219) ($23,020) ($23,020) ($23,020)

Add back depreciation $105,105 $180,075 $128,625 $91,875 $65,415 $65,415 $65,415

Net Incremental Cash Flows $10,787 $37,026 $64,519 $51,656 $42,395 $42,395 $42,395

84

Additional Cash Flows at the end of year 7:

Proceeds from sale of plane $500,000

Book value of plane $33,075

Taxable gain(loss) $466,925

Tax on gain $163,424

Net cash flow from sale of plane $336,576

(Salvage value less tax on gain)

SUMMARY OF NET CASH FLOWS:

Time: 0 1 2 3 4 5 6 7

($735,000) $10,787 $37,026 $64,519 $51,656 $42,395 $42,395 $378,972

Net present Value: ($400,138)

Internal rate of Return: -2.7%

11-10. a ) NWC = Current Assets - Current Liabilities

= ($8,000 + $10,000 + $12,000) - ($6,000 + $2,500) = $21,500

b ) Outflow

c ) Beginning of year 1

11-11. Given:

Initial Cost of new Equipment $90,000 End of year: 1 2 3 4

New revenues $50,000 $30,000 $20,000 $20,000 Discount rate 11%

Tax rate 30%

Year 1 2 3 4 MACRS depreciation percentages for three-year class life equipment 33.30% 44.50% 14.80% 7.40%

Resale value of equipment $10,000 at the end of the fourth year Calculations: Incremental Cash Flows:

Year 1 2 3 4 Revenues $50,000 $30,000 $20,000 $20,000

New depreciation expense (29,970) (40,050) (13,320) (6,660)

Change in Operating Income 20,030 (10,050) 6,680 13,340

Income tax on new income (6,009) 3,015 (2,004) (4,002)

Change in earnings after tax 14,021 (7,035) 4,676 9,338

Add back depreciation 29,970 40,050 13,320 6,660

Net incremental operating cash flows $43,991 $33,015 $17,996 $15,998




Total Net cash flows $43,991 $33,015 $17,996 $22,998

Present value of cash flows $39,632 $26,796 $13,159 $15,149

Total present value of cash flows $94,735

85


= NPV $4,735

11-12. MACRS 3 YEARS 33.30% 44.50% 14.80% 7.40%

PRICE OF NEW EQUIPMENT: 90,000

YEARS USED 4

INCOME TAX RATE: 40.00% COST OF CAPITAL 10.00% SALVAGE VALUE OF NEW EQPT. 10,000

MACRS CLASSIFICATION: 3 YEARS 1 2 3 4

DEPRECIATION RATE 33.30% 44.50% 14.80% 7.40%

ACCUM. DEP. %) 100%

CASH FLOW FROM SALE OF NEW EQUIPMENT 6,000

CASH FLOW FROM SALE OF OLD EQUIPMENT SALE PRICE 10,000 BOOK VALUE 20,000 TAXABLE GAIN (LOSS) (10,000) TAX (REFUND) (4,000) NET CASH FLOW 14,000

INCREMENTAL CASH FLOW YEAR 1 1 2 3 4

REVENUE STREAM 50,000 30,000 20,000 20,000 DEPRECIATION EXPENSE 29,970 40,050 13,320 6,660

CHANGE IN OPERATING INCOME 20,030 (10,050) 6,680 13,340 TAX ON NEW INCOME 8,012 (4,020) 2,672 5,336

CHANGE IN EARNINGS 12,018 (6,030) 4,008 8,004 ADD BACK DEPRECIATION 29,970 40,050 13,320 6,660

NET INCREMENTAL OP. CASH FLOW 41,988 34,020 17,328 14,664

NET CASH FLOW

0 1 2 3 4 NEW EQUIPMENT (90,000) OLD EQUIPMENT 14,000 OPERATING CF 41,988 34,020 17,328 14,664 SALVAGE VALUE

NET CASH FLOW (76,000) 41,988 34,020 17,328 14,664

DISCOUNT RATE 10.00% NPV $17,419.18

Comments: Yes, since the project has a positive NPV at the company's cost of capital, Flower Belle should recommend that it be accepted.

86

11-13. Initial Cost of new equipment $90,000

End of year: 1 2 3 4

New revenues $50,000 $30,000 $20,000 $20,000

Discount rate 10%

Tax rate 40%

Year 1 2 3 4

MACRS depreciation percentages for

three-year classlife equipment 33.30% 44.50% 14.80% 7.40%

Book value of old equipment $20,000

Resale value of old equipment $10,000

Resale value of new equipment $10,000 at the end of the fourth year

Additional current assets required $10,000

Expected increase in current liabilities $5,000 Calculations: Incremental Cash Flows:

Gain(loss) on sale of old equipment ($10,000)

(Tax)refund on transaction $4,000

Net cash received for old equipment $14,000

Cost of New Equipment ($90,000)

Net Cash Outflow at T-0 for equipment ($76,000)

Additional net working capital required ($5,000)

Total Net Cash Outflow at T-0 ($81,000)

Year 1 2 3 4

Revenues $50,000 $30,000 $20,000 $20,000










Recovery of net working capital investment 5,000




Less initial cash outflow at T-0 ($81,000)

= NPV $15,834

11-14. a ) Book Value = $20,000 - $12,000 = $8,000

b ) Taxable Gain = $18,000 - $8,000 = $10,000

c ) Tax on Gain = $10,000 X 0.3 = $3,000

d ) Cash Flow = $18,000 - $3,000 = $15,000

This is an inflow.

87

e ) Incremental Cash Flow for to = $40,000 - $15,000 = $25,000 outflow

f ) b ) Taxable Income (Loss) = $6,000 - $8,000 = ($2,000)

c ) Tax Credit on Loss = $2,000 X 0.3 = $600

d ) Cash Flow = $6,000 + $600 = $6,600

This is an inflow.

e ) Incremental Cash Flow for to = $40,000 - $6,600 = $33,400 outflow

88

11-15. MACRS 3 YEARS 33.30% 44.50% 14.80% 7.40%

PRICE OF NEW EQUIPMENT: $22,000 PRICE OF OLD EQUIPMENT: 0 RESALE VALUE OF OLD EQPT: 0 YEARS USED 4

INCOME TAX RATE: 40.00% COST OF CAPITAL 14.00%

SALVAGE VALUE OF NEW EQUIP. $0

MACRS CLASSIFICATION: 3 YEARS 1 2 3 4

DEPRECIATION RATE 33.30% 44.50% 14.80% 7.40%

ACCUMULATED DEPR.(%) 100%

CASH FLOW FROM CHANGE IN NWC CHANGE IN CURRENT ASSETS 5000 CHANGES IN CURRENT LIABS. 3000 CHANGE IN NWC 2000

INCREMENTAL CASH FLOW YEAR 1 2 3 4 CHANGE IN SALES: 20,000 20,000 10,000 10,000 INCREASE IN OPERATING EXPENSES (4,000) (4,000) (2,000) (2,000) TOTAL INFLOW

16,000 16,000

8,000

8,000

DEPRECIATION EXPENSE 7,326 9,790 3,256 1,628

CHANGE IN OPERATING INCOME 8,674 6,210 4,744 6,372 TAX ON NEW INCOME 3,470 2,484 1,898 2,549

CHANGE IN EARNINGS 5,204 3,726 2,846 3,823

ADD BACK DEPRECIATION 7,326 9,790 3,256 1,628

NET INCREMENTAL OP. CASH FLOW 12,530 13,516 6,102 5,451

NET CASH FLOW

0 1 2 3 4 a. NEW EQUIPMENT (22,000)

NWC (2,000) 2,000 b. OPERATING CF 12,530 13,516 6,102 5,451

c. NET CASH FLOW (24,000) 12,530 13,516 6,102 7,451

DISCOUNT RATE 14.00%

NPV $5,922.36 IRR 27.24% Yes, Brenners should add this machine to their factory.

89

11-16.

Given:

Initial Cost of new Equipment $150,000

Installation and calibration costs $7,500

Decrease in operating expenses $50,000 annually

Discount rate 10%

Tax rate 35%

Year 1 2 3 4

MACRS depreciation

percentages for three-year class 33.30% 44.50% 14.80% 7.40%

life equipment

Calculations:

Incremental Cash Flows at T-0:

Cost of New Equipment ($150,000)

Installation and calibration costs ($7,500)

Total Net Cash Outflow at T-0 ($157,500)

Incremental cash flows in years 1 - 5:

Year 1 2 3 4 5

Reduction in operating costs $50,000 $50,000 $50,000 $50,000 $50,000

New depreciation expense (52,448) (70,088) (23,310) (11,655) 0

Change in Operating Income (2,448) (20,088) 26,690 38,345 50,000

Income tax on new income 857 7,031 (9,342) (13,421) (17,500)

Change in earnings after tax (1,591) (13,057) 17,349 24,924 32,500

Add back depreciation 52,448 70,088 23,310 11,655 0

Net incremental

operating cash flows $50,857 $57,031 $40,659 $36,579 $32,500

a. NPV of the investment:

Present value of cash flows $46,233 $47,133 $30,547 $24,984 $20,180



a. NPV = $11,577 b. Yes, since the NPV of the investment is positive at RHPS's cost of capital, Weiss and Majors should go forward with the project.

90

11-17. Chemical Company of Baytown

Given:

Original cost of old equipment $40,000 on Dec 31, 2004

Resale value of old equipment $4,000 on Dec 31, 2006

Discount rate 6%

Tax rate 40%

Year 1 2 3 4

MACRS depreciation

percentages for three-year class 33.30% 44.50% 14.80% 7.40%

life equipment

Calculations:

a. Cash flows from sale of old equipment:

Year 2005 Year 2006

Depreciation expense on old equipment $13,320 $17,800

Total accumulated depreciation $31,120

Book value of old equipment $8,880 on Dec 31, 2006

Resale value of old equipment $4,000 on Dec 31, 2006

Gain(loss) on sale of old equipment ($4,880)

(Tax)refund on transaction $1,952

Net cash received for old equipment $5,952

b. New net working capital requirements:

Additional current assets required:

Cash $1,000

Receivables $5,000

Inventory $10,000

Total $16,000

Expected increase in current liabilities:

Accounts payable $6,000

Accrued expenses $3,000

Total $9,000

Incremental cash flow for net working capital $7,000

c. Net cash outflow at the end of 2006 if new process line is installed:

Cost of New Equipment $180,000

Additional net working capital $7,000

Less proceeds from sale of old equipment ($5,952)

Net cash outflow at the end of 2006 $181,048

d. Incremental cash flows for 2007 - 2010:

End of year: 2007 2008 2009 2010

New revenues $60,000 $60,000 $60,000 $60,000

Reduction in operating expenses 6,000 6,000 6,000 6,000






91


e. NPV and IRR of the investment:

(Given) Resale value of new equipment $20,000 at the end of the fourth year




Recovery of net working capital investment 7,000


Year 1 2 3 4


Total present value



= NPV $35,522

Summary of all cash flows:

Year 0 1 2 3 4

Net Cash Flow ($181,048) $63,576 $71,640 $50,256 $63,928

IRR 14.4%

f. NPV Profile Year 0 1 2 3 4

Net Cash Flow ($181,048) $63,576 $71,640 $50,256 $63,928

Assumed cost of capital 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

NPV of cash flows $68,352 $62,338 $56,556 $50,994 $45,641 $40,487 $35,522 $30,736 $26,122 $21,672 $17,377

NPV Profile, Chemical Company of Baytown Project

$68,352$62,338

$56,556$50,994

$45,641$40,487

$35,522$30,736

$26,122$21,672

$17,377

$0

$10,000

$20,000

$30,000

$40,000

$50,000

$60,000

$70,000

$80,000

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

Cost of Capital

NP

V

92

11-18.

PROBLEM 11-18

Real Options Decision Tree NPV Analysis

J & T's Double Diamond Brewhouse

|-------- Part b. --------| |- Part c.

-|

Time Time Time Time Time Time Joint Path

t0 1 2 3 4 5 Probability NPV JP x NPV

50% $400,000 $400,000 $400,000 12.5% $666,954 $83,369

25% $200,000 100% $100,000 30% $200,000 $200,000 $200,000 7.5% $309,669 $23,225

20% $90,000 $90,000 $90,000 5.0% $113,163 $5,658

($300,000) 50% $100,000 100% $100,000 100% $100,000 $100,000 $100,000 50.0% $43,308 $21,654

0% ($40,000) 100% ($40,000) ($40,000) ($40,000) 0.0% ($437,323) $0

25% ($40,000)

100% $0 100% $0 $0 $0 25.0% ($335,088) ($83,772)

Total NPV of the Deal: $50,135

Cost of Capital: 14%

The Time 2 cash flow for the smash hit scenario

is $200,000 from operations minus $100,000

for the expansion.

93



1. Describe the general pattern of cash flows from a bond with a positive coupon rate.

Cash flows from a bond with a positive coupon rate consist of periodic interest payments and the face

value payment at maturity. Coupon interest payments occur at regular intervals throughout the life of

the bond. The face value payment occurs on the maturity date.

2. How does the market determine the fair value of a bond?

The fair value of a bond is the present value of the bond's coupon interest payments plus the present

value of the face value payment at maturity, discounted at the market’s required rate of return for the

bond in question. Equation 9-1 in the text is use to solve for the fair (present) value of a bond.

3. What is the relationship between a bond's market price and its promised yield to maturity? Explain.

A bond's market price depends on its yield to maturity (YTM). When a bond has a YTM greater than

its coupon rate, it sells at a discount from its face value. When the YTM is equal to the coupon rate,

the market price equals the face value. When the YTM is less than the coupon rate, the bond sells at

a premium over face value.

4. All other things held constant, how would the market price of a bond be affected if coupon interest

payments were made semiannually instead of annually?

Most bonds issued in the United States pay interest semiannually (twice per year). With semiannual

interest payments, we must adjust the bond valuation model (Equation 9-1 in the text) by multiplying

n, the number of years to maturity, by two, and dividing k, the annual interest rate, by two.

5. What is the usual pattern of cash flows for a share of preferred stock? How does the market

determine the value of a share of preferred stock, given these promised cash flows?

Preferred stock has no maturity date, so it has no maturity value. Its future cash payments are

dividend payments that are paid to preferred stockholders at regular time intervals for as long as they

(or their heirs) own the stock. Cash payments from preferred stock dividends are scheduled to

continue forever. To value preferred stock, we adapt the discounted cash flow model to reflect that

preferred stock dividends are a perpetuity. See Equation 9-4 in the text.

6. Name two patterns of cash flows for a share of common stock. How does the market determine the

value of the most common cash flow pattern for common stock?

94

Cash flows for a share of common stock consist of dividend payments and the price received for the

eventual sale of the share. Common stock valuation is complicated by the fact that common stock

dividends are difficult to predict compared to the interest and principal payments on a bond, or

dividends on preferred stock. Indeed, corporations may pay common stock dividends irregularly, or

not pay dividends at all.

As with bonds and preferred stock, the market values common stock by estimating the present value

of the expected future cash flows from the common stock. See Equation 9-6 in the text.

7. Define the P/E valuation method. Under what circumstances should a stock be valued using this

method?

The P/E ratio indicates how much investors are willing to pay for each dollar of a stock's earnings. A

high P/E ratio indicates that investors believe the stock's earnings will increase, or that the risk of the

stock is low, or both.

Financial analysts often use a P/E model to estimate common stock value for businesses that are not

public. First, analysts compare the P/E ratios of similar companies within an industry to determine

an appropriate P/E ratio for companies in that industry. Second, analysts calculate an appropriate

stock price for firms in the industry by multiplying each firm's earnings per share (EPS) by the

industry average P/E ratio. See Equation 9-9 in the text.

8. Compare and contrast the book value and liquidation value per share for common stock. Is one

method more reliable? Explain.

The Book Value of a firm's common stock is found by subtracting the value of the firm's liabilities,

and preferred stock, if any, as recorded on the balance sheet, from the value of its assets. The result

is the book value or net worth of the company's common stock. To find the book value per share of

common stock, divide the company's book value by the number of outstanding common stock shares.

