Chapter 5 eng economics

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Sources ofFunds and Cost

of Capital

5

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CHAPTER 5 OUTLINE

5.1 Sources of funds

5.2 Debt and Equity: Long-term sources

5.3 Medium and short-term sources

5.4 Cost of Capital

5.5 Cost of individual sources

5.6 Capital structure

5.7 Weighted cost of all sources

5.8 Examples


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Professor R. Jassim Engineering Economy

3. Short-term Sources (temporary)Accounts Payable Bank Margin Account

2. Medium-term Sources (temporary) Leasing Term Debt (e.g. notes payable)

1. Long-term Sources (permanent)

DEBT Bonds Debentures Bank Loans

EQUITY Common Shares Preferred Shares

Retained Earnings

SOURCES OF FUNDS5.1


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Face Value

Coupon

Coupon Rate

7.75 %

Semi-annualpayment$968.75

MaturityDate

First coupon

5 August, 1993

Last coupon5 February, 1998

SOURCES OF FUNDS5.1

Bond


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Professor BilodeauMining EngineeringMcGill University

Number of shares

No Par Valueindicated

SOURCES OF FUNDS5.1


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SOURCES OF FUNDS5.1


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Consists of borrowing funds by:

Issuing

Bonds, using specific assets as collateral Debentures, secured by good credit rating of company

Obtaining

Bank loan or mortgage, using specific assets as collateral

DEBT AND EQUITY: LONG TERM SOURCES5.2

Debt


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Issued privately or publicly (by investment brokers) Issuing expenses Characteristics

Face Value Nominal amount written on bond or debenture; representsprincipal, i.e. investment by purchaser, unless a discount was given

Maturity Date End of bond life, i.e. date at which Face Value becomesdue to owner

Coupon Rate Pre-established interest rate (nominal) paid on Face Value


Bonds and Debentures


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Interest payments made by company are tax deductible, i.e. consideredan expense of carrying-out business; the after-tax cost is thereforelower than the actual coupon rate

Coupon rate depends on financial rating of company if potentialinvestors view company as risky, it will have to offer a higher coupon rate

and current market interest rate

Bonds and debentures are a relatively low risk type of investment

Interest must be paid

If company cannot service its debt payments, the principal becomes

due In case of bankruptcy, bondholders have priority over other creditors


Bonds and Debentures


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Maturity date

Interest and principal repayment schedule

Interest payments are tax deductible

Interest rate depends on rating of company

Bank has priority over all other creditors


Bank Loans and Mortgages


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Part of equity capital, but have particular characteristics setting them apartfrom common shares (e.g. no voting power in company management)

Issued privately or publicly (by investment brokers) Issuing expenses Characteristics

Face Value Nominal value written on certificate, also known as Parvalue

No Maturity Date Assumed to be issued indefinitely

Fixed Dividend

Paid on Face Value, specified as nominal rate; dividendis always payable


Preferred Shares


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Dividends are not tax deductible, i.e. not considered operating expenses;disbursement is therefore more costly to company

Dividend depends on financial rating of company and market interest rateat time of issue

Preferred shares allow the expansion of the companys equity baserequired for debt financing, without diluting the position of the common

shareholders


Preferred Shares

f


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Preferred shares are considered an intermediate risk type of investment

In case of bankruptcy, preferred shareholders recover theirinvestment after creditors, but before common shareholders.

The market price of preferred shares is much less volatile than thatof common shares, varies with current interest rates, and maydecrease if company is in difficulty

Dividends are always payable


Preferred Shares

P f R J i E i i E


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Nortel Preferred Shares

P f R J i E i i E


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Ford Preferred Shares

P f R J i E i i E


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Common shareholders are the owners of the company, and have access toall of the profits of the business, after preferred dividends have beendistributed.

