Post on 30-Nov-2015
description
transcript
RMIT International University- BAFI 3184
Exercise booklet 1
Exercise booklet
RMIT International University- BAFI 3184
Exercise booklet 2
Course guideCourse guideCourse guideCourse guide
Introduction
The theory of finance stems from the broad area of applied economics. Over the past thirty or so years extensive research and theoretical developments have resulted in the emergence of this discipline as a science in its own right. Today, the theory of finance is a field that equips the individual with techniques and skills that ensure the objective analysis and evaluation of alternatives, resulting in effective financial decision-making. These techniques and skills are applicable in a number of sectors of our economy, namely financial markets (including financial products such as derivative instruments), financial institutions and the financial management of companies.
The theory of finance plays a significant role in the area of business, or corporate, finance. The effective financial management of firms, large or small, private or publicly listed, is paramount for the wellbeing of any economy. However, not only does its importance lie in its benefit to the economy as a whole, but it is vital that financial managers are capable of developing sound financial policies for the benefit of the firm itself and its owners, the shareholders. Financial managers must have a sound framework that will provide the analytical tools to competently evaluate alternatives and make objective decisions both in the short term and in the long term. Investment options and financing choices must be analysed and assessed using techniques that have a solid theoretical base.
Business Finance provides an introduction to some of the key skills required for good financial management. It introduces financial concepts and issues that will provide the necessary guidelines to solve many corporate finance problems. It also introduces some of the more important theories in modern finance to provide a substantial grounding in the discipline.
Business Finance is a second year course and consequently is taught on the assumption that students
have an understanding of the basic concepts, principles and analytic techniques found in the
introductory courses in the fields of statistics and microeconomics.
You are requested to ensure that you are correctly enrolled in this course by checking that it appears on
your enrolment confirmation. If the course code does not appear, you will not have a result recorded for
this course. Please see the School’s student administration officer at once if you are not correctly
enrolled in this course.
RMIT International University- BAFI 3184
Exercise booklet 3
A. Course Identification
Course code: BAFI-3184
Course name: Business Finance
Duration: one semester
Credit points: 12 credit points
Contact hours: class contact - 3 hours per week comprising lectures and tutorials.
B. Course Outline
Topic 1: Introduction - Overview of Business/Corporate Finance
Topic 2: First Principles of Valuation: Financial Mathematics/Time Value of Money
Topic 3: Valuation of Bonds and Shares
Topic 4: Capital Budgeting/Project Evaluation
Topic 5: Risk and Return
Topic 6: Weighted Average Cost of Capital (WACC)
Topic 7: Capital Structure
C. Objectives/Learning Outcomes
At the conclusion of this course you should be able to:
a. demonstrate an understanding of fundamental concepts in finance b. apply the ideas of time value of money for decision making c. understand why wealth maximisation is an appropriate corporate goal d. assess the impact of interest rates on business decisions e. demonstrate an understanding of the concepts of portfolio theory and competence in calculating
portfolio returns and risk f. understand the applicability of the Capital Asset Pricing Model to share valuation g. determine whether shares are under/overvalued h. understand and use valuation models for equity, debt instruments and the firm as a whole
RMIT International University- BAFI 3184
Exercise booklet 4
i. understand the advantages and disadvantages of the most commonly used methods of investment evaluation
j. differentiate between the various costs of capital and calculate these costs k. evaluate the profitability of potential investments, using the net present value method l. understand the importance of capital structure in decision making
D. Prescribed Text
Frino, A., Hill, A., and Chen, Z., , Introduction To Corporate Finance, 4th Ed., Pearson Education Australia, Sydney, 2009.
myfinancelab e-workbook available at www.pearsoned.com.au/myfinancelab
E. Reference Texts
Bishop, S., Faff, R., Oliver, B., and Twite, G., Corporate Finance, 5th Ed., Pearson Education Australia, Sydney, 2004.
Correia, C., Mayall, P., O’Grady, B., and Pang, J., Corporate Financial Management, 2nd Ed., Skystone Investments Pty Ltd, Perth, 2005.
Peirson, G., Brown, R., Easton, S., and Howard, P., Business Finance, 8th Ed., McGraw-Hill, Sydney, 2002.
Petty, J., Keown, A., Scott Jr., D, Martin, J., Martin, P., Burrow, M., and Nguyen, H., Financial
Management, 4th Ed., Pearson Education Australia, Sydney, 2006.
Ross, S., Thompson, S., Christensen, M., Westerfield, R., and Jordan, B., Fundamentals of Corporate
Finance, 3rd Ed., McGraw-Hill/Irwin, Sydney, 2004.
E. Assessment schedule
Assessment Weight Release date Due date Topics covered
In-Class quiz 1 5% (TBA) TBA
In-Class quiz 2 5% (TBA) TBA
Midterm 20% Week 7/8 (TBA) 1-4
Homework assignment 1 5% TBA TBA
Homework assignment 2 5% TBA TBA
Final exam 60% Week 13/14 1-7
RMIT International University- BAFI 3184
Exercise booklet 5
TOPIC 2: Time value of moneyTOPIC 2: Time value of moneyTOPIC 2: Time value of moneyTOPIC 2: Time value of money
--------------------------------------------------------------------------------------------
Question 1
If you placed $1000 in a bank for one year, how much would you have accumulated in one year if the
rate of return was 6.75%?
Question 2
What is the rate of return on an asset priced at $4695 today that will pay $5000 in one year?