See Equation 9-10 in the text.

The liquidation value and book value valuation methods are similar, except that the liquidation

method uses the market values of the assets and liabilities, not book values. The market values of the

assets are the amounts the assets would earn on the open market if they were sold (or liquidated).

The market values of the liabilities are the amounts of money it would take to pay off the liabilities.

Since it is based on market values, the liquidation value method is more reliable than the book value

method. However, liquidation value is a worst-case valuation assessment. A company's common

stock should be worth at least the amount generated per share at liquidation.

9. Answer the following questions about the discounted free cash flow model illustrated in Figure 12-4:

a. What are “free cash flows?”

95

Free cash flows represent the total cash flows from business operations that are available to be

distributed to the suppliers of a firm’s capital each year either in the form of interest to the debt

holders, or dividends to the stockholders.

b. Explain the terminal value calculation at the end of the forecast period. Why is it necessary?

The firm whose business operation is being valued is not expected to suddenly cease operating at the

end of the discrete forecasting period, but to continue operating indefinitely into the future as a going

concern. The terminal value calculation estimates the values of the cash flows that occur in the year

following the discrete forecasting period and beyond.

c. Explain the term “present value of the firm’s operations” (also known as Enterprise Value). What

does this number represent?

The present value of the company’s free cash flows represents the market value of the firm’s core

income producing operations. In the world of finance and investing this is sometimes called the

firm’s Enterprise Value. It is not the total market value of the entire company, however, or the total

market value of the company’s assets, because the current, or non-operating assets of the company

have not yet been accounted for.

d. Explain the adjustments necessary to translate enterprise value to the total present value of common

equity.

To obtain the value of the company’s common stock, add the value of the firm’s current assets to the

enterprise value (this produces the value of the firm’s total assets). Next, subtract the values of

current liabilities, long-term debt, and preferred stock. The result is the present value of common

equity.

10. Explain the difference between the discounted free cash flow model as it is applied to the valuation of

common equity and as it is applied to the valuation of complete businesses.

The Free Cash Flow Model values the complete business as a part of the procedure to value common

equity. The value of a complete business is the sum of the values of the operating, or income-

producing assets, plus the value of the non-operating, or current assets. All that is necessary to use

the Free Cash Flow Model to value a complete business, then, is to add the value of the company’s

operations to the value of the company’s current assets.

11. Why is the replacement value of assets method not generally used to value complete businesses?

The replacement value of assets method is not often applied to complete business valuations because

it is frequently very difficult to locate similar assets for sale on the open market, and because some

of a business’s assets are difficult to define and quantify.

96


12-1. a ) $1,000 X .06 = $60

b ) $60 X [(1-1/1.0810)/.08] + $1,000 X [1/1.0810] = $865.80

c ) Yes.

12-2. a ) $1,000 X .12 = $120

b ) $120 X [(1-1/1.0815)/.08] + $1,000 X [1/1.0815] = $1,342.38

c ) $60 X [(1-1/1.0430)/.04] + $1,000 X [1/1.0430] = $1,345.84

12-3. 3 X $2,000 = $6,000

12-4. Semi-annual interest payment = .10 X $1,000 X 6/12 = $50

Price = $50 X [(1-1/1.0410)/.04] + $1,000 X [1/1.0410] = $1,081.11

12-5. Since $1,100 > $1,000, YTM < Coupon Rate; YTM < 9%

$90 * [1-1/ (1 + k)10/k] + $1,000 * (1/1 + k10) = $1,100

k = 7.54%

12-6. a ) Since, $1,125 > $1,000, YTM < Coupon Rate YTM < 12%

b ) $120 X [(1-1/1.1010)/.10] + $1,000 X [1/1.1010] = $1,122.89; YTM 10%

c ) YTM = 12%; YTM = Coupon Rate if Market Price = Par

12-7. Since $872 < $1,000, k > 7%

$70 X [(1-1/(1+k)10/k] + $1,000 X [1/(1+k)10] = $872

If k=8%, VB = $932.90

If k=9%, VB = $871.65. So, k 9%.

12-8. $10/0.12 = $83.33 per share

12-9. kP = $1.75 /$ 20 = 0.0875 or 8.75%

12-10. a ) VP = $8/0.13 = $61.54 per share

b ) kP = $8/$50 = 16 %

12-11. a ) $4/(.16-.01) = $26.67

b) $4/$26.67 = 15%

97

12-12. $2/$15 + .04 = 17.33%

12-13. a ) P0 = $8/(.14 - .03) = $72.72

b ) ks = $8/$65 + .03 = 15.31%

12-14. $90 * [1-1/ (1.12)5/0.12] + $1,000 * (1/1.125) = $891.86

12-15. $35 * [1-1/ (1.055)20/0.055] + $1,000 * (1/1.05520) = $761

12-16. $80/ (1 + 0.23)1 = $65.04

$150/ (1 + 0.23)2 = $99.15

$1,500/ (1 + 0.23)3 = $806.08

$65.04 + $99.15 + $806.08 = $970.27

12-17. $3.00/0.12 = $25.00

12-18. $2.20/(0.18 - 0.09) = $2.20/0.09 = $24.44

12-19. D6 = $1.22 (1+ 0.10) = $1.342

$1.342/ (0.12 – 0.10) = $67.10

$0.70 / (1+0.12)1 + $0.83 / (1+0.12)2 + $0.96 / (1+0.12)3 + $1.09 / (1+0.12)4 + $1.22 /

(1+0.12)5 + $67.10 / (1+.12)6

0.625 + 0.66167 + 0.6833 + 0.6927 + 0.6923 + $33.99

=$37.34

12-20. D1 = 3.82(1 + 0.07) = 4.09

k = 4.09/82 + 0.07

k = .1199 = 11.99%

12-21. $85 * [1-1/ (1 + k)10/k] + $1,000 * (1/1 + k10) = $1,250

k = 5.23%

12-22. $2,100,000 / (0.18 – 0.09) = $23,333,333.33

12-23. Find the present values of cash flows for each year. Add them together to get the present value of the

firm.

Year 1 = $1,231,920,000 * [1/ (1 + 0.12)1] = $1,099,928,571

Year 2 = $1,453,665,600 * [1/ (1 + 0.12)2] = $1,158,853,316

98

Year 3 = $1,686,252,096 * [1/ (1 + 0.12)3] = $1,200,240,935

Year 4 = $1,922,327,389 * [1/ (1 + 0.12)4] = $1,221,673,808

Year 5 = $2,153,006,676 * [1/ (1 + 0.12)5] = $1,221,673,809

Year 6 CF = Year 5 CF * (1 + .10) = $2,153,006,676 * 1.10 = 2,368,307,344

Year 6 - ∞ = (((2,368,307,344 / (0.12 - 0.10)) * (1/1.12)5 ) = $67,192,060,000

Enterprise value of the firm today = $1,099,928,571 + $1,158,853,316 + $1,200,240,935 +

$1,221,673,808 + $1,221,673,809 + $67,192,060,000 = $73,094,430,440

12-24. a ) $675,000 - $120,000 = $555,000

b ) $555,000/100,000 = $5.55 per share

12-25. a ) Net Worth = $38,400 - ($13,400 + $6,000) = $19,000 (in '000 dollars)

b ) Book Value = $19,000,000/500,000 = $38 per share

c ) EPS = $5,610,000/500,000 = $11.22

d ) Stock Price = EPS X P/E ratio = $11.22 X 6 = $67.32

e ) Since $67.32 (the stock price) > $38.00 (the book value), the firm seems to have going-

concern value.

f ) ($50,000,000 - $20,000,000)/500,000 = $60 per share.

12-26. a) Corporate Bond

Let YTM = k

$130 X [(1-1/(1+k)16)/k] + $1,000 X [1/(1+k)16] = 1,147.58

Solving, kd = 11%

b) Preferred Stock

k = $14/$140

kp = 10%

c) Common Stock

Let ks be the required rate of return for a similar common stock

ks = D1/Po + g = $39/$300 + .03 = .16 = 16%

Remember that these are three different companies. The cost of preferred stock for Supernova could be

lower than the cost of debt for Star, as suggested by the above numbers. Lucky should choose the alternative

that, in his opinion, gives the best return/risk tradeoff. There is no clear answer here as to which investment

is the best.

99

12-27. The Nonconstant, or Supernormal Dividend Growth Model

Flash in the Pan Corporation

Given: Year Year Year Year Year Year 1 2 3 4 5 6 and on

Dividend growth rates 20% 30% 20% 10% 5% Dividend expected in 1 year $3.00

Assumed required rate of return 15%

Calculations: a. Present value of Dividends during the supernormal growth period: Expected future dividends during

the supernormal growth period $3.00 $3.60 $4.68 $5.62 $6.18

Present values of dividends during

the supernormal growth period $2.61 $2.72 $3.08 $3.21 $3.07

Total $14.69

b. Present value of dividends during the normal growth period (year 6 and on) Terminal value at end of year 5

per Equation 12-7 $64.86

Present value of terminal value $32.25

c. Total present value per share of Flash in the Pan Corp. stock $46.94

100

12-28. The Discounted Free Cash Flow Model for Total Common Equity

Hardi-Pets Corporation

Forecasting Variables:

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Revenue growth factor 10% 15% 20% 25% 30% 25% 20% 15% 10% 5%

Expected gross profit margin 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%

S, G, & A expense % of revenue 20% 20% 20% 20% 20% 20% 20% 20% 20% 20%

Depr. & Amort. % of revenue 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

Capital expenditure growth factor 10% 10% 10% 10% -10% -10% -10% -10% -10% -10%

Net working capital to sales ratio 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

Income tax rate 40%

Assumed long-term sustainable growth rate 5% per year after 2016

Discount rate 20%

FORECAST: Years Ending December 31

Actual |--------------------------------------------------------- Forecast ----------------------------------------------------------------------------------|

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Total revenue $1,000,000 $1,100,000 $1,265,000 $1,518,000 $1,897,500 $2,466,750 $3,083,438 $3,700,125 $4,255,144 $4,680,658 $4,914,691

Cost of Goods Sold 500,000 550,000 632,500 759,000 948,750 1,233,375 1,541,719 1,850,063 2,127,572 2,340,329 2,457,346

Gross profit 500,000 550,000 632,500 759,000 948,750 1,233,375 1,541,719 1,850,062 2,127,572 2,340,329 2,457,345

Selling, general and administrative expenses 200,000 220,000 253,000 303,600 379,500 493,350 616,688 740,025 851,029 936,132 982,938

Earnings before interest, taxes, depr. & amort. (EBITDA)

300,000 330,000 379,500 455,400 569,250 740,025 925,031 1,110,037 1,276,543 1,404,197 1,474,407

Depreciation and amortization 100,000 110,000 126,500 151,800 189,750 246,675 308,344 370,013 425,514 468,066 491,469

Earnings before Interest and taxes (EBIT) 200,000 220,000 253,000 303,600 379,500 493,350 616,687 740,024 851,029 936,131 982,938

Federal and State Income Taxes 80,000 88,000 101,200 121,440 151,800 197,340 246,675 296,010 340,412 374,452 393,175

Net Operating Profit After-Tax (NOPAT) 120,000 132,000 151,800 182,160 227,700 296,010 370,012 444,014 510,617 561,679 589,763

Add back depreciation and amortization 100,000 110,000 126,500 151,800 189,750 246,675 308,344 370,013 425,514 468,066 491,469

Subtract Capital Expenditures (15,000) (16,500) (18,150) (19,965) (21,962) (19,766) (17,789) (16,010) (14,409) (12,968) (11,671)

Subtract New Net Working Capital (10,000) (16,500) (25,300) (37,950) (56,925) (61,669) (61,669) (55,502) (42,551) (23,403)

Free Cash Flow $205,000 $215,500 $243,650 $288,695 $357,538 $465,994 $598,898 $736,348 $866,220 $974,226 $1,046,158

Terminal value, 2016 $7,323,106

Present Value of Free Cash Flows @ 20% 179,583 169,201 167,069 172,424 187,273 200,570 205,501 201,455 188,812 1,351,683

101

Total Present Value of Company Operations $3,023,571

Plus Current Assets 100,000 from Hardi-Pets December 31, 2006 Balance Sheet

Less Current Liabilities (80,000) from Hardi-Pets December 31, 2006 Balance Sheet

Less Long-Term Debt (500,000) from Hardi-Pets December 31, 2006 Balance Sheet

Less Preferred Stock 0 from Hardi-Pets December 31, 2006 Balance Sheet

Net Market Value of Common Equity $2,543,571

12-29. The Discounted Free Cash Flow Model for a Complete Business

Great Expectations Company

Forecasting Variables: 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Revenue growth factor 20% 30% 40% 50% 60% 50% 40% 30% 20% 10% Expected gross profit margin 50% 51% 52% 53% 54% 55% 56% 57% 58% 59%

S, G, & A expense % of revenue 50% 40% 30% 29% 28% 27% 26% 25% 24% 23% Depr. & Amort. % of revenue 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

Capital expenditure growth factor 40% 35% 30% 25% 20% -10% -15% -20% -25% -30% Net working capital to sales ratio 19% 18% 17% 16% 15% 14% 13% 12% 11% 10%

Income tax rate 40%

Assumed long-term sustainable growth rate 5% per year after 2016 Discount rate 20%

FORECAST: Years Ending December 31

Actual |---------------------------------------------------------------------- Forecast -----------------------------------------------------------------------------|

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Total revenue $2,000,000 $2,400,000 $3,120,000 $4,368,000 $6,552,000 $10,483,200 $15,724,800 $22,014,720 $28,619,136 $34,342,963 $37,777,260

Cost of Goods Sold 1,200,000 1,200,000 1,528,800 2,096,640 3,079,440 4,822,272 7,076,160 9,686,477 12,306,228 14,424,045 15,488,676

Gross profit 800,000 1,200,000 1,591,200 2,271,360 3,472,560 5,660,928 8,648,640 12,328,243 16,312,908 19,918,918 22,288,584

Selling, general and administrative expenses 1,200,000 1,200,000 1,248,000 1,310,400 1,900,080 2,935,296 4,245,696 5,723,827 7,154,784 8,242,311 8,688,770

Earnings before interest, taxes, depr. & amort. (EBITDA)

(400,000) 0 343,200 960,960 1,572,480 2,725,632 4,402,944 6,604,416 9,158,124 11,676,607 13,599,814

Depreciation and amortization 200,000 240,000 312,000 436,800 655,200 1,048,320 1,572,480 2,201,472 2,861,914 3,434,296 3,777,726

Earnings before Interest and taxes (EBIT) (600,000) (240,000) 31,200 524,160 917,280 1,677,312 2,830,464 4,402,944 6,296,210 8,242,311 9,822,088

Available tax-loss carryforwards 0 (600,000) (840,000) (808,800) (284,640) 0 0 0 0 0 0

Net taxable earnings 0 0 0 0 632,640 1,677,312 2,830,464 4,402,944 6,296,210 8,242,311 9,822,088

Federal and State Income Taxes 0 0 0 0 253,056 670,925 1,132,186 1,761,178 2,518,484 3,296,924 3,928,835

Net Operating Profit After-Tax (NOPAT) (600,000) (240,000) 31,200 524,160 664,224 1,006,387 1,698,278 2,641,766 3,777,726 4,945,387 5,893,253

102

Add back depreciation and amortization 200,000 240,000 312,000 436,800 655,200 1,048,320 1,572,480 2,201,472 2,861,914 3,434,296 3,777,726

Subtract Capital Expenditures (1,000,000) (1,400,000) (1,890,000) (2,457,000) (3,071,250) (3,685,500) (3,316,950) (2,819,408) (2,255,526) (1,691,645) (1,184,151)

Subtract New Net Working Capital 76,000 129,600 212,160 349,440 589,680 733,824 817,690 792,530 629,621 343,430

Free Cash Flow ($1,400,000) ($1,324,000)

($1,417,200)

($1,283,880)

($1,402,386)

($1,041,113)

$687,632 $2,841,521 $5,176,644 $7,317,659 $8,830,257

Terminal value, 2016 $61,811,799

Present Value of Free Cash Flows @ 20% (1,103,333) (984,167) (742,986) (676,305) (418,400) 230,287 793,016 1,203,922 1,418,211 11,409,086

Total Present Value of Company Operations $11,129,331

Plus Current Assets 500,000 from Great Expectations' December 31, 2006 Balance Sheet

Total Market Value of Great Expectations' Assets $11,629,331

103



1. What is the operating leverage effect and what causes it? What are the potential benefits and

negative consequences of high operating leverage?