Common shareholders elect the Board of Directors, vote in majordecisions, and examine and approve the companys books and financial

statements. Shareholder liability is restricted to the amount of money invested

Issued privately or publicly (by investment broker)

Issuing expenses


Common Shares

P f R J i E i i E


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Characteristics

Par Value Nominal amount that may be written on certificate; this is theoriginal issue price

No Maturity Date Assumed to be issued indefinitely

Dividends may be variable, and are not necessarily paid; declared bymanagement and based on profits and company policy. Therefore, nofixed commitment from the company.

Dividends are not tax deductible; disbursement is therefore more costly tocompany


Common Shares


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Market Pricea common sharesmarket price has very little relationshipwith its Parvalue. The market value reflects the companyseconomicperformance and success, and responds to the law of supply anddemand (and sometimes speculation!)


Common Shares



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Bombardier Common Shares



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Ford Common Shares



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That part of net income reinvested in the business, i.e. to finance newprojects within the company

Considered part of common equity financing

No fixed cost, like common shares

There is however an implicit opportunity cost, like that of commonshares

The sum of common dividends and retained earnings (i.e.earnings per share) must be maintained at a level such that itwill keep current shareholders satisfied, and attract potential

investors. If not, the market price of the shares will decreasebecause investors will loose interest and sell their shares, i.e.supply will exceed demand on the market place.


Retained Earnings



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A spot measure of the cost of common equity is the ratio EPS / P(earnings per share to market price*). Thus, for a business maintaining aconstant EPS, the cost of equity will increase if P decreases due to a

change in supply/demand conditions.

Retained earnings policy guided by:

Availability of new projects within the company Investment options available to individual shareholders Tax rate on dividends received by shareholders

* The reciprocal of the price to earnings ratio


Retained Earnings



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BondsThe nomenclature generally used for bonds is face value(price at which abond is normally sold, and amount received by bondholder when bond isredeemed at maturity) and market price(value at which a bond trades onthe market at a particular time in its life, a function of time to maturity,coupon rate and market rate). The interest payment is determined by

multiplying the face value by the coupon rate. The face value of a bondmay be referred to aspar value.

Common SharesThe par value of a common share in the context of the stock market isirrelevant. The par value represents the price at which a common share

was originally issued, and has no direct relation with the shares actualmarket price(the value at which the share is traded on the stock market).The common stock entry in the balance sheet represents the par value ofall outstanding common shares.


Notes on Bond and Share Terminology



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Preferred Shares

Thepar valueof preferred shares is important because it is used to calculatethe preferred dividend (the dividend rate times the par value). The preferredshare is originally issued at par, but its market price may vary below or abovepar as a function of prevailing market rates.

Net ProceedsThe net proceedsare relevant only when a firm issues new bonds or shares.They represents the net monetary amount that the firm receives after issuingexpenses have been paid to the stock broker responsible for the issue. Aswell, because of unexpected short-term changes in the market, a firm maybe forced in issuing bonds below par (i.e. at a discount). Thus, the net

proceeds to the firm are always lower than the prices at which the newsecurities are sold.




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Agreement whereby a financial institution purchases an asset and rents itto a business firm on a long-term basis. Thus, the institution owns theasset and the firm operates the asset.

The leasing expense is similar to a rental expense and is tax deductible

(usually beginning-of-period payments)

Operating costs are paid by the lessee

Maintenance costs may be paid either by the lessor or lessee, dependingon the contract terms (of course, the lease payments will reflect this)

MEDIUM AND SHORT-TERM SOURCES5.3

Medium-term Sources

Leases



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The advantage of a leasing arrangement is the lowering of debt and equityfrom the balance sheet, i.e., funds need not be raised to purchase the asset

The disadvantage is the higher annual fixed operating cost to the firm,leading to increased financial risk

Consists of one- to two-year loans from financial institutions

May be in the form of a revolving fund, i.e. line of credit, to finance short-term capital requirements


Leasing

Term Debt



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o esso Jass g ee g co o y

Many businesses offer discounts if their clients pay their bills within 10 daysof invoicing. Otherwise, the full amount is typically due within 30 days. If acompany does not take advantage of this discount, it has the use of theamount due for the extra period of time. This is usually a costly short-term

source of funds.