Question 3
Would you pay $98,000 today for an asset that will pay $105,000 in one year if the rate of return is
currently 6% p.a. Explain.
Question 4
You bought a share at $10 which promised a dividend of $1.5 at the end of year 1. It is also expected
that you can sell the share at $16 at the end of year 1. What is the rate of return on this investment?
Question 5
$100 to be received at the end of 3 years is worth how much today, assuming a discount rate of
(i) 10 per cent
(ii) 100 per cent
(iii) 0 per cent?
Question 6
Would you rather receive $1,000 today or $2,000 in 10 years? Assume a discount rate of 8 percent?
Question 7
You have $30,000 today. You want to deposit in a bank at a simple interest rate of 10% for 4 years.
How much of interest will you receive at the end of year 4?
Question 8
You wish to place $1000 in a bank account for five years, at an interest rate of 7% p.a. How much
would you accumulate after five years assuming (a) simple interest and (b) compound interest? Explain
the difference between (a) and (b)
RMIT International University- BAFI 3184
Exercise booklet 6
Question 9
An investment repays $40,000 in five years and a further $60,000 in ten years. If the interest rate over
the period of investment is 12% p.a, compounded monthly, what is the investment’s present value?
Question 10
You are the lucky winner of yours state’s lottery of $5 million after taxes. You invest your winning in a
five year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7 percent
per year compounded annually. This institution also let you reinvest the interest at that rate for the
duration of the CD. How much will you have at the end of five years?
Question 11
An institution offers you the following terms for a contract. For an investment of ¥2,500,000, the
institution promises to pay you a lump sum six years from now at an 8 percent annual interest rate.
What future amount can you expect?
Question 12
An Australian bank offers to pay you 6 percent compounded monthly. You decide to invest A$1
million for one year. What is the future value of your investment if interest payments are reinvested at
6 percent?
Question 13
Your grandmother has a debt that she may repay by paying $5,000 now or $10,000 in four years’ time.
If the interest rate is 14% compounded monthly, would you advise her to repay the debt now or in four
years.
Question 14
What is the amount of money a person must be given now to make them indifferent to receiving a
stream of 10 annual payments of $70 each, where the first payment is received immediately. Assume
the interest rate is 12%.
Question 15
How much would you pay for an investment which will help you earn an annual cash flow of $100 for
10 years given the interest rate of 15%?
Question 16
If Miss Smith is offered the choice of:
(iv) (a) $628.06 now; or
RMIT International University- BAFI 3184
Exercise booklet 7
(v) (b) $50 per quarter for four years at 12% per annum compounded
quarterly; or
(vi) (c) $1007.85 at the end of four years;
Assume that three investments are compounded quarterly, which alternative should you recommend
that she accept?
Question 17
A four year security is selling today for $25,000. The applicable interest rate is 8% and the security
offers an equal annual cash flow at the end of each year. What cash flow would the purchaser of this
security receive each year?
Question 18
Ms. Lan Huong wants to invest in raw land. She expects to own the property for 10 years and to sell it
at the end of the 10th year for $5 million. There are no other cash flows. What is the most she would be
willing to pay for the property if the appropriate discount rate is 12 percent?
Question 19
Suppose you deposit $1,000 in an account at the end of each of the next four years. If the account earns
12 percent annually, how much will be in the account at the end of seven years?
Question 20
After 3 years, how much will a $20,000 investment earning 11%, compounded quarterly accumulate
to? What is the effective interest rate?
Question 21
Your friend is celebrating his 35th birthday today and wants to start saving for his anticipated
retirement at age 65.
He wants to be able to withdraw $10,000 from his savings account on each birthday for 10 years
following his retirement; the first withdrawal will be on his 66th birthday.
Your friend intends to invest his money in the local savings bank, which offers 8 per cent interest per
year.
He wants to make equal, annual payments on each birthday in a new savings account he will establish
for his retirement fund. What are annual payments he needs to make from 36th birthday till 65th birthday
to meet his retirement spending?
RMIT International University- BAFI 3184
Exercise booklet 8
Question 22
A well-known insurance company offers a policy known as the ‘estate creator six pay’.
Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of
the policy are as follows:
The purchaser (say, the parent) makes the following six payments to the insurance company:
1st birthday $730 4th birthday $855
2nd birthday $730 5th birthday $855
3rd birthday $730 6th birthday $855
After the child’s 6th birthday, no more payments are made.
When the child reaches age 65, he or she receives $143,723.
If the relevant interest rate is 6 percent for the first 6 years and 7 per cent for all subsequent years, is the
policy worth buying?
Question 23
John H. Faustus, a naive business student, is considering an offer from Mephistopheles calling for 20
payments of $10,000.
The first payment will be 15 years from today.
Owing to an unexpected strike at the Hades Mint, the payment 17 years from today will be skipped;
however, $20,000 will be paid 18 years from today to make up for the skipped year.
No other gap in yearly payments will be allowed.
Discounting at 10%, Faustus wants to know the present value of the series of payments.
Question 24
Calculate an equivalent annual income for 20 years on the following income stream received over 30
years if the interest rate is 10% per annum compounded annually.
Year Income stream p.a
1 to 15 $15,000
16 to 20 $20,000
RMIT International University- BAFI 3184
Exercise booklet 9
21 to 30 $25,000
Question 25
Warren Reed just turned 40. He has decided that he would like to retire when he is 65.
He thinks that he will need $1,500,000 in his special retirement account at age 65 to maintain his
current lifestyle.