The operating leverage effect is the phenomenon whereby a small change in sales triggers a relatively

large change in operating income. It is caused by the presence of fixed operating costs. The

potential benefits are that if sales are rising operating income will rise more quickly. The negative

consequences are that falling sales will cause operating income to fall more quickly, including

negative values.

2. Does high operating leverage always mean high business risk? Explain.

High operating leverage does not always mean high business risk. If the companies sales are quite

stable then the variation in operating income would be small even if the degree of operating leverage

were large.

3. What is the financial leverage effect and what causes it? What are the potential benefits and negative

consequences of high financial leverage?

Financial leverage is the additional volatility of net income caused by the presence of fixed-cost

funds. The potential benefits are that if operating income is rising net income will rise more quickly.

The negative side is that if operating income is falling net income will fall more quickly, including

possibly negative values.

4. Give two examples of types of companies likely to have high operating leverage. Find examples

other than those cited in the chapter.

Long distance telephone companies and electricity generating companies are likely to have operating

leverage. These two types of companies have very high fixed costs, because they are capital

intensive, and have relatively low variable costs.

5. Give two examples of types of companies that would be best able to handle high debt levels.

Companies that handle local telephone service and those that handle natural gas delivery to

consumers would be expected to comfortably be able to handle high debt levels. This is because the

sales of these two types of companies tend not to react very much to the business cycle. Their sales

tend to grow with the population. They are often regulated and protected from competition, although

this is not so much true as it was a few years ago.

104

6. What is an LBO? What are the risks for the equity investors and what are the potential rewards?

A leveraged buyout is a purchase of a publicly owned corporation by a small group of investors using

a large amount of borrowed money. The risks for the equity investors are those that exist whenever a

high degree of financial leverage exists. So too are the rewards, where small returns become large

returns because of leverage.

7. If an optimal capital structure exists, what are the reasons why too little debt is as undesirable as is

too much debt?

Too little debt may be as undesirable as too much debt because if a firm has a very conservative

capital structure it may be losing the opportunity to reap the positive benefits of financial leverage.

A company with a bright future is probably not maximizing shareholder wealth if it has a very small

amount of debt in its capital structure. A more aggressive capital structure may create more value for

the owners.


13-1. a) Breakeven sales per month = $2,300/($50 – 5.75) = 51.98 units

b) New Breakeven sales per month = $2,300 x .7 / ($45 – 5.75) = 41.02 units

13-2. a) 30 x $125 + 30 x $90 + 30 x 55 = $8,100

b) $10,000 + 90 x $15 = $11,350

c) 10 x $125 + 15 x $90 + 35 x $55 = $4,525

d) $10,000 + 60 x $15 = $10,900

13-3. DOL = (17,900,000 – 9,220,000) / 9,220,000 ÷ (25,000,000 – 15,000,000) / 15,000,000 = 1.41

or DOL = (15,000,000 – 1,980,000) / (15,000,000 – 1,980,000 – 3,800,000) = 1.41

13-4. DOL = (11,333,000 – 5,257,000) / 5,257,000 ÷ (17,900,000 – 9,220,000) / 9,220,000 = 1.23

or DOL = 9,220,000 / (9,220,000 – 1,710,000) = 1.23

13-5. a) Contribution Margin = $28 - $16 = $12

b) Unit Sales b.e. = $20,000/($28 - $16) = 1,666.67 units; 1,667 units rounded up

DOLLARS b.e = $28 x 1,667 units = $46,676

c) (i) Operating profit (loss) = 1,500 units X $12/unit - $20,000 = ($2,000)

(ii) Operating profit (loss) = 3,000 units X $12/unit - $20,000 = $16,000

105

d)

13-6. a) Contribution Margin = $28 - $20 = $8

b) Unit Sales b.e. = $10,000/($28 - $20) = 1,250 units

DOLLARS b.e = $28 x 1,250 units = $35,000

c) (i) Operating profit (loss) = 1,500 units X $8/unit - $10,000 = $2,000

(ii) Operating profit (loss) = 3,000 units X $8/unit - 10,000 = $14,000

d)

$0

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

$160,000

$180,000

0

500

1,00

0

1,50

0

2,00

0

2,50

0

3,00

0

3,50

0

4,00

0

4,50

0

5,00

0

5,50

0

6,00

0

FIXED COST VAR. COST TOT. COST REVENUE

$0

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

$160,000

$180,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000

FIXED COST VAR. COST TOT. COST REVENUE

106

e) Howard Beal Co., having higher fixed costs, and a lower variable cost per unit, has a higher profit

potential once they break-even. However, they have a greater loss potential, and need to achieve a higher

sales level to break even, because of the high fixed costs.

13-7. YEAR

2006

2007

SALES IN UNITS

3000

3300

SALES IN DOLLARS

$84,000

$92,400

VAR.COST, $16/unit

$48,000

$52,800

FIXED COST

$20,000

$20,000

OP. INCOME (EBIT)

$16,000

$19,600

INTEREST EXP.

$2,000

$2,000

EBT

$14,000

$17,600

TAX @30%

$4,200

$5,280

NET INCOME

$9,800

$12,320

%CHANGE IN SALES

10.00% %CHANGE IN EBIT

22.50% %CHANGE IN NI

25.71%

a) Percentage change in operating income = ($19,600 - $16,000)/$16,000 = 22.5%

Percentage change in sales = ($92,400 - $84,000)/$84,000 = 10%

b) Due to presence of fixed costs a given percentage change in sales gives a higher percentage change in

operating income (EBIT) (10% and 22.5% respectively). This is the operating leverage effect.

c) (i) DOL = % EBIT/% SALES = [($19,600 - $16,000)/$16,000]/[($92,400 -

$84,000)/$84,000] = 22.5%/10% = 2.25

(ii) DOL = (SALES-VC)/(SALES-VC-FC) = ($84,000 - $48,000)/($84,000 - $48,000-

$20,000) = $36,000/$16,000 = 2.25

d) (i) shows the effect of operating leverage -- EBIT varies at a larger percentage than sales.

(ii) pinpoints the source of operating leverage -- fixed operating costs.

13-8. a) Percentage change in NI = ($12,320 - $9,800)/$9,800= 25.71%

Percentage change in operating income = ($19,600 - $16,000)/$16,000 = 22.5%

b) Due to presence of fixed interest expense a given percentage change in EBIT gives a higher

percentage change in net income (22.5% and 25.71% respectively). This is the financial leverage

effect.

c) (i) DFL = % NI/% EBIT = [($12,300 - $9,800)/$9,800]/[($19,600 - $16,000)/$16,000] =

25.71%/22.5% = 1.14

(ii) DFL = EBIT/(EBIT - I) = $16,000/($16,000 - $2,000) = 1.14

d) (i) shows the effect of financial leverage -- NI varies by a larger percentage than operating income

(EBIT).

107

(ii) pinpoints the source of financial leverage -- fixed interest expense.

13-9. a ) $9,000/($15 - $1.50) = 666.67 sq. yards

b ) Break-even point in sales units

c ) 666.67 X $15 = $10,000

d ) $9,000/($18 - $1.50) = 545.5 sq. yards, break-even units

545.5 X $18 = $9,819, break-even dollar sales

e) SALES IN UNITS

14,000 sq.yards

SALES IN DOLLARS, units x $18 each

$252,000

VAR.COST, units x $1.50 each

$21,000

FIXED COST

$9,000

OP. INCOME (EBIT)

$222,000

INTEREST EXP.

$3,000

EBT

$219,000

TAX @40%

$87,600

NET INCOME

$131,400

13-10. a ) Contribution Margin = $800 - $250 = $550 per unit

Sale of 600 suits: Op. Income = 600 X $550 - $200,000 = $130,000

Sale of 3,000 suits: Op. Income = 3,000 X $550 - $200,000 = $1,450,000

b ) Sale of 600 suits: DOL = [600 X ($800 - $250)]/[600 X ($800 - $250) - $200,000] = 2.5

Sale of 3,000 suits: DOL = [3,000 X ($800 - $250)]/[3,000 X ($800 - $250) - 200,000] = 1.1

c ) Unit Sales b.e. = $200,000/$550 = 363.64 units; rounded up to 364

DOLLARS b.e = 364 suits X $800 price per suit = $291,200

d ) Unit Sales b.e. = $200,000/($800 - $350) = 444.44 units; rounded up to 445

DOLLARS b.e = 445 suits X $800 price per suit = $356,000

e ) Let P be the selling price per unit.

3,000 units X (P - $350) - $200,000 fixed costs = $1,450,000 op. income

P - $350 = ($1,450,000 + $200,000)/$3,000 = $550

P = $550 + $350 = $900

Tom should increase price per unit by $100 ($900 - $800)

13-11.

COMPANY A

COMPANY B

COMPANY C SALES IN UNITS

12,000

12,000

12,000

SALES IN DOLLARS, units x $10 each

$120,000

$120,000

$120,000

VARIABLE COST, $5, $4, and $1 per unit respectively

$60,000

$48,000

$12,000 FIXED COST

$0

$10,000

$40,000

OPERATING INCOME (EBIT)

$60,000

$62,000

$68,000

108

b ) C, B, A.

13-12. a ) Year 1: $30 X 50,000 = $1,500,000

Year 1: $30 X 60,000 = $1,800,000

b ) ($1,800 - $1,500)/$1,500 = 0.2 or 20%

c ) METHOD 1 METHOD 2

YEAR 1 YEAR 2 YEAR 1 YEAR 2

UNITS 50,000 60,000 50,000 60,000

SALES, units x $29 each 1,500,000 1,800,000 1,500,000 1,800,000

FC 700,000 700,000 100,000 100,000

VC, units x $6 each for Method 1 and x $16.50 each for Method 2

300,000 360,000 825,000 990,000

EBIT $500,000 $740,000 $575,000 $710,000

d ) METHOD 1: % EBIT = ($740,000 - $500,000)/$500,000 = 0.48 OR 48%

METHOD 2: % EBIT = ($710,000 - $575,000)/$575,000 = 0.235 OR 23.5%

e ) METHOD 1: DOL = 0.48/0.20 = 2.4

METHOD 2: DOL = 0.235/0.20 = 1.175

f ) METHOD 1: DOL = ($1,500,000 - $300,000)/($1,500,000 - $300,000 - $700,000) = 2.4

METHOD 2: DOL = ($1,500,000 - $825,000)/($1,500,000 - $825,000 - $100,000)

= 1.175

g ) METHOD 1

h ) The high fixed operating costs

i ) METHOD 1 METHOD 2

YEAR 1 YEAR 2 YEAR 1 YEAR 2

UNITS 50,000 53,000 50,000 53,000

SALES, units x $30 each 1,500,000 1,590,000 1,500,000 1,590,000

FC 700,000 700,000 100,000 100,000

VC, units x $6 each for Method 1 and x $16.50 each for Method 2

300,000 318,000 825,000 874,500

EBIT $500,000 $572,000 $575,000 $615,500

% SALES = ($53,000 - $50,000)/$50,000 = .06 or 6%

METHOD 1: % EBIT = ($572,000 - $500,000)/$500,000 = 0.144 or 14.4%

METHOD 2: % EBIT = ($615,500 - $575,000)/$575,000 = 0.0704 or 7.04%

METHOD 1: DOL = 0.144/0.06 = 2.4

METHOD 2: DOL = 0.0704/0.06 = 1.17

109

13-13. a ) C, B, A.

b ) COMPANY A: DFL = $100,000/($100,000 - $0) = 1.0

COMPANY B: DFL = $100,000/($100,000 - $2,000) = 1.02

COMPANY C: DFL = $100,000/($100,000 - $40,000) = 1.67

Answer to part a) was correct.

c )

COMPANY A

COMPANY B

COMPANY C

CAPITAL STRUCTURE

ALL EQUITY

90% EQUITY

10% EQUITY

EBIT

$100,000

$100,000

$100,000

INTEREST EXP.

$0

$2,000

$40,000

EBT

$100,000

$98,000

$60,000

TAXES @40%

$40,000

$39,200

$24,000

NET INCOME

$60,000

$58,800

$36,000

13-14. a. MICHAEL DORSEY DOROTHY MICHAELS

YEAR 1 YEAR 2 YEAR 1 YEAR 2 EBIT $50,000 $60,000 $50,000 $60,000 INTEREST EXPENSE $9,100 $9,100 $900 $900 EBT $40,900 $50,900 $49,100 $59,100 TAXES @40% $16,360 $20,360 $19,640 $23,640 NET INCOME $24,540 $30,540 $29,460 $35,460

b. %CHANGE in NI 24.45% 20.37%

c. %CHANGE in EBIT 20.00% 20.00%

d. DFL 1.22 1.02

e. DFL 1.22 1.02

f. MICHAEL DORSEY'S COMPANY

g. HIGHER DFL DUE TO GREATER AMOUNT OF INTEREST EXPENSE

h. MICHAEL DORSEY DOROTHY MICHAELS

YEAR 1 YEAR 2 YEAR 1 YEAR 2 EBIT $50,000 $53,000 $50,000 $53,000 INTEREST EXPENSE $9,100 $9,100 $900 $900 EBT $40,900 $43,900 $49,100 $52,100 TAXES @40% $16,360 $17,560 $19,640 $20,840 NET INCOME $24,540 $26,340 $29,460 $31,260 DFL 1.22 1.02

110

13-15. DCL = (200,000 – 75,000) / 75,000 ÷ (400,000 – 230,000) / 230,000 = 2.25 13.16.

FUNNY GIRLS COMICS YEAR 1 YEAR 2 SALES $200,000 $225,000 EBIT $95,000 NET INCOME $30,000 DOL 1.35 DFL 1.09

a. %CHANGE in SALES = 12.50% %CHANGE in EBIT = DOL X %CHANGE in SALES 16.8750%

b. EBIT IN YEAR 2 = 1.1688*95,000 = $111,031.25

c. %CHANGE in NI = DFL X %CHANGE in EBIT 18.3938%

d. NI in YEAR 2 = 1.1839 X 30,000 = $35,518.13

e. DCL = DOL X DFL = 1.4715

f. %CHANGE in SALES = 20.00% %CHANGE in NI = DCL X %CHANGE in SALES 29.43% NI in YEAR 2 = 1.2943 X 30,000 = $38,829.00

13-17. Interest Expense = $2,000,000 X 0.10 = $200,000

DCL = DOL X DFL =1.4 X [$600,000/($600,000 - $200,000)= 1.4 X 1.5= 2.1

13-18. a) DOL = ($5,000,000 - $700,000)/($5,000,000 - $700,000 - $300,000) = 1.075

b) Interest Expense = $16,666,666.67 X 0.09 = $1,500,000

EBIT = $2,500,000 + $1,500,000 = $4,000,000

DFL = $4,000,000/($4,000,000 - $1,500,000) = 1.600

Also, DFL = DCL/DOL = 1.720/1.075 = 1.600

c) %NI = $Sales x DCL

%NI = 20% x 1.72

= 34.4%

111

13.19. Soccer International, Inc.

Given:

2005 2006

Sales $560,000 $616,000

Variable Costs $240,000 $264,000

Fixed Costs $160,000 $160,000

Interest Expense $40,000 $40,000

Price of each soccer ball $16

a. Completed income statements:

2005 2006

Sales $560,000 $616,000

Variable Costs $240,000 $264,000

Fixed Costs $160,000 $160,000 EBIT $160,000 $192,000

Interest Expense $40,000 $40,000 EBT $120,000 $152,000

Income Taxes (30%) $36,000 $45,600

Net Income $84,000 $106,400

b. Breakeven point in units:

2005 2006

Number of balls sold 35,000 38,500

Variable cost per ball $6.86 $6.86

Contribution margin $9.14 $9.14

Breakeven point in units 17,500 17,500

c. Breakeven point in dollars:

2006 2007

Breakeven point in dollars $280,000 $280,000

d. Unit sales required to produce $200,000 in operating income in 2005:

Fixed costs $160,000

Operating profit requirement $200,000

Total dollars needed $360,000

Contribution margin, each ball $9

Number of balls needed to be sold 39,375

e. Effect on operating profit of greater or lesser sales in 2005:

Assumed number of balls sold

18,000 24,000

Total contribution margin $164,571 $219,429

Fixed costs $160,000 $160,000

Operating profit $4,571 $59,429

f. Degree of Operating Leverage (DOL): 2005 2006

DOL 2.0 1.83

112

h. Degree of financial leverage (DFL):

2005 2006

DFL 1.33 1.26

j. Degree of combined leverage (DCL):

2005 2006

DCL 2.67 2.32

k. Effect of a price increase that produces higher sales:

2005 2006

Sales $560,000 $650,000 given 16.1%

% increase in net income 42.86%

Net income in dollars $84,000 $120,000

13-20. %NI = % x DFL

%NI = ($50,000 - $35,000)/$35,000 x 1.71

%NI = $15,000/$35,000 x 1.71

%NI = .429 x 1.71

%NI = .733, or 73.3%

113



1. How does a mortgage bond compare to a debenture?

A mortgage bond is a secured bond while a debenture is an unsecured bond.