Bank account in which the balance can become negative, i.e. the bankextends credit to the account owner. In this case, interest is charged onthe balance. This type of account is useful to finance working capitalrequirements.


Short-term Sources

Accounts Payable

Line of Credit



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g g y

Borrow $1000 today Pay interest of $100 per year Repay principal 8 years later

$100

$1000

$1000

$1000 = $100 (P/A, i, 8) + $1000 (P/F, i, 8)The value of i that satisfies the equation below is the cost of money.

The value obtained for any N is 10 % because the interest rate paidon the loan is 10 %. This represents the cost associated withborrowing the $1000.

1 2 3 4 5 6 7 8

0

PV=1000, PMT=-100, FV=-1000, N=8, CPT I/Y 10%

COST OF CAPITAL5.4

The Concept of the Cost of Money



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g g y

A company obtains investment funds from various sources, each with itsparticular cost.

The cost of capital, i.e. the cost of these investment funds, is theweighted-average cost of the total amount of money obtained by thecompany from all permanent sources.

The particular mixture of debt and equity sources is referred to as capitalstructure. The capital structure is based on market values, not parvalues.

By convention, the cost of capital is stated as an effective annual interestrate.

The cost of capital can be determined for a companysexistingcapital orfor raising additionalcapital through the issue of new debt and/or equity.In the latter case, the result is a marginalcost of capital.

COST OF CAPITAL5.4



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g g y

*Net Proceeds = Face Value - Issuing Expenses Discount in which thediscount is a reduction in price that may be offered by issuer to buyer dueto unforeseen short-term changes in the market.

Elements

Face value F

Net proceeds* NP (for new issue)

Market Price P (for existing debt)

Annual interest payment I (Coupon rate F)

Maturity n years

Cost of long-term debt capital Kd

COST OF INDIVIDUAL SOURCES5.5

Cost of Bonds and Debentures



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g g y

I

NP

F

1 2 n

0

NP = I (P/A, i, n) + F (P/F, i, n)

Solve for i, which is Kdon a before-tax basis.

If interest payments are made more than once per year, determine i on thebasis of actual payment interval and convert to an effective annual rate.


Cost of Bonds and Debentures- Before-tax case for new issue


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If there are issuing expenses (and perhaps a discount), then Kdmust be

found by solving the general time value relationship.

NP = 1000 - 75 - 25 = 900

Then, Kdis such that:

900 = 100 (P/A, Kd, 8) + 1000 (P/F, Kd, 8)

With financial calculator (PV=900, PMT= -100 and FV= -1000) or by trialand error, we find that Kd = 12 %.

In our example, assume that issuing expenses are $75 per bond and adiscount of $25 per bond is offered.

For cost of existing debt, determine yield-to-maturity and express as aneffective annual rate. I/ Pis referred to as a bondsyield.




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- Interest payments as they are paid- Issuing expenses at time of issue- Discount at time of redemption

Tax deductible

NP: F - Issuing Expenses (1 - t) - Discount Interest Payment: I (1 - t)

Amount sold for: F - DiscountAmount paid to bondholder at maturity: F Tax deductible at

maturityF = (F - Discount) + Discount

Kd on an after-tax basis is found by solving the general relationship with afinancial calculator or by trial and error. Same comment concerning interestpayments made more than once per year.

Thus, after-tax payment is: (F - Discount) + Discount (1 - t) = F - Discount (t)


Cost of Bonds and Debentures- After-tax case for new issue



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If there are neither issuing expenses nor a discount, then

Kd= I (1 - t) / F

In our example, say t = 40%.

Kd= 100 (1 - 0.4) / 1000 = 0.06 = 6 %

Note: This relationship applies to a new issue only. The bonds are sold atpar (i.e. F).