For the next 15 years he can afford to put $12,000 per year into the account.
At age 55 he will need to withdraw $40,000 to purchase membership in the local country club.
The retirement account earns 11% compounded annually.
Required:
How much will Warren’s account will be worth at age 55?
What will be the value of the account when Warren is age 65?
How much will Warren need to deposit into the retirement account each year for the last ten years of
his work career to attain the $1,500,000 goal?
Question 26
Assume you have won first prize in a national lottery and, as a consequence, you will receive an
annuity of $5,000 every six months for 10 years.
You will receive the first payment three years from today.
Required:
a) Determine the present value of this annuity if the required rate of return is 10 percent per annum?
b) If the organisers of the lottery offer you a lump sum of $50,000 today instead of the annuity, would
you accept the offer? Why or why not? Explain your answer.
Question 27
X originally borrowed $25,000 from the bank to be repaid over 15 years, at a nominal annual rate of
interest of 10%, compounded quarterly.
The bank now advises that the interest rate has increased to 12% per annum, compounded quarterly.
There is still 10 years to go before the loan is fully repaid.
(a) What are the present quarterly payments?
RMIT International University- BAFI 3184
Exercise booklet 10
(b) How much will the quarterly payments be after the interest rate rise?
Question 28
X borrows $20,000 to buy a house.
The loan involves equal annual repayments over 20 years and r = 10 %
(a) How much are the annual repayments?
(b) What is the value of the interest element of the 14th repayment?
(c) How much is needed to pay off the loan at the time of the 16th repayment assuming the 16th
repayment has not been made?
Question 29
You are considering the purchase of a new car at a total on-the-road cost of $12,500.
After saving diligently you have accumulated a deposit of $6,500.
Two alternatives are available to you to raise the remaining $6,000 required.
Alternative 1:
A personal loan of $6,000 from the ZNA Bank at the "low cost of 10% pa". Upon further enquiry, you
establish that interest is compounded quarterly.
Alternative 2:
The car dealer can arrange a hire - purchase agreement for the remaining $6,000. Repayments would
be $232.49 per month for two and a half years.
Required:
Which alternative provides the cheapest means of financing?
Question 30
Suppose your company’s defined contribution retirement plan allows you to invest up to €20,000 per
year. You plan to invest €20,000 per year in a stock index fund for the next 30 years. Historically, this
fund has earned 9 percent per year on average. Assuming that you actually earn 9 percent a year, how
much money will you have available for retirement after making the last payment?
Question 31
An insurance company has issued a Guaranteed Investment Contract (GIC) that promises to pay
$100,000 in six years with an 8 percent return rate. What amount of money must the insurer invest
today at 8 percent for six years to make the promised payment?
RMIT International University- BAFI 3184
Exercise booklet 11
Question 32
Suppose you own a liquid financial asset that will pay you $100,000 in 10 years from today. Your
daughter plans to attend college four years from today, and you want to know what the asset’s present
value will be at that time. Given an 8 percent discount rate, what will the asset be worth four years from
today?
Question 33
The manager of a Canadian pension fund knows that the fund must make a lump sum payment of C$5
million 10 years from now. She wants to invest an amount today in a GIC so that it will grow to the
required amount. The current interest rate of GICs is 6 percent a year, compounded monthly. How
much should she invest today in the GIC?
Question 34
Suppose you are considering purchasing a financial asset that promises to pay €1,000 per year for five
years, with the first payment one year from now. The required rate of return is 12 percent per year.
How much should you pay for this asset?
Question 35
You are retiring today and must choose to take your retirement benefits either as a lump sum or as an
annuity. Your company’s benefits officer presents you with two alternatives: an immediate lump sum
of $2 million or an annuity with 20 payments of $200,000 a year with the first payment starting today.
The interest rate at your bank is 7 percent per year compounded annually. Which option has the greater
present value?
Question 36
At retirement, a client has two payment options: a 20-year annuity at €40,000 per year starting after one
year or a lump sum of €500,000 today. If the client’s required rate of return on retirement fund
investment is 6 percent per year, which plan has higher present value and by how much?
Question 37
A German pension fund manager anticipates that benefits of €1 million per year must be paid to
retirees. Retirements will not occur until 10 years from now at time t=10. Once benefits begin to be
paid, they will extend until t=39 for a total of 30 payments. What is the present value of the pension
liability if the appropriate annual discount rate for plan liabilities is 5 percent compounded annually?
Question 38
RMIT International University- BAFI 3184
Exercise booklet 12
The British government once issued a type of security called a consol bond, which promises to pay a
level of cash flow indefinitely. If a consol bond paid £100 per year, what would it be worth today if the
required rate of return were 5 percent?
Question 39
Consider a level perpetuity of £100 per year with its first payment beginning at t=5. What is its present
value today (at t=0), given a 5 percent discount rate?
Question 40
You are planning to purchase a $120,000 house by making a down payment of $20,000 and borrowing
the remainder with a 30-year fixed rate mortgage with monthly payments. The first payment is due at
t=1. Current mortgage interest rates are quoted at 8 percent with monthly compounding. What will your
monthly mortgage payments be?
Question 41
Jill Grant is 22 years old (at t=0) and is planning for her retirement at age 63 (at t=41). She plans to
save $2,000 per year for the next 15 years (t=1 to t=15). She wants to have retirement income of
$100,000 per year for 20 years, with the first retirement payment starting at t=41. How much must
Grant save each year from t=16 to t=40 in order to achieve her retirement goal? Assume she plans to
invest in a diversified stock-and-bond mutual fund that will earn 8 percent per year on average?