2. How does a sinking fund function in the retirement of an outstanding bond issue?

A sinking fund is where a company puts payments that are then used to buy back outstanding bonds.

3. What are some examples of restrictive covenants that might be specified in a bond’s indenture?

An indenture might include limitations on future borrowings, restrictions on dividend payments,

and/or requirements that working capital be maintained at least at some minimum level.

4. Define the following terms that relate to a convertible bond: conversion ratio, conversion value, and

straight bond value.

The conversion ratio is the number of shares of common stock that would be obtained if a convertible

bond were converted. The conversion value is the total value of the common stock that would be

obtained. The straight bond is the value a convertible bond would have without the conversion

feature.

5. If a convertible bond has a conversion ratio of 20, a face value of $1,000, a coupon rate of 8 percent,

and the market price for the company’s stock is $15 per share, what is the convertible bond’s

conversion value?

The conversion value would equal the conversion ratio of 20 times the $15 market price of the stock

or $300.

6. What is a callable bond? What is a putable bond? How do each of these features affect their

respective market interest rates?

A callable bond can be retired early at the discretion of the issuer. A putable can be retired early at

the discretion of the investor. A call provision increases the market interest rate and a put provision

decreases it.

114


14-1. VB = $80 X [(1 - 1/1.1210)/.12] + $1,000 X 1/1.1210 = $773.99

14-2. VB = $40 X [(1 - 1/1.0620)/.06] + $1,000 X 1/1.0620 = $770.60

14-3. Conversion Value = $60 X 20 = $1,200

14-4. $32 * 26.5 = $848

$848 * 6 = $5,088.00

14-5. 22.5 [ 1-(1/(1.0375)60)/0.0375] + 1,000/(1.0375)60

22.5 * 23.7379 + 109.828 = $643.93

14-6. $85 * 30 = $2,550

14-7. 33.75 [1 – (1/1.0430)/0.04] + 1,000/1.0430 = $891.92

14-8. Funds required to buy 1,000 bonds from the open market = $800 X 1,000 = $800,000. Therefore

savings from buying the bonds back instead of depositing $1 million in the sinking fund =

$1,000,000 - $800,000 = $200,000.

14-9. (7.0% - 5.0%) * 30,000 * 1,000 = $600,000

14-10. Yearly savings = (10% - 8%) X 20,000 X $1,000 = $400,000

14-11. Face Value + Call Premium = $1,000 + 0.5 X $1,000 = $1,050

Annual interest paid over last ten years = 0.10 X $1,000 = $100

$950 = $100 X (PVIFAk,10) + $1,050 X (PVIFk,10)

Realized return for Brooks = k = 11.15%

YEARS

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

-950 100

100

100

100

100

100

100

100

100

100

1050

-950 100

100

100

100

100

100

100

100

100

1150

11.15%

IRR

115

14-12. a) Annual interest to be paid over next ten years = 0.08 X $1000

= $80

$950 = $80 X (PVIFAk,10) + $1,000 X (PVIFk,10)

Return for Brooks for the newly issued bond = k = 8.77%

Overall return if the is bond held to maturity = 10.52% (See table below)

b) Return on the bond in Problem #4 if they had not been called = 10.61% (See table below).

Brooks didn't welcome the recall (10.61% > 10.52%).

YEARS

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

PROB

14-12a

-950

80 80

80

80

80

80

80

80

80

80

1000

-950

80 80

80

80

80

80

80

80

80

1080

8.77%

IRR

-950

100 100

100

100

100

100

100

100

100

100

80

80

80

80

80

80

80

80

80

80

1050

1000

-950

-950

100 100

100

100

100

100

100

100

100

200

80

80

80

80

80

80

80

80

80

1080

10.52%

IRR

PROB

14-12b

-950

100 100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

1000

-950

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

1100

10.61%

IRR

14-13. Conversion Value = $70 X 20 = $1,400

14-14. VB = $90 X [(1 - 1/1.0714)/.07] + $1,000 X 1/1.0714 = $1,174.90

He would consider converting, but since the market value of the convertible bond would be greater

than the larger of the conversion value or straight bond value he would sell the bond instead if he

wanted to cash out.

14-15. Conversion Value = $30 X 30 = $900

VB = 110 X [(1 - 1/1.135)/.13] + 1,000 X 1/1.135 = $929.66

No, he should not convert. The straight bond value is greater than the conversion value.

14-16. VB = $90 X [(1 - 1/1.1314)/.13] + $1,000 X 1/1.1314 = $747.90

Since the putable bond can be redeemed at a higher price, i.e., $900, Ms. Carter should redeem the

bond.

116

$1,000 = $90 X (PVIFAk,6) + $900 X (PVIFk,6)

Realized return for Ms. Carter = k = 7.62%

14-17. VB = $90 X [(1 - 1/1.145)/.14] + $1,000 X 1/1.145 = $828.34

Since the bond can be redeemed at a higher price, i.e., $900, Diana should redeem the bond.

$1,000 = $90 X (PVIFAk,5) + $900 X (PVIFk,5)

Realized return for Diana from original bond = k = 7.27%

$900 = $130 X (PVIFAk,5) + $1,000 X (PVIFk,5)

Realized return for Diana from new bond = k = 16.06%

YEARS

0

1

2

3

4

5

6

7

8

9

10

-1000

90

90

90

90

90

900

-900

130

130

130

130

130

1000 CF

-1000

90

90

90

90

90

130

130

130

130

1130

0.1051 = 10.51%IRR

Realized overall return for Diana = k = 10.51%

14-18. VB = $80 X [(1 - 1/1.2510)/.25] + 1,000 X 1/1.2510 = $393.01

14-19.

Claim Received

1st Mortgage bonds $5 million 5 million

2nd Mortgage bonds 5 million 5 million

Senior Debentures 10 million 10 million

Subordinated Debentures 4 million 0

Common Stock 10 million 0

Total 34 million 20 million

14-20.

a) Call Premium paid $60,000,000 * .04 = $2,400,000

New Bond Underwriting Costs $60,000,000 * .03 = $1,800,000

Total incremental Cash Outflow $4,200,000

b) Savings = (8% - 6%) = 2% annually

Total Savings in interest payments = 2% * $60,000,000 = $1,200,000

c) Interest on old bonds:

$60,000,000 * .08 = $4,800,000

117

Interest on new bonds:

$60,000,000 * .06 = $3,600,000

$1,200,000 difference each year for 10 years

Less taxes on the additional income at 40%:

$1,200,000 * (1 - .40) = $720,000

Net Savings = $720,000 per year

d) Present value of the net savings for 10 years at 3.6%

$720,000 * ((1-(1/(1.036)10))/.036) = $720,000 * 8.274844044 = $5,957,887.71

e) Note: Call premiums are tax deductible and amortized over the life of the bond

$60,000,000 * .04 * .40 = $960,000

Amortized over 10 years =

$960,000/10 = $96,000 per year

f) Present Value of the annual tax savings for 10 years:

$96,000 * ((1-(1/(1.036)10))/.036) = $96,000 * 8.274844044 = $794,385.03

g) Unamortized amount =

$60,000,000 * .02 * (10/20) = $600,000 current deduction

PV of unamortized amount if bond is not called:

($600,000/10) * ((1-(1/(1.036)10))/.036 =

$60,000 * 8.274844044 = $496,490.64

Net Tax Savings = $600,000 - $496,490.64 = $103,509.36

h) ($60,000,000 * .03)/10 = $180,000 annual write off

Tax Savings = $180,000 * .40 = $72,000

i) PV of tax Savings =

$72,000 * ((1-(1/(1.036)10))/.036 = $72,000 * 8.274844044 = $595,788.77

j) PV Total Inflows = $5,957,887.71 + $794,385.03 + $103,509.36 + $595,788.77 =

$7,451,570.87

k) NPV of the bond proposal = PV of total cash inflows – Total outflows

NPV = $7,451,570.87 - $4,200,000 = $3,251,570.87

118

14-21. Aurora Glass Fibers Lease-Buy Analysis

Part a, the buy option:

Assumptions:

Cost of new computers $800,000

Expected Life 4 years

Salvage value $100,000

Amount to be borrowed $800,000

Interest rate on loan 10%

MACRS Depreciation: Yr 1 Yr 2 Yr 3 Yr 4

(3-year asset class) 33.3% 44.5% 14.8% 7.4%

Cost of capital 6% (after-tax cost of debt)

Tax rate 40%

Estimated Incremental Cash Flows to Equity:

Year: 0 1 2 3 4

Cost of new computers ($800,000)

Amount to be borrowed 800,000

Depreciation on new computers ($266,400) ($356,000) ($118,400) ($59,200)

Tax savings on depreciation 106,560 142,400 47,360 23,680

Interest payments on loan (80,000) (80,000) (80,000) (80,000)

Tax savings on interest 32,000 32,000 32,000 32,000

Repayment of principal on loan (800,000)

Salvage value of new computers 100,000

Tax on gain (40,000)

Net Incremental Cash Flows $0 $58,560 $94,400 ($640) ($764,320)

PV of Cash Flows $0 $55,245 $84,016 ($537) ($605,413)

Total PV of Cash Flows Associated With the Buy Option = ($466,689)

Part b, the lease option:

Assumptions:

Annual lease payment ($200,000) paid at the end of each year

Lease term 4 years

Value at termination of lease $0

Estimated Incremental Cash Flows to Equity:

Year: 0 1 2 3 4

Lease payment ($200,000) ($200,000) ($200,000) ($200,000)

Tax savings on lease payment $80,000 $80,000 $80,000 $80,000

Net Incremental Cash Flows $0 ($120,000) ($120,000) ($120,000) ($120,000)

PV of Cash Flows $0 ($113,208) ($106,800) ($100,754) ($95,051)

Total PV of Cash Flows Associated With the Lease Option = ($415,813)

119

Part c, comparison of alternatives and decision:

Total PV of Cash Flows Associated With the Buy Option = ($466,689)

Total PV of Cash Flows Associated With the Lease Option = ($415,813)

Net Advantage to Leasing (NAL) = $50,877

Decision: Lease

120



1. What are some of the government requirements imposed on a public corporation that are not imposed

on a private, closely held corporation?

Public corporations must submit audited financial statements to the government for release to the

public. Private corporations can keep their financial information confidential.

2. How are the members of the board of directors of a corporation chosen and to whom do these board

members owe their primary allegiance?

Members of a corporation’s board of directors are elected by the common stockholders and owe their

allegiance to these stockholders

3. What are the advantages and the disadvantages of a new stock issue?

A new stock issue raises funds and decreases the riskiness of the firm. It also tends to send a

negative signal to the market since many investors believe a company would only sell new stock if

future financial prospects were dim.

4. What does an investment banker do when underwriting a new security issue for a corporation?

When underwriting a new security issue an investment banker buys it and then resells it to investors.

5. How does a preemptive right protect the interests of existing stockholders?

A preemptive right protects the interests of existing stockholders by giving them the opportunity to

preempt other investors in the purchase of new shares. If these rights are exercised, existing

shareholders would maintain their same percentage of ownership after the new stock issue as before.

6. Explain why warrants are rarely exercised unless the time to maturity is small?

Warrants are rarely exercised until the time to expiration is small because the market price of the

warrant is greater than the exercise value. The holder of the warrant would therefore sell it in the

secondary market instead of exercising it if he or she wanted to cash in.

7. Under what circumstances is a warrant’s value high? Explain.

121

A warrant’s value would be high when the stock price, time to expiration, and/or expected stock

price volatility are high.


15-1. Original Ownership = 20,000/1,000,000 = 2%

Diluted Ownership = 20,000 /1,500,000 = 1.33%

15-2. 1. Book Value Approach: (200mil. - 150mil.)/5mil. = $10 per share

2. Liquidation Value Approach: (250 - 150)/5 = $20 per share

3. Replacement Value Approach: (400 - 150)/5 = $50 per share

4. Dividend Growth Model: $2/(0.13 - 0.08) = $40 per share

Ms. Phinlay should buy the stock as the share is selling at a price ($20) which is lower than what she is

prepared to pay ($40) to get her required rate of return.

15-3. a) .45(2,500,000) = 1,125,000

[(1,125,000 - 1) * (5 + 1)] / 2,500,000 = 2.669

2 directors

b) .55(2,500,000) = 1,375,000

[(1,375,000 – 1) * (5 + 1)] / 2,500,000 = 3.299

3 directors

15-4. a) [(1 * 2,500,000) / (5 + 1)] + 1 = 416,667

b) [(3 * 2,500,000) / (5 + 1)] + 1 = 1,250,001

c) [(5 * 2,500,000) / (5 + 1)] + 1 = 2,083,334

15-5. a) .35 (2,500,000) = 875,000

[(875,000 – 1) (5 + 1)] / 2,500,000 = 2.1

2 directors

b) [(2 * 2,500,000)/ (5 + 1)] + 1 = 833,334

15-6. Length of term = (9/3) X 3 = 9 years for each board members

15-7. NUM DIR = [(0.35 X 1,000,000 - 1) X (4 + 1)]/1,000,000 = 1.75 rounded down to 1

The minority group can elect 1 of their people to the board out of the 4 to be elected.

122

15-8. NUM VOTING SHARES NEEDED = [(1 X 200,000)/(7 + 1)] + 1 = 25,001. Since Ms. O'Niel holds

more shares than required, she can elect herself to the board.

15-9. a) How many directors can the young stockholders elect under

(i) cumulative voting procedure

NUM DIR = (600,000 X 0.30-1) X (13 + 1)/600,000 = 4.2 rounded down to 4

(ii) majority rule: NONE

b) What percentage of voting shares and/or proxies the dissident group must have to be able to elect

7 out of the 13 board members?

