17 COST OF CAPITAL - University of Waikatocms.mngt.waikato.ac.nz/webdocs/personal/evos/Textbookpdf/chap17p… · Chapter 17: Cost of Capital 341 This concept of business risk is often

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17 COST OF CAPITAL

IntroductionBusiness RiskCapital Asset Pricing Model and Financial LeverageWeighted Average Cost of Capital

- Cost of Debt- Cost of Preferred Shares- Cost of Ordinary Shares- Internally Generated Funds- Changes in the Cost of Capital

Summary

IntroductionWhen making investment decisions, the financial manager needs to know theminimum expected return that is acceptable to the investors. This minimumacceptable return, called the cost of capital, is the price the firm pays for the use ofmoney. Knowing the cost of capital, the manager can then make investmentdecisions by using the cost of capital as the discount rate in deciding upon whetheror not to make a capital investment. The subsequent chapter on capital investmentwill show in detail how these investment decisions are made. The cornerstone ofthe investment decision, however, is to first determine the correct cost of capital.

Two different approaches to determining the cost of capital are available: one usesthe Capital Asset Pricing Model (CAPM), and the other uses the Weighted AverageCost of Capital (WACC). The nature of the prospective investment underconsideration determines which approach should be used. In general, the CAPMprovides market driven costs of capital for investments in projects which are not inthe same business as the investing company. These market driven costs areadjusted for the financial leverage of existing firms, and the CAPM provides ameans for ‘ungearing’ the leverage. On the other hand, if the potential investmentunder consideration is in the same business (has the same ‘business risk’ as definedbelow) and does not intend to alter its existing capital structure (that is, financialleverage of the business), then WACC is an appropriate and somewhat more

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340 Financial Management and Decision Making

reliable way of determining the cost of capital.

The CAPM developed earlier provides the financial manager with a tool fordetermining the expected rate of return on an investment. Remember that theCAPM determines the expected return on equity investment in a firm by adding arisk premium to the risk free rate. This expected return is adjusted for the amountof financial leverage (debt) used in the firm. As discussed, the CAPM has severalproblems in arriving at an exact figure for the cost of capital, but it is useful inproviding a ‘reasonable range’ of the cost of capital. This range can then be used asupper and lower bounds to help in the decision making process.

The WACC approach to determining the cost of capital uses a weighted average ofthe costs for all sources of finance in a firm - equity, debt, preferred shares, etc.With the weighted average approach it is evident that there are different costs fordifferent levels of capital raised. The weighted average approach also provides thefinancial manager with an additional check on the CAPM-determined costs, thusadding more understanding to the ‘reasonable range’ of costs.

This chapter will examine both the CAPM and WACC approaches to determiningthe cost of capital. The concept of business risk will be discussed. The implicationsof financial leverage (debt) will be explored in the CAPM model and the changinglevels of costs will be discussed in the weighted average approach. Whencalculating a cost of capital, it is the marginal cost of capital which is sought, that is,the cost for the next additional amount of capital. The CAPM approach should beused when there are changes to the leverage of the firm and/or when the marginalinvestment is not identical in risk to the existing firm. The weighted average costshould be used when there are no changes in the mix of capital being used and whenthe anticipated investment will be identical in risk to the existing firm.

Business RiskRisk has already been defined as the variability of expected returns. Business riskis therefore the variability of expected returns in a specific line of business. In otherwords, business risk is the risk of being in a particular activity or business. Thepassenger airline business has a different risk profile from the silicon chipmanufacturing business or the wholesale food distribution business.

The return that investors expect is a function of the variability of the expectedreturns - in other words, the investors have different expectations of return from thedifferent businesses they invest in. Since the reason for calculating the cost ofcapital is to establish a discount rate which can be used in evaluating investments,the obvious first question which must be addressed is what is the business risk ofthe investment under consideration? If a passenger airline is considering aninvestment in the wholesale food distribution business, the business risk that mattersis that of the wholesale food distribution business and not the passenger airlinebusiness. It would be unrealistic to expect the two businesses to have the samebusiness risk. It would likewise be foolish for the financial manager to impose thecost of capital of the airline or silicon chip business onto a decision for investmentin the wholesale food distribution business.