Question 42
Suppose you plan to send your daughter to college in three years. You expect her to earn two thirds of
her tuition payment in scholarship money, so you estimate that your payments will be $10,000 a year
for 4 years. Assume that you can earn 8 percent annually on your investment. How much should you
set aside now to cover these payment?
RMIT International University- BAFI 3184
Exercise booklet 13
TOPIC 3: VALUATION OF BONDS AND STOPIC 3: VALUATION OF BONDS AND STOPIC 3: VALUATION OF BONDS AND STOPIC 3: VALUATION OF BONDS AND SHARESHARESHARESHARES
--------------------------------------------------------------------------------------------------------
Question 43
Lisholm Ltd has issued bonds earning a 7 percent coupon rate. The interest is paid semi-annually and
the bonds mature in eight years. The bond face value is $1,000.
If your required rate of return is 8 per cent, what is the current price of the bond?
Question 44
You have some money to invest and you are considering purchasing unsecured notes (a bond-type
instrument) that have been issued by St Marks Ltd. The notes mature in five year time and have a
coupon rate of 10.75%, with coupons paid annually. What price (value) would you be prepared to pay
for the notes if your required rate of return is 10% per annum?
Question 45
You have some money to invest and you are considering purchasing unsecured notes (a bond-type
instrument) that have been issued by St Marks Ltd. The notes mature in five year time and have a
coupon rate of 10.75%, with coupons paid semi-annually. What price (value) would you be prepared to
pay for the notes if your required rate of return is 10% per annum?
Question 46
Abner Corporation’s bonds matures in 15 years and pay 9% annual coupons. If you purchased the
bonds for $1,250, what is your expected rate of return?
Question 47
An issue of Australian treasury bonds with par of $1,000 matures in 15 years and pays 8% interest
annually. The market price of the bonds is $1,085 and your required rate of return is 10%?
(a) Compute the bond’s expected rate of return
(b) Determine the value of the bond to you, given your required rate of return
(c) Should you purchase the bond?
Question 48
You have just purchased 10 newly issued $100 five year ABC Company Ltd. debentures at par.
These debentures pay $6 (per debenture) in interest semi-annually.
RMIT International University- BAFI 3184
Exercise booklet 14
You are also negotiating the purchase of 10 $100 debentures issued by the DEF Company Ltd. 4 years
ago, that return $3 per debenture in semi-annual interest payments and have six years remaining to
maturity.
What is the maximum price you should offer for the DEF Company Ltd. Debentures, assuming the
DEF company is in the same risk class as the ABC company?
Question 49
A debt security has a face value of $20,000 that will pay $1,500 interest annually for five years. The
required rates of return are 4% for the first year, 6% for the second year, 3% for the third year and 5%
for the fourth year and 4.5% for fifth year. What is the debt security’s price?
Question 50
Consider the following four bonds:
Bond Years to Maturity Coupon rate (% p.a.)
A 2 10
B 3 12
C 3 10
D 3 8
Each bond has a face value of $100 pays interest twice a year and the current market interest rate is 9
per cent per annum.
• Calculate the current price of each bond
• Calculate what the price of each bond would be if the market interest rate increased to 11 per
cent per annum.
• What would be the percentage capital loss on each bond?
• Keeping the Coupon rate constant what is the relationship between the change in price and the
time to maturity?
• Keeping the time to maturity constant what is the relationship between the change in price and
the coupon rate?
Question 51
The current interest rates on government bonds are as follows;
RMIT International University- BAFI 3184
Exercise booklet 15
Years to maturity Interest rate (% p.a.)
1 6.00
2 6.50
3 6.90
4 7.20
5 7.40
Assume that the term structure of interest rates can be explained by the expectations theory, of future
interest rates. Calculate the expected 1-year interest rates for the next 4 years.
Explain why it is not possible in this market for the interest rate on government bonds with 6 years to
maturity to be 6 per cent per annum.
Question 52
If at t=0 the one period rate of interest is 6% , the two year is 8% per annum and the three year rate is
10% per annum what is the expected two period interest rate expected to prevail at t=1?
Question 53
You buy a two year bond with an interest rate of 7%. In year 5, you plan to purchase another two year
bond with an interest rate of 9%. What is the interest rate of three year bond sold in year 2 according to
expectation theory given the 7 year-bond rate of 8.5%.
Question 54
Gromixs Ltd is experiencing a period of rapid growth. Earnings and dividends are expected to grow at
a rate of 18 per cent during the next two years, 15 per cent in the third year, and then at a constant rate
of 6 per cent thereafter. Gromix’s last dividend, which has just been paid, was $0.115. If the required
return on the shares is 12 per cent, what is the price of a share today?
Question 55
Newsite Ltd is expanding rapidly. Its dividend growth rate for the coming year is projected at 25 per
cent. This rate will decline by 5 percentage points per year until it reaches the industry average of 5 per
cent. Once it reaches 5 per cent, it will stay there indefinitely. The most recent dividend was $0.85 per
share, and the market requires a return of 16 per cent on investments such as this one. What is the price
per share for Newsite?
RMIT International University- BAFI 3184
Exercise booklet 16
Question 56
You have predicted the following dividends for the next three years on Noitall’s Production’s
shares:
Year Projected dividend
1 $0.50
2 0.60
3 0.70
Beginning in the fourth year, you project that the dividend will grow at an 8 per cent rate
indefinitely. The required return is 15 per cent.