NUM VOTING SHARES NEEDED=[(7 X 600,000)/(13 + 1)] + 1=300,001

Percentage of voting shares and/or proxies = 300,001/600,000 50% (slightly greater than 50%)

15-10. Number of rights required to buy a share = 500,000/50,000 = 10

15-11. N = 2,000,000/500,000 = 4

Approx. Market Value of a Right = R = (65 - 55)/(4 + 1) = $2

15-12. Market Price of stocks selling ex-rights = 65 - 2 = $63

Approx. Market Value of a Right = R = (63 - 55)/(4) = $2

15-13. N = 7

Approx. Market Value of a Right = R = (77 - 65)/(7 + 1) = $1.50

Market Price of stocks selling ex-rights = 77 - 1.5 = $75.50

15-14. a) Approx. Market Value of a Right = R = (72 - 60)/(4 + 1) = $2.40

b) Maximum number of new shares that Johnny can buy = 700/4 = 175

c) Amount Johnny would spend = 175 X 60 = $10,500

d) Selling price of all of Johnny's rights = 700 X 2.40= $1,680

15-17. a) Approx. Market Value of a Right = R = (62 - 50)/(4 + 1) = $2.40

b) Ex-rights price = $62 - $2.40 = $59.60 per share

Diluted price after issue of new stock = $59.6 X 4/5 = $47.68

123

Option I: Sell rights and hold stocks at diluted value:

Amount obtained by selling rights = $2.40 X 60 = $144.00

Value of stocks held at diluted price = 60 X $47.68 = $2,860.80

Unused Cash = $750.00

Net worth from Option I = $3,784.80

Option II: Buy new shares:

Number of shares Selena can buy = 60/4 = 15

Amount to be spent to buy 15 shares = $50 X 15 = $750. So, Selena can buy all the 15 new shares

with her available cash.

Diluted price of stocks = $47.68

Net worth from Option II = $47.68 X (60 + 15) = $3,576.00

So, Selena should go for Option I, that is, Sell rights and hold her stocks at diluted value.

15-18. XV = (100 - 85) X 5 = $75

What happens to the exercise value of the warrant if the stock price changes to

a) $110 : XV = (110 - 85) X 5 = $125

b) $80 : XV = $0

15-19. Issue of new common stock by Wilkerson Corporation:

Current Market Price per share of Common Stock $40 Number of Common Shares outstanding 600,000 Amount of additional funds needed $2,000,000 Net Income for the year $1,000,000 Number of shares owned by Guy Hamilton 10,000

Possible Subscription Prices $36 $33 $29 $26

a. Number of shares to be issued 55,556 60,606 68,966 76,923

Number of Rights required to buy one share 10.8 9.9 8.7 7.8

b. EPS before the rights issue $1.67 $1.67 $1.67 $1.67 EPS after the rights issue $1.53 $1.51 $1.49 $1.48

c. Max number of new shares Guy can buy 926 1,010 1,149 1,282 Guy's claim to earning before the rights issue $16,667 $16,667 $16,667 $16,667 Guy's claim to earning after the rights issue $16,667 $16,667 $16,667 $16,667

124



1. Explain the role of cash and of earnings when a corporation is deciding how much, if any, cash

dividends to pay to common stockholders.

In the long-run earnings are necessary to maintain dividend payments, but at the time an actual

dividend payment is made, adequate cash is necessary.

2. Are there any legal factors that could restrict a corporation in its attempt to pay cash dividends to

common stockholders? Explain.

A firm may be legally restricted as to the dividends it can pay by existing bond indentures or loan

agreements. It may also be restricted as to the payment of common stock dividends is scheduled

preferred stock dividends have not been paid.

3. What are some of the factors that common stockholders consider when deciding how much, if any,

cash dividends they desire from the corporation in which they have invested?

Common stockholders would consider the company’s investment opportunity, their need for income,

and their tax bracket when deciding on their desire for dividends.

4. What is the Modigliani and Miller theory of dividends? Explain.

The Modigliani-Miller theory of dividends says that dividend theory is irrelevant. They claim that it

is the income produced by assets that is important, not how funds are distributed.

5. Do you believe an increased common stock cash dividend can send a signal to the common

stockholders? If so, what signal might it send?

An increase in cash dividends is often seen as a positive signal. A company would be unlikely to

increase its dividend if it did not believe its future prospects were good enough to sustain the higher

level of dividends. This is because the market usually frowns upon a cut in dividends.

6. Explain the bird in the hand theory of cash dividends.

The bird in the hand dividends theory says that dividends received now are better than a promise of

future dividends. Uncertainty is resolved when a dividend is paid.

125

7. What is the effect of stock (not cash) dividends and stock splits on the market price of common

stock? Why do corporations declare stock splits and stock dividends?

Stock splits and stock dividends decrease the price per share of the common stock but should not

increase the total market value of all common stock outstanding unless other positive things are

perceived to occur. Many companies believe that a stock split or stock dividend makes their stock

more affordable and therefore more attractive to a wider range of potential investors.


16-1. Retention Ratio = $600/$1,000 = 0.6 or 60%

∴ Payout Ratio = 1-.6 = .4 = 40%

16-2. Dividend Paid = 0.4 X $50 million = $20 million

Addition to Retained Earnings = $50 mil. - $20 mil. = $30 million

16-3. Retained Earnings Maintain $1,000,000

Retained Earnings end of 2005 750,000

Additional needed for maintenance $250,000

Earnings Avail. to Common Stockholders $800,000

Needed for maintenance 250,000

Dividend Payout $550,000

$550,000 / $800,000 = .6875 = 68.75%

16-4. Net income $4,000,000

Dividend Payout (35%) 1,400,000

Addition to retained earnings $2,600,000

Retained earnings end of 2005 $1,200,000

Addition to retained earnings 2,600,000

Retained earnings end of 2006 $3,800,000

16-5.

(Figures in $ millions) Year 1 Year 2 Year 3

Net Income 30 20 25

Dividend Payout ratio 0.3 0.3 0.3

Dividend Paid 9 6 7.5

Addition to RE 21 14 17.5

Total Addition to RE = 21 + 14 + 17.5 = 52.5

126

16-6.

(Figures in $ millions) Year 1 Year 2 Year 3

Net Income 30 20 25

Dividend Paid 10 10 10

Dividend Payout ratio 0.33 0.5 0.4

Addition to RE 20 10 15

Total Addition to RE = 20 + 10 + 15 = 45

16-7. Equity Investment = $14mil. X 0.6 = $8.4 million

Dividend to be Paid = $10mil. - $8.4 mil. = $1.6 million

16-8.a) Equity Investment = $14mil. X 0.6 = $8.4 million

Dividend to be Paid = $16 mil. - $8.4 mil. = $7.6 million

b) Equity Investment = $14 mil. X 0.6 = $8.4 million

Dividend to be Paid = $0

16-9. Equity funds needed $12,000,000 * .80 = $9,600,000

Amount avail. to stockholders $24,000,000 – 9,600,000 = $14,400,000

Dividend per share $14,400,000 / 20,000,000 = $0.72

16-10. 20% Stock Dividend ($000s)

Increase in number of shares = 0.2 X $2 million = 400 thousand

Increase in common stock account = 400 X $1 = $400

Increase in capital in excess of par account = 400 X $30 = $12,000

Total increase = $12,000 + $400 = $12,400

This increase is greater than the Retained Earnings of $10,000. Hence it is not possible to pay a 20%

stock dividend.

10% Stock Dividend($000s)

Increase in number of shares = 0.1 X $2 million = 200 thousand

Increase in common stock account = 200 X $1 = $200

Increase in capital in excess of par account = 200 X $30 = $6,000

Total increase = $6,000 + $200 = $6,200

This increase can be covered by a matching decrease in the retained earning account keeping the total

equity capital unchanged. The new retained earning will be 10,000 - 6,200 = $3,800. Hence it is

possible to pay a 10% stock dividend.

127

16-11. ($000s)

Common Stock ( 2 million shares, $1 par) 2,000

Capital in excess of par 8,000


Total Common Equity 20,000

After Payment of Dividend:

($000s)

Common Stock ( 2.2 million shares, $1 par) 2,200

Capital in excess of par = 8,000 + 6000 = 14,000

Retained Earnings = 10,000 - 6,000 - 200 = 3,800


New Market Price of the Stock = $31 X 2,000/2,200 = $28.18 per share.

16-12. a) 800,000 * (1 + 0.30) = 1,040,000 new total shares

1,040,000 – 800,000 = 240,000 new shares

b) CIEP = Capital in Excess of Par

CIEPbefore = $13,600,000

CIEPafter = $13,600,000 + (240,000 new shares * ($40 - $3))

CIEPafter = $22,480,000

c) CS = Common Stock

CSbefore = 800,000 * $3 = $2,400,000

CSafter = 1,040,000 * $3 = $3,120,000

RE = Retained Earnings

REbefore = $60,000,000

REafter = $60,000,000 – ($3,120,000 - $2,400,000) – ($22,480,000 - 13,600,000)

REafter = $50,400,000

16-13. 800,000 * $40 = $32,000,000

x = new stock price

1,040,000 * x = $32,000,000

New stock price = $30.77

16-14. Before the stock split

Common Stock ( 3 million shares, $1.00 par) 3,000




128

After the stock split

Common Stock ( 9 million shares, $0.33 1/3 par) 3,000




New Market Price of the stock = 33 X 1/3 = $11.00 per share.

16-15. EPS (Before the stock split) = $800,000/3,000,000 = $0.27

EPS (After the stock split) = $800,000/9,000,000 = $0.09

The P/E ratio will remain the same (123.75) before and after the split unless other factors influence

the market’s perception of this stock’s value.

16-16. a) Dividend per share last year = $1.33 X 5/1 = $6.65

b) Dividend per share last year = $1.33/1.1 X 5/1 = $6.05

16-17. Dividend per share = EPS X Payout Ratio = ($10/1) X 0.4 = $4

Price of stock (ex-dividend) = $30 - $4 = $26 per share.

16-18. Spring Field Manufacturing Company's Dividend Payments:

NUMBER OF SHARES OF COMMON STOCK OUTSTANDING = 500,000

NUMBER OF SHARES OF COMMON STOCK OWNED BY YOU = 500

NET CAPITAL EQUITY DIVIDEND DIVIDEND DIVIDEND

YEAR INCOME INVESTMENTS FINANCING PAYMENT PER SHARE RECEIVED

2007 $1,000,000 $800,000 $480,000 $520,000 $1.04 $520

2008 $1,100,000 $1,000,000 $600,000 $500,000 $1.00 $500

2009 $1,200,000 $2,000,000 $1,200,000 $0 $0.00 $0

2010 $1,300,000 $800,000 $480,000 $820,000 $1.64 $820

2011 $1,400,000 $1,000,000 $600,000 $800,000 $1.60 $800

129

16-19. Spring Field Manufacturing Company's Dividend Payments:

NUMBER OF SHARES OF COMMON STOCK OWNED BY YOU = 500

AMOUNT NO. OF NET CAPITAL EQUITY FROM SHARES DIVIDEND DIVIDEND DIVIDEND

YEAR INCOME INVESTMENTS FINANCING NEW SHARES

OUTSTANDING PAYMENT PER SHARE

RECEIVED

2007 $1,000,000 $800,000 $480,000 500,000 $520,000 $1.04 $520 2008 $1,100,000 $1,000,000 $600,000 500,000 $500,000 $1.00 $500 2009 $1,200,000 $2,000,000 $1,200,000 $600,000 600,000 $600,000 $1.00 $500 2010 $1,300,000 $800,000 $480,000 600,000 $820,000 $1.37 $683 2011 $1,400,000 $1,000,000 $600,000 600,000 $800,000 $1.33 $667

16-20. Comprehensive Problem:

a) Expected Dividend per share = $3,000,000 X 0.5/500,000 = $3

Repurchase Price = $47 + $3 = $50 per share

b) Number of shares that could be repurchased = $3,000,000/$50 = 60,000

c) Before Repurchase of Stock

($ 000s)

Common Stock (500,000 shares, $3 par) 1,500

Capital in excess of par ($7/share) 3,500



After Repurchase of Stock

($ 000s)

Common Stock (440,000 shares, $3 par) 1,320

Capital in excess of par = 7 X 440 = 3,080

Retained Earnings = 5,000 + (1,500 - 1,320)

+ (3,500 - 3,080) = 5,600


d) If net income next year is expected to be $4 million, what would be the EPS next year with and

without the repurchase?

EPS (without repurchase) = $4,000,000/500,000 = $8

EPS (with repurchase) = $4,000,000/440,000 = $9.09

e) If you own 50 shares of common stock of the company, would you like the company's decision of

buying back the stocks instead of paying a dividend?

Without Repurchase:

Dividend Earning Last Year = $3/Share X 50 shares = $ 150

Value of stock = $47/share X 50 shares = $2,350

Total = $2,500

130

With Repurchase:

Price of stock = $50/share X 500/440 = $56.82 per share

Value of stock = $56.82 X 50 = $2,841.00

The decision to buy back instead of paying a dividend would be preferred if the stock price were to

increase to $56.82 per share with the repurchase. The taxes that may be owed on the $150 in dividends

under the no repurchase scenario would decrease further the attractiveness of this alternative.

16-21. Before the split

# of shares 300,000

Common Stock $1,200,000

Par Value $4

Capital in Excess of Par $1,500,000

Retained Earnings $10,000,000

Total Common Stock Equity $12,700,000

After the split

# of shares 1,200,000

Common Stock $1,200,000

Par Value $1

Capital in Excess of Par $1,500,000

Retained Earnings $10,000,000

Total Common Stock Equity $12,700,000

131



1. What is working capital?

Working capital consists of the current assets of the firm.

2. What is the primary advantage to a corporation of investing some of its funds in working capital?

By investing in working capital a firm gets the liquidity it needs helping it to pay its bills. The risk of

the firm is therefore reduced.

3. Can a corporation have too much working capital? Explain.

A firm can have too much working capital if it is losing the opportunity to invest in high returning

fixed assets and if it goes beyond the amount of working capital needed for reasonable liquidity

needs.

4. Explain how a firm determines the optimal level of current assets.

The optimal level of working capital is determined by finding the amount that balances the need for

liquidity and for profitability.

5. What are the risks associated with using a large amount of short-term financing for working capital?

Using a large amount of short-term financing generally allows funds to be raised at a lower cost but

increases the firm’s risk.

6. What is the matching principle of working capital financing? What are the benefits of following this

principle?

The matching principle is when short-term financing is used for temporary current assets while long-

term financing is used for permanent current assets and fixed assets. The main benefit of this

approach is that as temporary current assets are sold off the proceeds can be used to pay off the short-

term debt.

7. What are the advantages and disadvantages of the aggressive working capital financing approach?

An aggressive working capital financing approach usually results in a lower cost of funds for a firm

but a higher level of risk.

132

8. What is the most conservative type of working capital financing plan a company could implement?

Explain.

An all equity capital structure would be the most conservative type of working capital financing plan

approach. The more long-term financing used the more conservative the financing plan, and equity

is permanent financing.


17-1. a) ($150,000 + $120,000 + $80,000) = $350,000

b) $350,000 – ($100,000 + $90,000) = $160,000

c) ($150,000 + $120,000 + $80,000) * 0.25 = $87,500

d) ($150,000 + $120,000 + $80,000) * 0.75 = $262,500

17-2. Firm 1:

$10,000 + $3,000 + $2,500 = $15,500 (working capital)

$15,500 - $7,500 - $4,000 = $4,000 (net working capital)

Current ratio = $15,500 / ($7,500 + $4,000) = 1.35

Quick ratio = ($15,500 - $3,000) / $11,500 = 1.09

Firm 2:

$8,000 + $6,000 + $3,500 = $17,500 (working capital)

$17,500 - $3,500 - $11,000 = $3,000 (net working capital)

Current ratio = $17,500 / ($3,500 + $11,000) = 1.21

Quick ratio = ($17,500 - $6,000) / $14,500 = 0.79

Firm 1 is more liquid due to its higher liquidity ratios.

17-3. Company A: NWC = ($1,000 + $400) - $900 = $500

Company B: NWC = ($80 + $880) - $600 = $360

Company A has the higher net working capital and would therefore generally be considered the more

liquid company. Although Company A has a slightly smaller current ratio value (1.56 for A and 1.6

for B) Company A has a much higher percentage of cash in its current assets, so would likely be

considered by most analysts the more liquid firm.