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Chapter 17: Cost of Capital 341

This concept of business risk is often overlooked or misunderstood. It is clear thattwo potential investors in, for example, the fertilizer manufacturing business shoulduse the same cost of capital for evaluating their investment in that business. If oneinvestor uses a higher cost of capital than the next, it is possible for both investors toexpect exactly the same returns from the fertilizer manufacturer under considerationbut come to different financial conclusions about the investment. (It must beremembered that the final investment decision will be based not just upon financialconsiderations. Strategic planning and personal preferences, as discussed morefully in the next chapter, also play significant roles.) Thus, the financial managershould not use the cost of capital established in one business in the evaluation of adifferent business. If parent companies impose one cost of capital on all of theirsubsidiaries, regardless of the differences in the business risk of their subsidiaries,then they are not demanding enough return from the businesses with high businessrisk and are demanding too much return from those with less business risk, whencompared with the ‘average’ for the parent company.

Capital Asset Pricing Model and Financial LeverageThe amount of debt used to finance the assets of the company determines theamount of financial leverage. The return on debt to the debt holders is fixed byagreement between the company and the lenders. Equity holders finance theremainder of the assets of a company. The return on equity varies not only with theamount of business risk, but also with the amount of financial leverage being usedby the company.

Using the CAPM to determine cost of capital has a difficulty not mentioned in theprevious chapter. When looking into the share market to determine the returns of ashare, it must be remembered that it is the return on equity that is being examined -not return on assets. But it is the return on assets that determines the business risk.When attempting to determine the cost of capital, the first step is to determine thereturn on assets for a business similar to the investment under consideration.

Business risk is measured by a Beta coefficient in the CAPM. The Beta coefficientfor assets is calculated according to the following formula:

Betaassets = (Betaequity) x (% Equity) + (Betadebt) x (% Debt)

Example ABC Company is considering an investment in the oil exploration business. Inorder to evaluate the potential of the investment, it is first necessary to determinethe cost of capital, or the cost of using money for oil exploration. In examining theshare market, the financial manager of ABC notices that XYZ Company is inexactly the type of oil exploration business that is under consideration.

By doing a regression analysis of the returns on XYZ shares against the returns ofthe market, it is determined that:

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BetaequityXYZ = 1.7

By examining the Balance Sheet of XYZ Company, it is determined that 40% of theassets of XYZ are financed by debt and 60% are financed by equity. Discussionswith XYZ’s bankers about the perceived risk of lending to XYZ indicate that XYZdoes not borrow risk-free, and thus it can be assumed that:

BetadebtXYZ = 0.2

What is the cost of capital that ABC should use in their project evaluation if the riskfree rate is 12%, the excess return on the market is 8%, and ABC will use 30% debtand 70% equity?

From the above formula:

BetaassetsXYZ = 1.7 x .60 + .2 x .40 = 1.1

By using the CAPM, the expected return on assets for an oil exploration project is:

E(r) = .12 + (1.1 x .08)= .208 or 20.8%

This is the cost of capital in the oil exploration business. This is a measure of thebusiness risk of this type of business.

A further question could be: what is the expected return that ABC equity holderswill require? Because ABC plans on using less debt (30% compared with 40% forXYZ), then Betaequity for ABC’s project can be solved from the above equation byusing 1.1 for a measure of the business risk and by using the debt and equitypercentages under consideration. (Discussions with bankers lead to an assumptionthat the level of riskiness of the debt of ABC is slightly higher than the debt risk forXYZ. Thus, it is assumed that Betadebt of ABC is .3.) Knowing that 1.1 is Betaassets

of this line of business, it is possible to solve for Betaequity of ABC given theirpreferred capital structure:

1.1 = BetaequityABC x .70 + (.3 x .30)

Therefore:

BetaequityABC = (1.1 - .09)/.7 = 1.443

Using this beta in the CAPM to determine the cost of equity capital to ABC for theproject gives:

E(r) = .12 + (1.443 x .08)= .235 or 23.5%

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Comparing this cost of equity capital to the cost of equity capital for XYZ, we findthat for XYZ, E (r) = 25.6% (E(r) = .12+ (1.7 x .08)), where E(r) is the expectedreturn from equity capital. It is not surprising that ABC’s cost of equity capital at23.5% is lower than XYZ’s at 25.6% since ABC is considering using less financialleverage - in spite of the fact that the assumed level of debt risk for ABC was higherthan the assumed level of debt risk for XYZ. Yet both companies have the samecost of capital at 20.8% since they both have the same business risk, as defined bybeta of the assets, since they are in the same kind of business.