Calculate the price today P0
Calculate the prices P1 P2 P3
Calculate the dividend yield and capital gains yield in each of the first four years. What do you
observe?
Question 57
Atorus Pty Ltd last paid a dividend of $0.30 per share.
This dividend is expected to grow at 12% per annum for three years, then at 10% per annum for the
next three years, after which it is expected to grow at a 4% rate forever.
Required:
What is the price you would pay for the share if your required rate of return is 8%?
Would the price change if you expected to hold the share for only three years? Explain.
Question 58
In the year ended December 2007, National Australia Bank (NAB) generated EPS of 269 cents, paid a
dividend of 182 cents per share and its return on (book) equity was estimated at 17%. Assuming that
ROE and the payout ratio of NAB are stable, what is its expected future earnings and dividend growth
rate?
Question 59
BBB Ltd is a shoe manufacturing business. Its finance manager expects earnings of $0.75 per share at
the end of this year and has forecast that these earnings will growth at a rate of 4% p.a in perpetuity.
The company’s historical dividend payout ratio has been constant at 60% of EPS and is expected to
RMIT International University- BAFI 3184
Exercise booklet 17
remain at that level. At what price should BBB Ltd shares be trading if the required return on equity is
12% p.a?
Question 60
Suppose that an investor is contemplating at the beginning of the year the purchase of RMI Ltd.
ordinary shares and has gathered the following data. At the end of the year RMI is expected to pay an
ordinary share dividend of $1.64 and the market price for each share is projected to be $22. The rate of
return required by the company’s ordinary shareholders is 18%. Determine the intrinsic value of RMI
ordinary shares?
Question 61
An ordinary share has just paid a $2 dividend to shareholders and is expected to continue paying
dividends every year from now to infinity, with the dividend amount expected to grow at a rate of 10%
per annum. Based on an assessment of the riskiness of the shares, the rate of return required by
investors is 15%. What should the price of share be?
Question 62
You intend to purchase Marigo Ltd’s ordinary shares at $50 per share, hold them for one year, and sell
after a dividend of $6 is paid. How much will the share price have to appreciate if your required rate of
return is 15%?
Question 63
Wayne Co.’s outstanding ordinary shares are currently selling in the market for $33. Dividends of
$2.30 per share were paid last year, and the company expects annual earnings and dividend growth to
be 5% per annum.
(a) Given that you require a 15% rate of return, what is the value of a share to you?
(b) Determine the return that can be expected from a Wayne Co. share
(c) Should you purchase Wayne Co. shares
RMIT International University- BAFI 3184
Exercise booklet 18
TOPIC 4: CAPITAL BUDGETING/PROJECT VALUATIONTOPIC 4: CAPITAL BUDGETING/PROJECT VALUATIONTOPIC 4: CAPITAL BUDGETING/PROJECT VALUATIONTOPIC 4: CAPITAL BUDGETING/PROJECT VALUATION
------------------------------------------------------------------------------------------------------------------------------------------------
Question 64
What is the payback if the initial investment is $60,000 and the cash flows are:
Year 1 $20,000
Year 2 $25,000
Year 3 $30,000
Year 4 $10,000
Year 5 $ 5,000
Question 65
Year 0 1 2 3 4
Net cash flows ?? 1500 2500 3000 1500
The payback period is 2.5 years and the cost of capital is 11%. What is the NPV of this project?
Question 66
A firm with a cost of capital of 15% is evaluating three projects. The rates of return for each project are
as follows:
Project 1 IRR = 14%
Project 2 IRR = 17%
Project 3 IRR = 16%
Question 67
An investment of $100,000 is expected to generate an after-tax cash flow of $40 in year 1, $80 in year
2, and $120 in year 3. The required rate of return is 20 percent. What is the net present value?
Question 68
Kim Corporation is considering an investment of 750 million won with expected after-tax cash inflows
of 175 million won per year for seven years. What is the project’s payback period?
RMIT International University- BAFI 3184
Exercise booklet 19
Question 69
Shirley Shea has evaluated an investment proposal and found that its pay-back period is one year, it has
a negative NPV and it has a positive IRR. Is this combination of results possible?
Question 70
Project 1 and 2 have similar outlays, although the patterns of future cashflows are different. The cash
flows as well as the NPV and IRR for the two projects are shown below. For both projects, the required
rate of return is 10 percent.
Cash flow
Year 0 1 2 3 4 NPV IRR
Project 1 -50 20 20 20 20 13.4 21.86%
Project 2 -50 0 0 0 100 18.3 18.92%
If the two projects are mutually exclusive, what is the appropriate investment decision?
If the two projects are independent, what is the appropriate investment decision?
Question 71
You are evaluating a project that requires an initial investment of $350,000, and which will provide a
net cash flow of $30,000 during the first year. The net cashflow is projected to grow at 8% p.a
constantly forever. Assuming the cost of capital is 15%:
(a) Is this project acceptable?
(b) If you are uncertain about the projected 8% growth rate, at what constant growth rate will the
company just break even?
Question 72
The Salte Corporation is an Australian-based company with a large proportion of foreign shareholders.
Its core business is the production of machinery used in the heavy-industry sector. It has recently
completed a $400,000 two year marketing study on whether to introduce a new machine to the market.