17-4. a) CA = $30,000 + $15,000 + $130,000 = $175,000

b) CL = $100,000 + $60,000 = $160,000

c) NWC = $175,000 - $160,000 = $15,000

d) 160/(175 X .5) or 183.86% of TCA is financed by CL. This is an aggressive approach since

all TCA and most of PCA are being financed with riskier short-term funds.

133

17-5. a) CA = $30,000 + $15,000 + $130,000 = $175,000

b) CL = $30,000 + $20,000 = $50,000

c) NWC = $175,000 - $50,000 = $125,000

d) 50/(175 X .5) or 57.14% of TCA is financed by CL. This is a relatively conservative

approach. Long-term financing of $625,000 exceeds the total of fixed assets and permanent

current assets, $587,500, by $37,500. Only $50,000 of the $87,500 in temporary current

assets is being financed with short-term funds.

17-6. a) CA = $50 + $0 + $40 + $70 = $160

b) CL = $80 + $90 = $170

NWC = $160 - $170 = ($10)

c) All of LuLu Belle’s current assets, and some of the fixed assets, are financed with short-term

funds (current liabilities). This is an aggressive approach.

d) Reduce short-term debt, increase long-term debt and equity and invest in marketable

securities. This will increase net working capital and the current ratio.

17-7.

Cash $100,000

Inventory $200,000

Accounts Receivable $150,000

Net Fixed Assets $550,000

Total Assets $1,000,000

Permanent assets, net fixed assets and a small portion of temporary assets are financed with long-term debt

and equity. This is using a very conservative approach. Your exact numbers are likely to be different, but

the point is that long-term debt and equity financing are emphasized.

17-8. PCA = $225,000 * 0.60 = $135,000

PCA + FA = $135,000 + $475,000 = $610,000

LTD + CSEQ = $410,000 + $200,000 = $610,000

a)

Cash $50,000 Accounts Payable__$40,000_

Accounts Receivable 25,000 Notes Payable ___50,000_

Inventory 150,000 Long-term Debt __410,000_

Fixed Assets 475,000 Common Equity __ 200,000_

$700,000

Accounts Payable $35,000

Notes Payable $60,000

Long-term Debt $505,000

Common Equity $ 400,000

Total Liabilities and Equity $1,000,000

134

b)

Cash $50,000 Accounts Payable__$30,000_

Accounts Receivable 25,000 Notes Payable ___60,000_

Inventory 150,000 Long-term Debt __185,000_

Fixed Assets 475,000 Common Equity __425,000_

$700,000

17-9. a) Accounts payable = $180,000

Notes payable = $320,000

Long-term debt = $0

Common Equity = $200,000

Your exact numbers are likely to be different, but the point is that short-term debt is emphasized.

17-10. CA = $30,000 + $15,000 + $130,000 = $175,000

Perm. CA = $15,000 + $5,000 + $80,000 = $100,000

Temp. CA = $175,000 - $100,000 = $75,000

CL = Short-Term Debt + $20,000 = $75,000 = Temp.CA (By Matching Principle)

Short-Term Debt = $75,000 - $20,000 = $55,000

Long-Term Debt = $675,000 - $450,000 - $55,000 - $20,000 = $150,000

17-11. NWC = CA - CL

$25,000 = ($30,000 + $15,000 + $130,000) - ($20,000 + Short-Term Debt)

Short-Term Debt = $175,000 - $25,000 - $20,000 = $130,000

Long-Term Debt = $675,000 - $450,000 - $130,000 - $20,000 = $75,000

17-12. AGG.(A)(HIGH

RISK) MOD.(M)(MOD. RISK)

CON.(C)(LOW RISK)

COMMENTS

Temporary CA 75 75 75

Permanent CA 100 100 100

Fixed Assets 500 500 500

Total Assets 675 675 675

Current Liabilities 160 75 50

Long Term Debt 90 150 150

Stockholders' Equity 425 450 475

Net Income 70 70 70

NWC 15 100 125 LOWEST FOR A, HIGHEST FOR C

Current Ratio 1.09 2.33 3.50 LOWEST FOR A, HIGHEST FOR C

Debt to Asset 0.37 0.33 0.30 HIGHEST FOR A, LOWEST FOR C

ROE 16.47% 15.56% 14.74% HIGHEST FOR A, LOWEST FOR C

135

17-13. Assumption (i)

(a) Interest Expense: 0.13 X 5 X $500,000 = $325,000

(b) Interest Expense: .11 X 5 X $500,000 = $275,000

Alternative (b) will save $50,000

Assumption (ii)

(a) Interest Expense: 0.13 X 5 X $500,000 = $325,000

(b) Interest Expense: (0.11 X 2 X $500,000) + (.14 X 2 X $500,000) + (.16 X $500,000)

= $330,000

Alternative (a) will save $5,000

17-14. Data for graph:

Permanent Temporary Current Liabilities

Total assets Fixed assets Current Current if Matching Principle

Date (given) (given) Assets Assets is Followed

31-Jan $45 $14 $14 $17 $17

28-Feb $46 $14 $14 $18 $18

31-Mar $34 $14 $14 $6 $6

30-Apr $48 $14 $14 $20 $20

31-May $40 $14 $14 $12 $12

30-Jun $30 $14 $14 $2 $2

31-Jul $28 $14 $14 $0 $0

31-Aug $39 $14 $14 $11 $11

30-Sep $45 $14 $14 $17 $17

31-Oct $39 $14 $14 $11 $11

30-Nov $52 $14 $14 $24 $24

31-Dec $50 $14 $14 $22 $22

Working Capital Trends

$0

$10

$20

$30

$40

$50

$60

31-

Jan

28-

Feb

31-

Mar

30-

Apr

31-

May

30-

Jun

31-

Jul

31-

Aug

30-

Sep

31-

Oct

30-

Nov

31-

Dec

Fixed Assets

Permenant Current Assets

Temporary Current AssetsTemporary Current Assets

136

17-15.

b) Sep. of year 4: Aug. of year 5:

TA= $52.04 TA= $54.80

TCA= $4.00 TCA= $5.00

PCA= $9.04 PCA= $10.80

FA= $39.00 FA= $39.00

c) Sep. of year 4:

(i) aggressive approach

CL = over $4.00

LT Financing = the remainder of $52.04

(ii) moderate approach

CL = $4.00

LT Financing = $48.04

(iii) conservative approach

CL = less than $4.00


Aug. of year 5:


CL = over $5.00



CL = $5.00






$30

$35

$40

$45

$50

$55

$60

Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct

MONTH/ YEAR

Temporary Current Assets

Permanent Current Assets

Fixed Assets

137

17-16.

17-16. b) Sep. of year 2: Oct. of year 4:

TA = $89.00 TA = $101.00

TCA = $18.00 TCA = $22.50

PCA = $16.00 PCA = $23.50

FA = $55.00 FA = $55.00

Year 5 minimum total assets occur in January in the amount of $79.40.

Year 5 maximum total assets occur in December in the amount of $115.70.

c) Sep. of year 2:


CL = over $18.00



CL = $18.00





Oct. of year 4:


CL = over $22.50



CL = $22.50






$40

$50

$60

$70

$80

$90

$100

$110

$120

Jan May Sep Jan May Sep Jan May Sep Jan May Sep Jan May Sep

MONTH/ YEAR

Temporary Current Assets

Permenant Current Assets

Fixed Assets

138



1. What are the primary reasons that companies hold cash?

Companies hold cash to make necessary payments, to take advantage of opportunities as they arise,

and to cover unforeseen emergencies.

2. Explain the factors affecting the choice of a minimum cash balance amount.

The minimum cash balance amount is determined by how easy it is to raise funds when needed, how

predictable the cash flows are, and how risk averse managers are.

3. What are the negative consequences of a company holding too much cash?

A company holding too much cash would be giving up the opportunity to invest more in income

producing assets

4. Explain the factors affecting the choice of a maximum cash balance amount.

The maximum cash balance amount is determined by available investment opportunities, the

expected return on investments, and the transaction cost of making investments.

5. What is the difference between pro forma financial statements and a cash budget? Explain why pro

forma financial statements are not used to forecast cash needs.

Pro forma income statements deal with revenues and expenses that are not always cash flows while

cash budgets deal only with projected cash inflows and outflows.

6. What are the benefits of “collecting early” and how do companies attempt to do this?

Money has time value. The sooner cash is collected, the better. Companies use regional collection

centers and lock boxes to facilitate this.

7. What are the benefits of “paying late” (but not too late) and how do companies attempt to do this?

Because money has time value, the later cash is paid, but not too late, the better. Companies use

remote disbursement banks to facilitate holding onto funds longer.

139

8. Refer to the Bulldog battery company’s cash budget in Table 18-7. Explain why the company would

probably not issue $1 million worth of new common stock in January to avoid all short-term

borrowing during the year.

Common stock financing is long-term financing so it would probably not be used to meet this short-

term financing need.


18-1. Miller-Orr Model:

H = 3Z - 2L

Target Cash Balance = Z = (H + 2L)/3 = ($9,000 + 2 X $3,000)/ 3 = $5,000


a)

OR

Target Cash Balance = Z = $2,424 + $2,200 = $4,624

b) Upper Limit of cash balance = H = 3Z -2L = 3 X $4,624 - 2 X $2,200 = $9,472


a)

OR

Target Cash Balance = Z = $2,667 + $3,900 = $6,567

b) Upper Limit of cash balance = H = 3Z -2L = 3 X $6,567 - 2 X $3,900 = $11,901

3

18-4. Z = √ [(3 * $25 * $65,580) / (4 * (.05/365))] + $15,000

L+4r

V X TC X 3=Z 3

$2,200+.03/365 X 4

$39,000 X $40 X 3=Z 3

L+4r

V X TC X 3=Z 3

$3,900+.03/365 X 4

$52,000 X $40 X 3=Z 3

140

3

Z = √ (4,918,500 / .000547945) + $15,000

3

Z = √ 8,976,265,866 + $15,000

Z = $2,078.25 + $15,000

Z = $17,078.25

18-5. H = (3 * $17,078.25) – (2 * $15,000)

H = $51,234.75 – $30,000

H = $21,234.75

141

18-6. Lifelong Appliances Cash Collections

Given:

20% of customers pay off their accounts in month of sale

70% of customers pay off their accounts in first month following sale

10% of customers pay off their accounts in second month following sale

2006 ---> 2007 ---> 2008 --->

Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb

Sales ($000s) $131 $129 $126 $133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139

Monthly Cash Collections Worksheet:

(in $000s)

2006 ---> 2007 ---> 2008 --->


Cash collections:

in month of sale $25 $27 $28 $29 $38 $45 $48 $45 $37 $35 $33 $29

first month after sale 90 88 93 97 100 134 158 169 157 129 121 116

second month after sale 13 13 13 13 14 14 19 23 24 22 18 17

Total monthly cash collections $129 $128 $134 $139 $152 $193 $226 $237 $218 $186 $173 $162

18-7. Lifelong Appliances Cash Collections with Stricter Credit Terms

Given:




2006 ---> 2007 ---> 2008 --->


Sales ($000s) $131 $129 $126 $133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139

Monthly Cash Collections Worksheet:

(in $000s)

2006 ---> 2007 ---> 2008 --->


Cash collections:

in month of sale $50 $53 $56 $57 $76 $90 $97 $90 $74 $69 $66 $57

first month after sale 71 69 73 76 79 105 124 133 123 101 95 91


Total monthly cash collections $128 $129 $135 $140 $162 $203 $231 $234 $209 $182 $171 $157

142

18-8. a) ($18,366 * .45) + ($16,523 * .40) + ($17,956 * .15) =

$8,264.70 + $6,609.20 + $2693.40 =

$17,567.30

b) ($22,980 * .45) + ($22,890 * .40) + ($19,500 * .15) =

$10,341 + $9,156 + 2,925 =

$22,422

c) ($21,650 * .45) + ($23,000 * .40) + ($23,157 * .15) =

$9,742.50 + $9,200 + $3,473.55 =

$22,416.05

18-9. a) $2,000 + ($17,956 * .05) + $62.50 = $2,960.30

b) $2,000 + ($22,890 * .05) + $62.50 +$1,125 = $4,332.00

c) $2,000 + ($19,250 * .05) + $62.50 = $3,025.00

18-10. Lifelong Appliances Cash Expenditures

Given:

2006 ---> 2007 ---> 2008 --->


Sales ($000s) $131 $129 $126 $133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139

Dec Jan Feb Mar

Materials purchasing Schedule: Order materials Manufacture Appliances Sell appliances Repeat each month

Cost of materials = 30% of sales

Payment for materials one month after purchase

Production costs other than purchases = 80% of purchases

Selling and marketing Expenses = 19% of sales

General and Administrative Expenses = $11 thousand each month

Interest Payments = $31 thousand, paid in December

Tax payments = $100 thousand, paid in 4 installments in April, June, September, and December

Dividend payments = $50 thousand each, paid in June and December

143

Monthly Cash Expenditures Worksheet:

(in $000s)

2006 ---> 2007 ---> 2008 --->


Materials Purchases $40 $42 $43 $57 $68 $73 $67 $55 $52 $50 $43 $41 $42

(reference only; not a cash flow)

Payments for materials purchases: $40 $42 $43 $57 $68 $73 $67 $55 $52 $50 $43 $41

Other cash payments:

Production costs other than purchases $33 $34 $46 $54 $58 $54 $44 $42 $40 $34 $33 $33

Selling and marketing Expenses $24 $25 $26 $27 $36 $43 $46 $43 $35 $33 $32 $27

General and Administrative Expenses $11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11

Interest Payments $31

Tax payments $25 $25 $25 $25

Dividend payments $50 $50

Total Cash Outflows $108 $112 $126 $175 $173 $255 $168 $150 $163 $128 $118 $218

18-11. Lifelong Appliances Cash Expenditures, Revised

Given:

2006 ---> 2007 ---> 2008 --->


Sales ($000s) $131 $129 $126 $133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139

Dec Jan Feb Mar

Materials purchasing Schedule: Order materials Manufacture Appliances Sell appliances Repeat each month

Cost of materials = 30% of sales

Payment schedule for materials:

30% paid in cash in month of purchase

70% paid in cash in month following month of purchase





Tax payments = $100 thousand, paid in 4 installments in April, June, September, and December


144

Monthly Cash Expenditures Worksheet:

(in $000s)

2006 ---> 2007 ---> 2008 --->




Payments for materials purchases:

in month of purchase $13 $13 $17 $20 $22 $20 $17 $16 $15 $13 $12 $13

in month following month of purchase $28 $29 $30 $40 $47 $51 $47 $39 $36 $35 $30 $29






Tax payments $25 $25 $25 $25


Total Cash Outflows $109 $113 $130 $178 $175 $254 $165 $149 $162 $126 $117 $219

18-12. Fit-and-Forget Fittings Cash Budget

Given:

Sales: 2006 ---> 2007 ---> 2008 --->


Sales ($000s) $2,266 $2,230 $2,116 $2,300 $2,402 $2,420 $3,390 $3,909 $4,164 $3,933 $3,163 $2,912 $2,886 $2,424 $2,353 $2,442

Collections:




Purchases & Expenses:

Dec Jan Feb Mar

Materials purchasing Schedule:

Order materials

Manufacture Products

Sell Products

Repeat each month

Cost of materials =

20% of sales

Payment schedule for materials:

20% paid in cash in month of purchase

80% paid in cash in month following month of purchase

145





Tax payments = $1,600 thousand, paid in 4 installments in April, June, September, and December


Cash Inflows: (in $000s)

2006 ---> 2007 ---> 2008 --->


Cash collections:

in month of sale $635 $690 $721 $726 $1,017 $1,173 $1,249 $1,180 $949 $874 $866 $727

first month after sale 1,450 1,375 1,495 1,561 1,573 2,204 2,541 2,707 2,556 2,056 1,893 1,876


Total monthly cash collections $2,198 $2,177 $2,321 $2,402 $2,710 $3,497 $3,960 $4,082 $3,714 $3,126 $2,917 $2,749

Cash Outflows: (in $000s)

2006 ---> 2007 ---> 2008 --->




Payments for materials purchases:

in month of purchase $96 $97 $136 $156 $167 $157 $127 $116 $115 $97 $94 $98

in month following month of purchase $368 $384 $387 $542 $625 $666 $629 $506 $466 $462 $388 $376






Tax payments $400 $400 $400 $400


Total Cash Outflows $1,050 $1,097 $1,182 $1,775 $1,631 $2,994 $1,691 $1,513 $1,748 $1,273 $1,190 $2,865

Net Cash Gain(Loss) $1,148 $1,080 $1,139 $627 $1,079 $503 $2,269 $2,569 $1,965 $1,854 $1,727 ($117)

Cash Flow Summary: (in $000s)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1. Cash Balance at start of month $1,133 $2,281 $3,361 $4,500 $5,127 $6,206 $6,709 $8,978 $11,547 $13,512 $15,366 $17,093

2. Net Cash Gain(Loss) during month 1,148 1,080 1,139 627 1,079 503 2,269 2,569 1,965 1,854 1,727 (117)

3. Cash balance at end of month before financing 2,281 3,361 4,500 5,127 6,206 6,709 8,978 11,547 13,512 15,366 17,093 16,976

(line 1 plus line 2)

4. Minimum Cash Balance Desired 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110

5. Surplus cash(deficit) (Line 3 minus line 4) $1,171 $2,251 $3,390 $4,017 $5,096 $5,599 $7,868 $10,437 $12,402 $14,256 $15,983 $15,866

146

External Financing Summary: (in $000s)

6. External financing balance at start of month $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0

7. New financing required 0 0 0 0 0 0 0 0 0 0 0 0

(negative amount from line 5)

8. Financing repayments 0 0 0 0 0 0 0 0 0 0 0 0

(positive amount from line 5)

9. External financing balance at end of month 0 0 0 0 0 0 0 0 0 0 0 0

10. Cash balance at end of month after financing $2,281 $3,361 $4,500 $5,127 $6,206 $6,709 $8,978 $11,547 $13,512 $15,366 $17,093 $16,976

147



1. Accounts receivable are sometimes not collected. Why do companies extend trade credit when they

could insist on cash for all sales?