After-tax Cost



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NP: 1000 - 75 (1 - 0.4) - 25 = 930

Interest payment: 100 (1 - 0.4) = 60

After-tax amount paid to bondholder at maturity: 1000 - 25 (0.4)= 990

Tax credit

Then, Kdis such that:

930 = 60 (P/A, Kd, 8) + 990 (P/F, Kd, 8)

With financial calculator or by trial and error, we find that Kd= 7.1 %

In our example with issuing expenses and discount of $75 and $25,respectively,

If there are issuing expenses, Kdmust be found by solving the general timevalue relationship

For cost of existing debt, use current market price and after-tax interestpayments, ignore discount unless known, and express as an effectiveannual rate.





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Approximation for maturity periods greaterthan 20

Kd = I (1 - t) / NP (for existing debt: I (1t) / P)

In our example,

Kd = 100 (1 - 0.4) / 930 = 6.5 % (Not so accurate comparedto 7.1 % because n is muchless than 20)

There is no need to use this approximation when a financial calculator isavailable.





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Par value F


Annual dividend D (Annual dividend rate F)

Cost of preferred equity capital Kp

* Net Proceeds = Par Value - Issuing Expenses (1 - t)

For after-tax case

Elements

Market Price P (for existing equity)


Cost of Preferred Shares



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D

NP

NP = D (P/A, i,)

Solve for i, which is Kp.

As (P/A, i, ) = 1 / i, i = D / NP.

Kp= D / NP (for existing preferred: D / P, i.e. the shares dividend yield)

1 2 3 4 5 6 7 80

If dividend payments are made more than once per year, determine i on thebasis of actual payment interval and convert to an effective annual rate.


Cost of Preferred Shares- New Issue



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As with other sources of funds, the cost of common equity is based on thepremise that investors pay for what they expect to get

Par value F


Market price P (for existing equity)

Annual dividend D (variable)

Cost of common equity capital Ke

* Net Proceeds = Market Price - Issuing Expenses (1 - t)

For after-tax case

Elements


Cost of Common Shares

Dividend Evaluation Model



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No growth in dividends and price expectedKe= D / NP (for existing common: D / P)

Geometric growth in dividends and price expected (compound growth rateof g per year)

D0: Current dividend (assumed paid)

D1: Expected year-end dividend (D0[1 + g])

Ke= [D1/ NP] + g (for existing common: [D1/ P]*+ g

If dividend payments are made more than once per year, determine i on thebasis of actual payment interval and convert to an effective annual rate.

* D1/ P is referred to as the shares dividend yield.


Cost of Common Shares



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Shareholders expect that profits retained in the business will earn at leastthe same return as their current investment

Implicit cost the same as that of existing common equity, i.e.:

Kre= D / P Kre= [D1/ P] + g

If dividend payments are made more than once per year, determine i onthe basis of actual payment interval and convert to an effective annualrate.


Cost of Retained Earnings



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As indicated earlier, an alternate measure of the overall cost of commonequity (i.e. initial shareholder investment plus retained earningscombined) is:

Ke= Earnings per shareP

RetainedEarnings

Market controlled

This relationship measures the cost of existing equity in the absence ofdividend payments (a growth rate assumption is built into EPS1).

Expected

Business

performance

Value based

on investor

expectations

1


Overall Cost of Common Equity



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Consists of the proportions of the different sources of funds in a firmspermanent financing structure.

Long-term Debt

Preferred Equity

Common Equity (initial shareholder investment plus retained earnings)

Most companies have a policy of maintaining a particular capital structureover the long-term. The objective of this strategy is to minimize thecompanys cost of capital, which is a function of its capital structure andbusiness risk.

CAPITAL STRUCTURE5.6



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Ke

Kaverage

Kd

To maintain overthe long term

100% equityMore debt

Debt/Equity

After-taxCost

The optimal capital structure is conceptualized in the diagram below:




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Increase return on equity (high cost source of funds) by including long-termdebt (lower cost source of funds) in capital structure.