Based on the results of the study, Salte has estimated that 10,000 of its new machines can be sold
annually over the next six years at a price of $9,615 each. Variable costs per machine are $7,400 and
fixed costs total $12 million a year. Working capital specifically for this project is estimated to be $2
million and will be returned at the end of the project’s life.
The cost of the machine includes $40 million to build production facilities and $2.4 million in land.
The $40 million investment will be depreciated to zero over the life of the project. At the end of the
RMIT International University- BAFI 3184
Exercise booklet 20
project the facilities, including the land, will be sold for an estimated $8.4 million. The market value of
the land, which is not tax-deductible, is not expected to change.
Finally, start-up costs also entail fully tax-deductable expenses of $1.4 million, which are deductable at
the end of the first year of production. The tax rate applicable to Salte is 30%. The after-tax discount
rate is 10%.
Calculate the NPV of the project and advise Salte whether it should proceed with the project.
Question 73
A company has the opportunity of buying a new high-tech metal cutter that will save the company
$14,000 each year in labour costs. This metal cutter will cost $70,000 and will have a useful life of 7
years. It is expected to have a salvage value of $16,000 and will be depreciated using a straight-line
method of depreciation.
If the company purchases the metal cutter it can sell its old cutter for $5,000, even though it has a book
value for tax purposes of $8,000.
The new machine will require a working capital injection of $4,500 for the acquisition of additional
scrap metal. The working capital will be recovered at the end of the 7 year period. The company’s
required rate of return is 10% and the tax rate is 30%.
Should the company acquire the new metal cutter?
Question 74
You have been observing the surge in health awareness in Australia for some time and realise the time
is right to start and run an aerobic fitness centre. Your family owns a wharehouse which will meet your
needs, and is currently being rented out at $48,000 p.a.You estimate you will need to spend $100,000 in
total, made up of an initial cost of $50,000 to renovate the premises, $45,000 for new equipment, and
$5,000 to install the equipment. You have done a market survey, at a cost of $3,000, which leads you to
believe that you will get 500 memebers each paying $1,000 p.a.
You have also found five instructors you can hire at $30,000 each p.a. For tax reasons you will expense
the renovation costs immediately and depreciate the equipment 9including the installation cost) over
ten years using the straight-line method. Howver, you will expect the equipment to be fully functional
for 15 years, which is the life of the operation. Due to the nature of fitness equipment it will be unlikely
to have a salvage value at the end of ten years. Assume the initial investment is made today and all
cash-flows are received or paid at the end of each year. Your discount rate is 15% and your tax rate is
40%.
Should you invest in the project?
RMIT International University- BAFI 3184
Exercise booklet 21
Question 75
What is the present value at a 15 percent discount rate of depreciation tax shield which occurs in the
third year for a firm in the 40 percent tax bracket that purchases a $50,000 asset being depreciated
straight line over ten years to zero salvage value?
Question 76
Firm X borrows $40,000 which will be repaid in terms of annual payment for next 5 years. At an
discount rate of 10%, what is the interest tax shield’s present value?
RMIT International University- BAFI 3184
Exercise booklet 22
TOPIC 5: RISK AND RETURNTOPIC 5: RISK AND RETURNTOPIC 5: RISK AND RETURNTOPIC 5: RISK AND RETURN
----------------------------------------------------------------------------------------------------------------
Question 77
You are given the following information about the possible returns from an investment.
Return Probabilities
12% .15
9% .60
6% .25
Required:
(a) Calculate the expected return
(b) Calculate the variance of the return
(c) Calculate the standard deviation of the return.
Question 78
An investor invests 40 per cent of her funds in Company A's shares and the remainder in Company B's
shares. The standard deviation of the returns on A is 20 per cent and on B is 10 per cent. Calculate the
variance of return on the portfolio assuming the correlation between the returns on the two securities is:
A) +1.0
B) +0.5
C) 0
D) -0.5
RMIT International University- BAFI 3184
Exercise booklet 23
Question 79
Consider the following information:
Economy Probability Share A
Returns
Share B
Returns
Share C
Returns
Boom .40 10% 15% 20%
Bust .60 8% 4% 0%
a) What are the expected returns on the three shares? What are the standard deviations of the three
shares?
b) What is the expected return on an equally weighted portfolio of the three shares?
Question 80
Assume you have obtained forecasts of the following data on three securities, (as well as the market
portfolio and the risk less asset) in a large and well-traded securities market. Calculate the expected
return and standard deviation of return on the following portfolios? Which portfolio is preferable?
Portfolio X 40% A 0% B 60% C
Portfolio Y 20% A 30% B 50% C
Return SD A B C M
Correlation Matrix
Security A 0.09 0.24 1.0 0.4 0.5 0.6 0.0
Security B 0.10 0.18 0.4 1.0 0.8 0.7 0.0
Security C 0.06 0.15 0.5 0.8 1.0 0.8 0.0
Market
Portfolio(M)
0.15
0.12
0.6
0.7
0.8
1.0
0.0
RisklessAsset (F) 0.10 0.00 0.0 0.0 0.0 0.0 1.0
RMIT International University- BAFI 3184
Exercise booklet 24
Question 81 a) If the expected return on the market is 12% while the risk-free rate is 5%, does the following
description of securities constitute an equilibrium situation?
Security Actual
Return
ββββ i
1 15.5% 1.5
2 6.4% 0.2
3 1.5% -0.5
4 9.5% 0.8
5 14.8% 1.2
b) For those securities that are not in equilibrium, are the securities expected to rise in price or fall in price?