Extending trade credit almost always leads to more sales. If the incremental cashflows, including the

investment in accounts receivable give a positive NPV, the decision to extend trade credit would

increase the value of the firm.

2. Inventory is sometimes thought of as a necessary evil. Explain.

Inventory ties up funds and these funds are not earning an explicit return. Some inventory is often

necessary, however, as companies try to hold the lowest acceptable amount.

3. What are the primary variables being balanced in the EOQ inventory model? Explain

The primary variables being balanced in the EOQ model are carrying costs and ordering costs. The

more frequent orders are placed the lower the firm’s carrying costs and the higher its ordering costs.

4. What are the benefits of the JIT inventory control system?

The just-in-time (JIT) inventory control system lowers inventory carrying costs and tends to increase

quality.

5. What are the primary requirements for a successful JIT inventory control system?

For a JIT system to be successful the supplier must be willing and able to deliver materials

immediately and the quality of delivered materials must be high.

6. Can a company have a default rate on its accounts receivable that is too low? Explain.

A company could have a default rate on AR that would be considered too low if by liberalizing credit

terms a significant increase in sales revenue and cash inflows were to result. If the increase in the

default rate is more than offset by the increase in sales revenue, after all incremental cash flows are

considered a positive NPV could result.

7. How does accounts receivable factoring work? What are the benefits to the two parties involved?

What are the risks?

148

Factoring is when one firm sells accounts receivable (AR) to another. The purchasing firm is called

a factor. The factor makes a profit by purchasing the AR at a discount. Its risk is that some of the

AR may default. The selling firm gets the cash it needs.


19-1. Accounts Receivable, ACP:

Accounts Receivable = ACP X Sales/365 = 22 X $8,030,000/365 = $484,000

19-2. Accounts Receivable, ACP:

Accounts Receivable = ACP X Sales/365 = 26 X $7,600,000/365 = $541,369.86

The company appears to have relaxed its credit policy since accounts receivable increased as did the

average collection period.

19-3. Accounts Receivable, ACP, Credit Policy:

(a) ACP = 0.4 X 15 + 0.57 X 60 + 0.03 X 100 = 43.2 days

(b) AR = 43.2 X $730,000/365 = $86,400

19-4. Accounts Receivable, ACP, Credit Policy:

ACP = 0.4 X 10 + 0.58 X 30 + 0.02 X 100 = 23.4 days

AR = 23.4 X $657,000/365 = $42,120

19-5. (0.25 * 10) + (0.60 * 20) + (0.15 * 30) =

2.5 + 12 + 4.5 = 19 days

19-6. (0.32 * 10) + (0.67 * 30) + (0.01 * 45) =

3.2 + 20.1 + 0.45 = 23.75 days

No, the new policy should not be implemented because the ACP would increase.

149

19-7 Effect of Change of Credit Policy: Given:

All sales on credit

Old credit terms 2/15, n40

New credit terms 2/15, n60

Sales expected under old credit policy: $350,000

Sales change expected with new credit policy: 20% increase

Under old credit policy: 40% of customers take discount, pay in 15 days

58% of customers pay at the end of 40 days

2% of customers pay in 100 days

Under new credit policy: 40% of customers take discount, pay in 15 days



Bad debt expenses under old credit policy: 2% of sales

Bad debt expenses under new credit policy: 3% of sales

Short-term interest rate 7%

Long term interest rate 10%

Income tax rate 40%

Cost of capital 11%

Cost of goods sold 80% of sales

Other operating expenses $10,000 under old credit policy

Question a:

Average collection period under old policy 31.2 days (weighted average of customers paying)

Average collection period under new policy 43.2 days (weighted average of customers paying)

Accounts Receivable under old policy $29,918 AR = ACP * Credit sales per day

Accounts Receivable under new policy $49,710 AR = ACP * Credit sales per day

Question b:

East-West Trading Company Financial Statements

INCOME STATEMENT

With old With new

credit credit

terms: terms:

2/15, n40 2/15, n60

(given) (pro forma)

Sales (all on credit) $350,000 $420,000 20% increase

Cost of Goods Sold 280,000 $336,000 increase in proportion with sales


Bad debt expenses 7,000 12,600 from assumptions

Other operating expenses 10,000 $12,000 increase in proportion with sales


Interest Expense 5,450 5,940 (ST Debt * ST Cost of Debt) + (LT Debt * LT Cost of Debt)

Before-Tax Income 47,550 53,460

Income Taxes 19,020 21,384

Net Income $28,530 $32,076

150

BALANCE SHEET, as of Dec 31

Assets

Current Assets:

Cash & Securities $15,000 $18,000 increase in proportion with sales

Accounts Receivable 29,918 49,710 from Tab a

Inventory 50,000 60,000 increase in proportion with sales

Total Current Assets 94,918 127,710

Property, Plant & Equipment, Net 120,000 120,000 same

Total Assets $214,918 $247,710

Liabilities & Equity

Current Liabilities:

Accounts Payable $14,918 $17,902 increase in proportion with sales

Notes Payable 35,000 $42,000 increase in proportion with sales

Total Current Liabilities 49,918 59,902

Long-Term Debt 30,000 30,000 same

Total Liabilities 79,918 89,902

Common Stock 25,000 25,000 same

Capital in Excess of Par 60,000 60,000 same

Retained Earnings 50,000 50,000 same

Total Stockholders' Equity 135,000 135,000

Total Liabilities & Equity $214,918 $224,902

AFN to balance: $22,808 obtain from ST sources

Question c:

Incremental cash flows associated with the credit policy change

Initial investment at T-0 ($22,808) AFN from Tab B

Future incremental cash flows, T-1 onward:

Inflows:

Increase in Sales $70,000

Outflows:

Increase in Cost of Goods Sold $56,000

Increase in Bad Debt Expense $5,600

Increase in Other Operating Exps $2,000

Increase in Interest Expense $490

Increase in Taxes $2,364

Total Outflows $66,454

Net future incremental cash flows $3,546 each year from T-1 onward

Question d, Investment Decision:

NPV of the Credit Policy Change:

Initial Investment Future Cash Flows

($22,808) $3,546 per year

NPV = $9,428 at a cost of capital of 11%

151

19-8. Given:

All sales on credit



Sales expected under old credit policy: $350,000

Sales change expected with new credit policy: 20% increase











Income tax rate 40%

Cost of capital 11%



Question a:

Average collection period under old policy 31.2 days (weighted average of customers paying)


Accounts Receivable under old policy $29,918 AR = ACP X Credit sales per day

Accounts Receivable under new policy $58,110 AR = ACP X Credit sales per day

Question b:

East-West Company Financial Statements

INCOME STATEMENT

With old With new

credit credit

terms: terms:

2/15, n40 2/15, n60

(given) (pro forma)

Sales (all on credit) $350,000 $420,000 20% increase

Cost of Goods Sold 280,000 $336,000 increase in proportion with sales



Other operating expenses 10,000 $12,000 increase in proportion with sales


Interest Expense 5,450 5,940 (ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of Debt)



152

Net Income $28,530 $29,556


Assets

Current Assets:

Cash & Securities $15,000 $18,000 increase in proportion with sales

Accounts Receivable 29,918 58,110

Inventory 50,000 60,000 increase in proportion with sales



Total Assets $214,918 $256,110



Accounts Payable $14,918 $17,902 increase in proportion with sales

Notes Payable 35,000 $42,000 increase in proportion with sales









AFN to balance: $31,208 obtain from ST sources

Question c:


Initial investment at T-0 ($31,208) AFN


Inflows:


Outflows:


Increase in Bad Debt Expense $9,800



Increase in Taxes $684






($31,208) $1,026 per year

NPV = ($21,881) at a cost of capital of 11%

153

19-9. Effect of Change of Credit Policy:

Given:

All sales on credit



Sales expected under old credit policy: $2,000,000

Sales change expected with new credit policy: -10% decrease











Income tax rate 40%

Cost of capital 13%



Question a:

Average collection period under old policy 37 days (weighted average of customers paying)


Accounts Receivable under old policy $202,740 AR = ACP X Credit sales per day

Accounts Receivable under new policy $120,329 AR = ACP X Credit sales per day

Question b:

A-Z Trading Company Financial Statements

INCOME STATEMENT

With old With new

credit credit

terms: terms:

3/10, n40 3/15, n30

(given) (pro forma)

Sales (all on credit) $2,000,000 $1,800,000 10% decrease

Cost of Goods Sold 1,600,000 $1,440,000 decrease in proportion with sales

Gross Profit 400,000 360,000


Other operating expenses 60,000 $54,000 decrease in proportion with sales





Net Income $147,114 $152,874

154


Assets

Current Assets:

Cash & Securities $86,000 $77,400 decrease in proportion with sales

Accounts Receivable 202,740 120,329

Inventory 285,000 256,500 decrease in proportion with sales



Total Assets $1,225,740 $1,106,229



Accounts Payable $85,000 $76,500 decrease in proportion with sales

Notes Payable 200,000 $180,000 decrease in proportion with sales








Total Liabilities & Equity $1,225,740 $1,197,500

AFN to balance: ($91,271) excess financing

Question c:


Initial investment at T-0 $91,271


Inflows:

Increase in Sales ($200,000)

Outflows:

Increase in Cost of Goods Sold ($160,000)

Increase in Bad Debt Expense ($42,000)

Increase in Other Operating Exps ($6,000)

Increase in Interest Expense ($1,600)


Total Outflows ($205,760)





$91,271 $5,760 per year


155

19-10. Economic Order Quantity

EOQ = [2 X 500 X $250/$300] = 28.87 units 29 units

Number of orders per year = 500/29 = 17.24 orders 17 orders

Ordering Cost = 17 X $250 = $4,250

19-11. Economic Order Quantity:

EOQ = [2 X 500 X $250/$330] = 27.52 units 28 units

Number of orders per year = 500/28 = 17.86orders 18 orders

Ordering cost = 18 X $250 = $4,500

19-12. a) √ (2 * 1,200 * $250) / $100 =

√ 6,000 = 77.46 units per order

b) 1200 / 78 = 15.38 orders per year

19-13. Sales (2007) = 200 * (1 + 0.25) = 250 units

Carrying Costs = $150 * (1 + 0.10) = $165

Ordering Costs = $50 * (1 + 0.10) = $55

√ (2 * 250 * $55) / $165 = √ 166.66 = 12.91 units

19-14. Credit Scoring

Total Score = 3 + 4 + 3 + 4 + 3 + 2 = 19 > 12. Yes, Danny should approve the credit.

19-15.

Criteria Points Score

Length of time since last delinquent

payment:

Greater 2.5 years

2-2.5 years

1.5-2 years

1-1.5 years

Less than 1 year

4

3

2

1

0

___4____

_______

_______

_______

_______

Length of Time in Business

Greater 5 years

4-5 years

3-4 years

2-3 years

Less than 2 years

4

3

2

1

0

___4____

_______

_______

_______

_______

156

Net Income

Greater $100,000

$75,000-$100,000

$50,000-$75,000

$25,000-$50,000

Less than $25,000

4

3

2

1

0

_______

_______

___2____

_______

_______

Total Score: 10

$1,200,000 * 0.30 = $360,000

Yes, they will be approved. TWI will be approved for $360,000.

19-16.

Sunrise Corporation Inventory Policy

Given:

Present inventory level 60

Proposed inventory level 100

Sales expected under old inventory policy: 350 units per year

Sales expected with new inventory policy: 450 units per year

Ordering cost $200 per order

Carrying cost $600 per unit per year

Unit sales price $10,000

Unit purchase price $8,000



Income tax rate 40%

Cost of capital 11%


Other operating expenses $100,000 under current inventory policy

Question a:

Under old inventory policy Under new inventory policy

60 units 100 units

E.O.Q 15 17

Number of orders per year 23 26

Ordering cost $4,583 $5,196

Carrying cost $36,000 $60,000

Total inventory cost $40,583 $65,196

157

Question b:

Sunrise Company Financial Statements

INCOME STATEMENT

Under old inventory policy

Under new inventory policy

60 units 100 units

(given) (pro forma)

Sales (all on credit) $3,500,000 $4,500,000 unit sales x price, from assumptions

Cost of Goods Sold 2,800,000 3,600,000 unit sales x purchase price, from assumptions

Gross Profit 700,000 900,000

Inventory costs 40,583 65,196 from Tab a

Other operating expenses 100,000 128,571 increase in proportion with sales


Interest Expense 13,150 15,050 (ST Debt * ST Cost of Debt) + (LT Debt * LT Cost of Debt)


Income Taxes 218,507 276,473

Net Income $327,760 $414,709


Assets

Current Assets:

Cash & Securities $55,000 70,714 increase in proportion with sales

Accounts Receivable 105,000 135,000 increase in proportion with sales

Inventory 480,000 800,000 assumed inventory level x unit purchase price, from assumptions

Total Current Assets 640,000 1,005,714

Property, Plant & Equipment, Net

100,000 100,000 same

Total Assets $740,000 $1,105,714



Accounts Payable $100,000 128,571 increase in proportion with sales

Notes Payable 95,000 122,143 increase in proportion with sales









AFN to balance: $310,000

Question c:




Inflows:

158

Increase in Sales $1,000,000

Outflows:


Increase in Inventory Expense $24,614


Increase in Interest Expense $1,900







($310,000) $86,949 per year


19-17. Given:

Present inventory level 60

Proposed inventory level 90

Sales expected under old inventory policy: 350 units per year

Sales expected with new inventory policy: 390 units per year







Income tax rate 40%

Cost of capital 11%



Question a:


60 units 90 units

E.O.Q 15 16

Number of orders per year 23 24

Ordering cost $4,583 $4,837

Carrying cost $36,000 $54,000

Total inventory cost $40,583 $58,837

159

Question b:

Sunrise Company Financial Statements

INCOME STATEMENT


60 units 90 units

(given) (pro forma)