$Return onequity withall equityfinancing

Return on equity withpartial debt financing

Debt


Leverage



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Purchase of an apartment building for $500 000Two financing options:

Use $500 000 of equity earning 15 % elsewhere

Use bank loan of $400 000 at 12 %, and $100 000 of equity earning

15 % elsewhere


Example 5.1-Leverage



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Scenario 1: Sell building for $600 000 one year later

Using all equity financing

Profit: 600 000 - 500 000 = 100 000

Time Value Return on Equity: 100 000 / 500 000 = 20 %

Using debt and equity financing

Profit: 600 000 - 500 000 - 48 000 = 52 000

Time Value Return on Equity: 52 000 / 100 000 = 52 %

Interest payment


Solution



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Scenario 2: Sell building for $400 000 one year later

Using all equity financing

Profit:400 000 - 500 000 = (100 000)

Time Value Return on Equity: (100 000) / 500 000 = -20 %

Using debt and equity financing

Profit: 400 000 - 500 000 - 48 000 = (148 000)

Time Value Return on Equity:(148 000) / 100 000 = -148 %

Interest payment


Solution



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The cost of capital is the weighted-average cost of all permanent (i.e. long-term)

sources of funds.

Weighted average cost of capital (WACC or COC):n

WACC = (Kj Propj)j=1

in which Kj is the cost of each source, Propj is the proportion of source jrelative to the total sources, and nis the number of sources.

This relationship is applied to assess either the existing cost of capital or thecost of raising new capital (i.e. marginal cost of capital). In either case, boththe costs and the weights must be based on market value, and not onface/par value, except for new issues sold at par.

WEIGHTED COST OF ALL SOURCES5.7



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A firm has a capital structure with the following characteristics:

40% debt with Kd= 8 % (B-T) 10% preferred equity with Kp= 9 % 50% common equity with Ke = 10.5 %

Tax rate: 45%

B-TWACC = 8% (0.4) + 9% (0.1) + 10.5% (0.5) = 9.3 %

A-TWACC = 8% (1 - 0.45)*(0.4) + 9% (0.1) + 10.5% (0.5) = 7.9 %

*This is an approximation. The exact after-tax cost must be determinedfrom the current market price, the coupon rate, the maturity period, the

corporate income tax rate, and the discount given at purchase, ifapplicable and known.

WEIGHTED COST OF ALL SOURCES5.7

Example 5.2- Existing Cost of Capital



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Retained Earnings $1.5 mil.

Bonds $9.5 mil.

Face value: $100Issuing expense: $10

Maturity: 10 yearsCoupon rate: 8 % paid quarterlyDiscount: $2

A firm has financed a new project with the following:

Preferred Shares $2.0 mil.

Par value: $100Issuing expense: $10

Dividend: 7 % paid annually

Common Shares $20.0 mil.

Current market price: $25Issuing expense: $2Current dividend: $1.75

(paid annually)Annual growth rate: 6.2 %

The firmstax rate is 45 %. What isthe weighted-average after-tax costof capital associated with raisingthese funds?

EXAMPLES5.8

Example 5.3- Cost of Capital Associated with Raising New Funds


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Cost of Common Shares (new issue)

Ke= 1.75 (1 + 0.062) + 0.062 = 13.98 %[25 - 2 (1 - 0.45)]

Cost of Retained Earnings

Kre= 1.75 (1 + 0.062) + 0.062 = 13.63 %25

WACC = 5.41(9.5/33) + 7.41(2.0/33) + 13.98(20/33) + 13.63(1.5/33) = 11.1 %

Cost of Capital or WACC

EXAMPLES5.8

Solution



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Kuipers, Inc.Balance Sheet as of 31 December, 2003

(million $)

Cash 121 Accounts payable 350Accounts receivable 425 Notes payable 370Inventory 410 Total 720

Total 956 Long-term debt 550Shareholders equity

Net fixed assets 1804 Common stock 580Retained earnings 910Total 1490

Total assets 2760 Total Liab. & S.E. 2760

Bonds: Par value of $1000, market price of $900, Kdof 5 %Common shares: Par value of $20, market price of $60, Keof 12 %

EXAMPLES5.8

Example 5.4- Existing Cost of Capital



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Using balance sheet values as weights:

Debt + Equity: 550 + (580 + 910) = 550 + 1490 = 2040

WACC: 5% (550/2040) + 12% (1490/2040) = 10.1 %

WACC based on market values (correct method)

Retained earnings are included implicitly in the market value of the shares.