Question 82
Asset A has an expect return of 10% and a beta of 1.2.
Asset B has an expected return of 14% and a beta of 1.4
a) If the risk free rate is 6% what is the reward to risk ratio for Asset A? b) If the risk free rate is 6% what is the reward to risk ratio for Asset B? c) Expalin why Asset B is undervalued or overvalued compared to Asset A.
Question 83
Consider two investors, Henry and John, each of whom have $100,000 to invest. Both investors wish to
hold a well-diversified portfolio which comprises some cash and fixed interest and some growth assets.
They have both selected a growth fund which has an annual expected return of 16% and a standard
deviation of 12%. The return on 90-day treasury bonds is a proxy for the risk free rate of interest and is
currently 6%. Their concern is in determining the proportion of their investment that they will place in
the growth fund and the proportion they will place in cash and fixed interest (“risk-free” assets).
RMIT International University- BAFI 3184
Exercise booklet 25
Henry is relatively risk tolerant and you have been able to determine that he would be comfortable with
his total portfolio having a standard deviation of 10%. John is relatively risk averse. He is only
comfortable with a standard deviation in his portfolio of 7%.
Question 84 You have obtained forecasts of the following data on three securities, the market portfolio and the risk-
free asset in a large and well-traded securities market.
Correlation Matrix
E(Ri) σ(Ri) A B C M F
Security A 0.08 0.14 1.0 0.3 0.7 0.5 0
Security B 0.1 0.16 0.3 1.0 0.4 0.6 0
Security C 0.13 0.2 0.7 0.4 1.0 0.8 0
Market Portfolio M 0.1 0.1 0.5 0.6 0.8 1.0 0
Risk-free Asset F 0.05 0 0 0 0 0 1.0
You are contemplating investing in a portfolio with the following asset weights:
Weight
Security A 40%
Security B 25%
Security C 35%
Required:
(a) Calculate the standard deviation of the portfolio. (b) Calculate the beta coefficient of Securities A, B and C. (c) Calculate the equilibrium returns for Securities A, B and C based on the Capital Asset Pricing
Model. (d) State whether Securities A, B and C are correctly priced, underpriced or overpriced based on the
CAPM.
RMIT International University- BAFI 3184
Exercise booklet 26
EFFICIENT MARKET HYPOTHESIS
------------------------------
Question 85
Assume that the Australian stock market is weak-form efficient only. Which of the following
situations should not provide an opportunity to earn excess (abnormal) returns? Explain
your answers.
(a) Your investment adviser calls to tell you that his company’s technical analyst has been tracking
the performance of Patrick Corporation Ltd stock for the past 12 months and is certain that its
price is about to increase by 40-60% in the next two weeks. You should buy some quickly.
(b) BHP announces an earnings-per-share figure that is 20% higher than the majority consensus of
market analysts.
(c) A friend who works at a solicitor’s office has advised you to buy shares in a company that is in
confidential negotiations to be taken over.
(d) You have discovered that each time the price of gold-mining stock drops by 25% in any four-
week period it falls by another 20% before the price increases again.
(e) CBA pays a dividend that is 25% higher than the prior dividend.
Question 86
Assume that the Australian stock market is semi-strong form efficient. Which of the
following situations could be expected to provide an opportunity to earn excess (abnormal)
returns? Explain your answers.
(a) BHP announces an earnings-per-share figure that is 20% higher than the average consensus of
market analysts.
(b) Your friend who works at BHP tells you that tomorrow the company will announce an earnings-
per-share figure that is 20% higher than the average consensus of market analysts.
(c) A listed Australian company, Large Ltd, announces a takeover bid for a company that you are
thinking of investing in, Small Ltd.
RMIT International University- BAFI 3184
Exercise booklet 27
(d) An analyst tells you that company ABC will announce an earnings-per-share figure that is
double previous levels. However, the higher EPS will arise as a result of a change in the
company’s accounting practices.
(e) You have discovered that each time the price of a gold-mining stock drops by 20% in any four-
week period it falls by another 20% before the price increases again.
(f) CBA pays a dividend that is 25% higher than the prior dividend.
RMIT International University- BAFI 3184
Exercise booklet 28
TOPIC 6: WEIGHTED AVERAGE COST OF CAPITALTOPIC 6: WEIGHTED AVERAGE COST OF CAPITALTOPIC 6: WEIGHTED AVERAGE COST OF CAPITALTOPIC 6: WEIGHTED AVERAGE COST OF CAPITAL
------------------------------------------------------------------------------------------------------------------------------------------------
Question 87
Calculate the weighted average cost of capital for the Peach Computer Company. The book value of
Peach’s outstanding debt is $10 million. Currently, the debt is trading at 90 percent of book value and
is priced to yield 12 percent. The 1 million outstanding shares of Peach stock are selling for $20 per
share. The required return on Peach stock is 20 percent. The tax rate is 30 percent.
Question 88
Assume that ABC Corporation has the following capital structure: 30 percent debt, 10 percent preferred
stock, and 60 percent equity. ABC Corporation wishes to maintain these proportions as it raise new
funds. Its before-cost of debt is 8 percent, its cost of preferred stock is 10 percent, and its cost of equity
is 15 percent. If the company’s marginal tax rate is 40 percent, what is ABC’s weighted average cost of
capital?