Sales (all on credit) $3,500,000 $3,900,000 unit sales x price, from assumptions

Cost of Goods Sold 2,800,000 3,120,000 unit sales x purchase price, from assumptions

Gross Profit 700,000 780,000

Inventory costs 40,583 58,837

Other operating expenses 100,000 111,429 increase in proportion with sales




Income Taxes 218,507 238,330

Net Income $327,760 $357,494


Assets

Current Assets:

Cash & Securities $55,000 61,286 increase in proportion with sales

Accounts Receivable 105,000 117,000 increase in proportion with sales

Inventory 480,000 720,000 assumed inventory level x unit purchase price, from assumptions



Total Assets $740,000 $998,286



Accounts Payable $100,000 111,429 increase in proportion with sales

Notes Payable 95,000 105,857 increase in proportion with sales









AFN to balance: $236,000

Question c:




Inflows:


Outflows:


160

Increase in Inventory Expense $18,255









($236,000) $29,734 per year


19-18. Given:

Inventory Level in Units Expected Sales

Present inventory level 70 340 units per year

Proposed inventory level (1) 80 375 units per year









Income tax rate 40%

Cost of capital 13%



Question a:


Under new inventory policy (1)



70 units 80 units 90 units 100 units

E.O.Q 16 17 18 18

Number of orders per year

21 22 22 22

Ordering cost $3,298 $3,464 $3,533 $3,578

Carrying cost $28,000 $32,000 $36,000 $40,000

Total inventory cost $31,298 $35,464 $39,533 $43,578

161

Question b:

Windermere Corporation

INCOME STATEMENT





70 units 80 units 90 units 100 units

(given) (pro forma) (pro forma) (pro forma)

Sales (all on credit) $5,440,000 $6,000,000 $6,240,000 $6,400,000

Cost of Goods Sold 4,352,000 4,800,000 4,992,000 5,120,000

Gross Profit 1,088,000 1,200,000 1,248,000 1,280,000

Inventory costs 31,298 35,464 39,533 43,578

Other operating expenses

130,000 143,382 149,118 152,941

Operating Income 926,702 1,021,154 1,059,350 1,083,481

Interest Expense 13,800 14,485 14,778 14,974

Before-Tax Income 912,902 1,006,669 1,044,572 1,068,508

Income Taxes 365,161 402,668 417,829 427,403

Net Income $547,741 $604,001 $626,743 $641,105


Assets

Current Assets:

Cash & Securities $65,000 71,691 74,559 76,471

Accounts Receivable 114,000 125,735 130,765 134,118

Inventory 896,000 1,024,000 1,152,000 1,280,000

Total Current Assets 1,075,000 1,221,426 1,357,324 1,490,588

Property, Plant & Equipment, Net 113,000 113,000 113,000 113,000

Total Assets $1,188,000 $1,334,426 $1,470,324 $1,603,588



Accounts Payable $110,000 121,324 126,176 129,412

Notes Payable 95,000 104,779 108,971 111,765

Total Current Liabilities 205,000 226,103 235,147 241,176

Long-Term Debt 65,000 65,000 65,000 65,000

Total Liabilities 270,000 291,103 300,147 306,176

Common Stock 80,000 80,000 80,000 80,000

Capital in Excess of Par 320,000 320,000 320,000 320,000

Retained Earnings 518,000 518,000 518,000 518,000

Total Stockholders' Equity 918,000 918,000 918,000 918,000

Total Liabilities & Equity $1,188,000 $1,209,103 $1,218,147 $1,224,176

AFN to balance: $125,324 $252,176 $379,412

Question c:

Incremental cash flows associated with the credit policy changes




80 units 90 units 100 units

Initial investment at T-0 ($125,324) ($252,176) ($379,412) Excess financing (AFN)

162


Inflows:

Increase in Sales $560,000 $800,000 $960,000

Outflows:

Increase in Cost of Goods Sold

$448,000 $640,000 $768,000

Increase in Inventory Expense $4,166 $8,234 $12,279

Increase in Other Operating Exps

$13,382 $19,118 $22,941

Increase in Interest Expense $685 $978 $1,174

Increase in Taxes $37,507 $52,668 $62,242

Total Outflows $503,740 $720,998 $866,636

Net future incremental cash flows

$56,260 $79,002 $93,364 each year from T-1 onward



Initial Investment Future Cash Flows per Year NPV at a cost of capital of 13%

Under new inventory policy (1) ($125,324) $56,260 $307,449



Comments: All three proposed inventory policy changes have positive NPVs, and would therefore

be acceptable at the firm's cost of capital of 13%. Policy #2, inventory level of 90 units, has the

highest NPV, so it should be the alternative selected.

163



1. Companies with rapidly growing levels of sales do not need to worry about raising funds from

outside the firm. Do you agree or disagree with this statement? Explain.

Disagree. Rapidly growing firms need more assets to accommodate the increasing sales. Such firms

are more likely, not less, to seek outside financing. Internal funds are often insufficient.

2. Banks like to make short-term, self-liquidating loans to businesses. Why?

Banks like to be able to see where the funds are likely to come from such that the borrower is able to

use to make the required loan payments. Short term, self-liquidating loans do this since the borrowed

funds are used to purchase assets that generate the needed funds.

3. What are compensating balances and why do banks require them from some customers? Under what

circumstances would banks be most likely to impose compensating balances?

Compensating balances are funds that a bank requires a customer to maintain in a non-interest

bearing account until the loan is retired. Banks sometimes impose compensating balance

requirements so as to increase the bank’s return on a loan. Compensating balances are most likely to

be used when the stated interest rate on a loan is below the bank’s required rate of return.

4. What happens when a bank charges discount interest on a loan?

When a bank charges discount interest on a loan the required interest payment is subtracted from the

loan proceeds at the time the loan is made. This makes the effective interest rate greater than the

stated rate.

5. What is trustworthy collateral from the lenders’ perspective? Explain whether accounts receivable

and inventory are trustworthy collateral.

Assets that are readily marketable, of stable value, and not likely to “disappear” make for trustworthy

collateral. Accounts receivable and inventory could meet this test depending upon their particular

characteristics.

6. Trade credit is free credit. Do you agree or disagree with this statement? Explain.

Trade credit is not free. It has a cost. Who bears that cost depends on the terms of the transaction

between the grantor and the recipient of the trade credit.

164

7. What are the pros and cons of commercial paper relative to bank loans for a company seeking short-

term financing?

Commercial paper is usually a cheaper source of short-term financing for a firm, compared to bank

loans. Also, a larger amount of funds can often be raised by issuing commercial paper. Bank loans

are usually a more flexible source of short-term financing and establishing an on-going business

relationship with a bank may prove beneficial when money is tight.


20-1. a) at the end of the year $1,600/$20,000 = 8%

b) at the beginning of the year (discount loan) $1,600/($20,000 - $1,600) = 8.696%

20-2. Effective annual interest = $2,400/($40,000 - $2,400 - $40,000 X 0.10)

= $2,400/$33,600 = 7.143%

20-3. a) Effective annual interest = 1,800/20,000 = 9%

b) Interest = $20,000 X 0.08 = $1,600

Effective annual interest = 1,600/(20,000-1,600) = 1,600/18,400 = 8.70%

c) Interest = $20,000 X 0.075 = $1500

Compensating balance = $20,000 X 0.10 = $2,000

Effective annual interest = $1,500/($20,000 - $2,000) = 1,500/18,000 = 8.33%

(i) Which alternative is best for Ralph from minimum effective interest rate point of view?

Alternative c

(ii) Let B be the amount Ralph should borrow

So, X - 0.1 X B = $20,000

Solving, B = $22,222.22

So, Ralph should borrow $22,222.22 and

Interest payment = 22,222.22 X .075 = $1,666.67

20-4. Interest = 14,000 X (0.16/4) = $560

Compensating Balance = 14,000 X 0.10 = $1400

Effective annual interest = {1 + [560/(14,000 - 1,400 - 560)]}4 - 1 = 19.94%

20-5. Duration of loan = 2 weeks = 1/26 year

Interest = 10,000 X (0.07/26) = $26.92

Compensating Balance = 10,000 X 0.10 = $1,000

Effective annual interest = [1 + 26.92/(10,000 - 1,000 - 26.92)]26 - 1 = 8.10%

165

20-6. a) Discount = 0.06 X $1,000,000 X 60/360 = $10,000

b) Price = $1,000,000 - $10,000 = $990,000

c) Effective annual interest rate = [$1,000,000/$990,000]365/60 - 1 = 6.305%

20-7. Discount = 0.04 X $2,000,000 X 60/360 = $13,333.33

Price = $2,000,000 - $13,333.33 = $1,986,666.67

Effective annual interest rate = [$2,000,000/$1,986,666.67]365/60 - 1 = 4.15%

20-8. [1 + 2/98]365/(45 - 15) - 1 = 27.86%

20-9. a) 3/10, n 60 [1 + 3/97]365/(60 - 10) - 1 = 24.90%

b) 2/15, n 30 [1 + 2/98]365/(30 - 15) - 1 = 63.49%

Re-calculate the costs assuming payments were made on the 40th day in each of the above cases. Compare

your results.

a) 3/10, n 60 [1 + 3/97]365/(40 - 10) - 1 = 44.86% (Higher)

b) 2/15, n 30 [1 + 2/98]365/(40 - 15) - 1 = 34.31% (Lower)

20-10. k = [1 + (3 / (100 – 3)) (365 / (45 –15))] – 1

k = .4486 = 44.86%

20.11. a) (.038 * $2,000,000 * 90) / 360 = $19,000

b) $2,000,000 - $19,000 = $1,981,000

c) ($2,000,000 / $1,981,000)(365/90) – 1 = .03947 = 3.95%

20-12. $20,000 * 0.065 = $1,300 (interest)

$1,300 / ($20,000 - $1,300) = .0695 = 6.95%

20-13. $30,000 * 0.10 = $3,000

$30,000 * 0.13 = $3,900

$3,000 / ($30,000 - $3,900) = .1149 = 11.5%

20-14. a) 1.00512 – 1 = 0.0617 = 6.17%

b) 1.00612 – 1 = 0.0744 = 7.44%

c) 1.0075 12 – 1 = 0.0938 = 9.38%

d) 1.008 12 – 1 = 0.1003 = 10.03%

166

20-15. a) [1 + 1/99]365/(45 - 10) - 1 =11.05% (Lower)

b) Interest = $100,000 X 0.10 = $10,000

Effective annual interest = $10,000/($100,000 - $10,000) = 11.11%

a is the better source since 11.11% is higher than 11.05%.

20-16. a) [1 + 1/99]365/(60 - 15) - 1 = 8.49%

b) Interest = $100,000 X 0.10 = $12,000

Compensating Balance = $100,000 X 0.12 = $12,000

Effective annual interest = $10,000/($100,000 - $10,000 - $12,000) = 12.82%

a is still the better source.

20-17. $1,500,000 / (1 - 0.09 – 0.12) = $1,898,734.18

167



1. What does it mean when the U.S. dollar weakens in the foreign exchange market?

When the U.S. dollar weakens in the foreign exchange market one U.S. dollar buys fewer units of

another country’s currency. It costs more U.S. dollars to buy a given quantity of another country’s

currency.

2. What kinds of U.S. companies would benefit most from a stronger dollar in the foreign exchange

market? Explain.

U.S. companies that import goods from other countries would benefit from a stronger dollar. More

units of a foreign currency could be purchased for a given number of dollars. Other things equal, this

would lower the cost of foreign goods for the U.S. importer.

3. Under what circumstance would the U.S. dollar and the Canadian dollar be said to have achieved

purchasing power parity?

The U.S. dollar and the Canadian dollar would be considered to have achieved purchasing power

parity when the exchange rate reflects the relative prices of a market basket of traded goods and

services at the current exchange rate. There would be no incentive to convert U.S. dollars to

Canadian dollars nor to convert Canadian dollars to U.S. dollars and purchase goods or services in

the other country.

4. What are some of the primary advantages when a corporation has operations in countries other than

its home country? What are some of the risks?

Foreign operations may reduce a company’s labor or material costs, and may increase its sales.

Risks include possible seizure of company assets by a foreign government, possible cultural blunders

that lead to lost sales, and exchange rate risks.

5. What is GATT, and what is its goal?

GATT is the General Agreement on Tariffs and Trade. It is a treaty that seeks to reduce trade

barriers among participant nations.

168


21-1. a) British pound 1,000,000/1.8508 = £540,307

b) Indian rupee 1/.02122 = Rs47.125 million

c) Japanese yen 1/.008800 = ¥113.636 million

d) Australian dollar 1/.7514 = A$1.331 million

e) Mexican peso 1/.0900 = Peso 11.111 million

f) Israeli shekel 1/.2315 = Shekel 4.320 million

21-2. a) Chilean pesos 1/.001855 = Pesos 539.084 million

b) HK dollars 1/.1287 = HK$7.770 million

c) Singaporean dollars 1/.6321 = S$1.582 million

d) euros 1,000,000/1.2810 = 780,640.12

e) Indian rupees 1/.02122 = Rs47.125 million

f) Mexican pesos 1/.0900 = Peso 11.111 million

g)Thai bahts 1/.0314 = Baht 31.847 million

21-3. a) 2 million Australian dollars 2 X 0.7514 = $1,502,800

b) 1.6 million Singaporean dollars 1.6 X 0.6321 = $1,011,360

c) 5 million euros 5 X 1.2810 = $6,405,000

d) 2.6 million Mexican pesos 2.6 X 0.0900 = $234,000

e) 2 million Japanese yen 2 X 0.00880 = $16,000

f) 25 million Thai bahts 25 X 0.02186 = $546,500

21-4. a) 1.2810

b) (1) $100,000 * 113.6363636 = 11,363,636

(2) $100,000 * 0.540306894 = 54,031

(3) $100,000 * 1.113957892 = 111,396

(4) $100,000 * 11.1111111 = 1,111,111

21-5. a) 113.6363636 * 0.0900 = 10.2273 ¥ / peso

b) 11.1111111 * 1.8508 = 20.5644 pesos / ₤

c) .780640125 * 0.8977 = 0.7008 € / Canadian Dollar

d) 113.6363636 * 0.8977 = 102.0114 ¥ / Canadian Dollar

21-6. 0.6471 X 1/0.2003 = 3.23

21-7. 1 euro = 58 rupees = 9.67 HK dollars

1 HK dollar = 58/9.67 = 6.00 rupees

21-8. 1 British pound = 16.9 Mexican pesos = 2.8 Singapore dollars

10 million Mexican pesos = 10 X 2.8/16.9 = 1.657 million Singapore dollars

169

21-9. If one British pound is equivalent to 1.5 euros, and one euro can purchase 60 baht, how many baht

can one purchase with 1 million British pounds?

1 British pound = 1.5 euros = 60 X 1.5 = 90 baht

1 million British pounds = 90 million baht

21-10. British pound = 1.5 euros; .8 X 1.5 euros = 1.2 dinars; 1.2 dinars X 160 yen

= 192 yen;

1 million British pounds = 192 million yen

21-11. a) 16.5 * 1/.9188 = $17.96 per share

$17.96 * 100 = $1,796

b) 16.5 * 1/.70 = $23.57 per share

$23.57 * 100 = $2,357

c) 16.5 * 1/1.212 = $13.61 per share

$13.61 * 100 = $1,361

21-12. 55,150 * 1.020408163 = $56,275.51

21-13. 230,000 ¥ / $2,000 = 115 ¥ / $

21-14. Initial Investment = $100,000

Current Value = $100,000 X 119/100 = $119,000

Return on Investment = ($119,000 - $100,000)/$100,000 = 19%

21-15. Initial Investment = 1,000 shares X $37/shareXRs42/$ = Rs1,554,000

Current Value = 1,000 shares X $37/shareXRs44/$ = Rs1,628,000

Return on Investment = (Rs1,628,000 - Rs1,554,000)/Rs1,554,000 = 4.76%

Date post:	20-Jul-2015
Category:	Business
Upload:	indrahayuni
View:	73 times
Download:	0 times