WACC based on book values

Using market values as weights:

Debt + Equity: 900 (550 / 1000) + 60 (580 / 20)

900 (0.55 mil. bonds) + 60 (29 mil. shares)

495 + 1740 = 2235

WACC: 5% (495/2235) + 12% (1740/2235) = 10.4 %

EXAMPLES5.8

Solution



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Byron Inc. needs $50 million for a new project. As all of its retainedearnings have been used, the firm plans to issue new equity and debt toobtain the additional funds required, while maintaining its current capitalstructure of 60 % equity and 40 % debt. On an after-tax basis, Byron willnet 90 % of selling price for the common equity issued and 95 % for thedebt issued. The common shares are to be issued at the current market

price of $50 per share and the new bonds will be sold at their par value of$1000 per bond.

How many shares and bonds does Byron Inc. need to issue?

To maintain the current capital structure, the following relationship must be

respected with respect to the total monetary amount (T) of equity and debtissued:

(0.90) 0.6 T + (0.95) 0.4 T = 50 million0.54 T + 0.38 T = 50 million

T = $54.348 million

EXAMPLES5.8

Example 5.5- Raising Capital for a New Project



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Number of common shares to be issued:

(0.6) 54.348 = $32.609 in common sharesNumber of shares 32.609 (106) / 50 = 652 176

Number of bonds to be issued:

(0.4) 54.348 = $21.739 million in bondsNumber of bonds 21.739 (106) / 1000 = 21 740

EXAMPLES5.8

Solution



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The analysis of a firm's capital markets and associated costs has producedthe following information:

Given that the cost of debt and equity are specified on a before-tax basisand that the firm is subject to a corporate income tax rate of 45 percent,determine the optimal capital structure, i.e. the debt to equity ratio thatminimises the after-tax cost of capital.

Debt/EquityCost of debt

(%)

Cost of equity

(%)

0.2 10.0 16.0

0.6 10.0 16.3

1.0 10.4 17.0

1.5 11.1 18.0

2.0 12.3 19.4

2.5 13.8 21.2

3.0 15.6 23.3

EXAMPLES5.8

Example 5.6- Optimal Capital Structure



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The proportion of debt for each debt to equity ratio is:Debt/Equity Debt Equity Debt + Equity Debt/Total

0.2 0.2 1.0 1.2 0.167

0.6 0.6 1.0 1.6 0.375

1.0 1.0 1.0 2.0 0.500

1.5 1.5 1.0 2.5 0.600

2.0 2.0 1.0 3.0 0.667

2.5 2.5 1.0 3.5 0.714

3.0 3.0 1.0 4.0 0.750

The weighted-average after-tax cost of capital for each debt to equity ratio is:

Debt/Equity Cost of Capital0.2 10% (1 - 0.45) 0.167 + 16% (1 - 0.167) = 14.2%0.6 10% (1 - 0.45) 0.375 + 16.3% (1 - 0.375) = 12.2%1.0 10.4% (1 - 0.45) 0.5 + 17% (1 - 0.5) = 11.4%1.5 11.1% (1 - 0.45) 0.6 + 18% (1 - 0.6) = 10.9%2.0 12.3% (1 - 0.45) 0.667 + 19.4% (1 - 0.667) = 11.0%2.5 13.8% (1 - 0.45) 0.714 + 21.2% (1 - 0.714) = 11.5%3.0 15.6% (1 - 0.45) 0.75 + 23.3% (1 - 0.75) = 12.3%

EXAMPLES5.8

Solution

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Chapter 5 eng economics

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