Question 89
Jorge Ricard, a financial analyst, is estimating the costs of capital for the Zeale Corporation. In the
process of this estimation, Ricard has estimated the before-tax costs of capital for Zeal’s debt and
equity as 4 percent and 6 percent, respectively. What are the after-tax costs of debt and equity if Zeal’s
marginal tax rate is 30 percent?
Question 90
Alcoa has one class of preferred stock outstanding, a $3.75 cumulative preferred stock, for which there
are 546,024 shares outstanding. If the price of this stock is $72, what is the estimate of Alcoa’s cost of
preferred equity?
Question 91
Valence Industries wants to know its cost of equity. Its CFO believes the risk-free rate is 5 percent,
equity risk premium is 7 percent, and Valence’s equity beta is 1.5. What is Valence’s cost of equity
using the CAPM Approach?
Question 92
John Smith Ltd. recently asked a team of management consultants to determine an appropriate cut-off for
investment projects with the same risk as the firm. Unfortunately, part of the report was lost and, as the
investment manager of Smith, you have been asked to calculate the missing figures. Fortunately, the
following facts were available from the report.
RMIT International University- BAFI 3184
Exercise booklet 29
• The consultants estimated that the required rate of return was 13.635%
• Shares were selling for $1.20.
• The Beta of Smith's equity was estimated at 0.7, rm at 20% and rf at 12%.
• The interest rate on debentures was 13% per annum.
• A balance sheet extract showed:
Liabilities $ (000)
Mortgage loan 1,500
Debentures 2,500
Shareholders funds
Paid-up capital ($1 par) 5,000
Reserves 3,500
Total 12,500
• Debt items were recorded as market values.
• The consultants believed the market value capital structure was optimal.
• The corporate tax rate as 40%.
Compute the before-tax rate of interest on mortgage loans to arrive at the consultants' estimate of the
cut-off rate.
Question 93
Pluto Ltd. commenced operations many years ago. Relevant details relating to the company include
the following:
Extract from Balance Sheet
Liabilities
Debentures ($100 par, 8% coupon rate) $4,000,000
Bank Overdraft $500,000
Owners Equity
Ordinary Shares $5,500,000
Retained Earnings $2,500,000
Preference Shares (7% cumulative) $1,500,000
RMIT International University- BAFI 3184
Exercise booklet 30
Additional Information
i. An interest payment in relation to the debentures has just been made. Interest is paid annually and they will mature three years from today.
ii. If the company were to issue debentures today it would have to offer a coupon rate of 10 percent.
iii. The preference shares are trading on the market at $3.00 and a dividend of 21 cents per share has just been paid.
iv. Forecasts in relation to market returns are: expected risk-free rate of return is 6.5 percent; expected return on the market portfolio is 12 percent. Pluto’s beta co-efficient is 0.9.
v. Pluto has 500,000 issued preference shares. vi. Pluto’s ordinary shares, which were issued at 50 cents each, are trading on the market at 63
cents each. vii. The company’s after-tax weighted average cost of capital is 9.25%. Assuming a corporate tax rate of 30 percent, calculate the before-tax cost of the bank overdraft.
CAPITAL
BASE
MARKET
VALUE
WEIGHT
COST
BEFORE
TAX
COST
AFTER
TAX
AFTER TAX
WEIGHTED
COST OF
CAPITAL
????
0.13635
RMIT International University- BAFI 3184
Exercise booklet 31
TOPIC 7: CAPITAL STRUCTURETOPIC 7: CAPITAL STRUCTURETOPIC 7: CAPITAL STRUCTURETOPIC 7: CAPITAL STRUCTURE
------------------------------------------------------------------------------------------------
Question 94
It has been suggested that if the equity and long-term capital of a company is valued at market price,
and if the rate of return on that capital is calculated from earnings before loan interest, and taxation is
ignored, then that rate of return will be identical for all companies having the same total risk. The
relevant data for two such companies are given below:
Company A
(levered)
Company B
(un-levered)
Current value of capital:
Number of ordinary shares 90,000 150,000
Market price per share $1.20 $1.00
Market value of equity $108,000 $150,000
6% secured non-redeemable debt
at par $60,000
Earnings before interest (NOI) $18,000 $18,000
NI
$14,400
i.e. $18,000 less $3,600 (i.e.
NOI less interest) $18,000
Return on equity (re)
13.33%
i.e. $14,400/$108,000
12%
i.e. $18,000/$150,000
Value of Company
$168,000
i.e. $108,000 (equity) plus
$60,000 (debt) $150,000
All income after loan interest is distributed as dividend (i.e. NOI less interest = NI)
RMIT International University- BAFI 3184
Exercise booklet 32
Required:
a) Explain and illustrate the process by which, through investors’ actions, the market values of the two companies might be brought into equilibrium. Suppose the individual has 900 shares in A.
b) List the further assumptions implicit in your calculations. c) Comment on the likely effect of taxation on the market values of the two companies. No
calculations are required.
Question 95
Company A and Company B are in the same risk class, and are identical in every respect except that
Company A is levered while Company B is not. Company A has $3m in 5% debentures. Both firms
earn 10% before interest and taxes on their $5m of total assets. Assume a company tax rate of 60%, and
a capitalization rate of 10% for equity be it in the levered or un-levered company.
Required:
(a) Compute the value of each firm using net income.
(b) The values for firms A and B computed in part (a) above are not in equilibrium. If a situation like
this exists, an investor in the overvalued firm can, through the arbitrage process, secure the same
income at lower cost. Assuming you own 1% of A’s shares, show the process which will give you the
same amount of income but at less cost.