Determining the Betadebt coefficient for a company requires sensitivity analysis. Itmay be possible to examine the Balance Sheet and determine the interest rate beingpaid on the debt carried. By knowing that the ‘prime’ lending rate of banks is therisk free lending rate, that is, Betadebt = 0, it is possible to measure the amount abovethe ‘prime’ rate being paid by the firm. The difference between the ‘prime’ rate andthe cost of borrowing only provides a measure of lending risk. It is important not toassume a linear relationship between Betadebt and increased cost of borrowing.When undertaking cost of capital calculations, it is helpful to try several Betadebt

levels, for instance from 0 to .5, in order to see the effect it has on the cost of equitycapital. A Betadebt of 1 would mean that the variability of the expected returns ofdebt is equal to the variability of the market - which would imply that debt hasextremely variable returns and this would not be acceptable to lenders (with thepossible exception of ‘junk bond’/high risk holders). Using this approach, it ispossible to see how sensitive the cost of capital, and therefore the investmentdecision, is to the various risk levels of debt. If minor levels of debt are beingconsidered (less than 35%) in an extremely sound investment, it is reasonable toassume that Betadebt equals zero.

Attempts to refine the relationship between geared and ungeared Beta and tomeasure the components of the cost of geared equity capital have been criticised formaking unreliable approximations which significantly distort the resulting values.While formulae have been proposed for ‘ungearing’ Beta many of them are overlysimplistic (Buckley, 1989).

Weighted Average Cost of CapitalIt is common for the financial manager to seek funding for projects which have thesame business risk as the ongoing operations; in other words, to expand existingoperations. For example, a jewellery business which expands by opening additionalretail shops in new locations using the same business strategy and capital structure.The weighted average cost of capital (WACC) is a commonly used approach fordetermining the cost of capital assuming that business risk, financial risk anddividend policy all remain constant.

Capital invested in the firm in the form of debt and equity can take many forms. Theforms of debt and equity typically consist of bonds, ordinary shares, and preferredshares. The weighted average cost of capital approach takes the weighted averageof the costs of the capital being used in the firm. For simplicity, this chapterexamines this process using just these three sources of financing.

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The procedure is to first determine the present weighting of debt, ordinary sharesand preferred shares. Then the cost of each of these sources of funding isdetermined. Finally a weighted average of the costs is calculated.

Example Examination of the market value weightings of ABC Company reveals that thefollowing sources of financing are being used:

Debt $12,000,000Ordinary Shares $10,000,000Preferred Shares $3,000,000

What are the percentage weightings of each financing source? Using the formula:

Assets = Debt + Equity,Total Assets = 12,000,000 + 10,000,000 + 3,000,000

= $25,000,000

To find the percentage of total assets being financed by each source, divide theamount being used by the total assets:

Debt 12/25 = 48%Ordinary Shares 10/25 = 40%Preferred Shares 3/25 = 12%

Cost of Debt When issuing debt, the firm agrees to a coupon rate and a face value payable atmaturity. As discussed in the chapter on valuation of bonds, the present value of thefuture income stream is the market value of the bond. The market value will be theamount the lender (purchaser) of the bond is willing to pay for the future income.The discount rate used to discount the future cash flows so that these add up to themarket value of the bond, is the rate of return for the bond. This rate of return isarrived at iteratively (by trial and error).

Example ABC Company debt consists of bonds with an annual coupon rate of 9% on a$1,000 face value over 14 years. If the present market value of the bonds is$860.36, what is the rate of return of the bonds? In other words, what discount ratemust be used in order that the sum of the discounted cash stream for the bondsequals $860.36, or find ‘r’ such that:

860.36 = Annuity Factor14 yrs at r% x 90 + Discount Factor14 yrs at r% x 1,000

By substituting different values for r, the equation is solved for r of 11%, which istherefore the rate of return for these bonds. Hence, 11% would be the prevailinginterest rate for bonds of the particular risk class under consideration.

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However, when ABC Company wishes to issue new debt it will have to pay for theservice of having the debt issued. Accountants’ fees, legal fees and underwritingfees must all be deducted from the amount which is finally issued to the company.The net amount the company receives will be reduced, thus increasing the effectivecost of issuing debt.

Example If ABC Company has determined that it will cost $59.21 per bond in issuingexpenses, what is the effective cost of debt? The same approach is taken to solveiteratively for r, but this time using the net proceeds to ABC Company.

860.36 - 59.21 = Annuity Factor14 yrs at r% x 90 + Discount Factor14 yrs at r% x 1,000

In this equation, when r equals 12% the Net Present Value is $801.15. Thus, ABCis not paying 11% for debt, but 12%.

The true cost of debt to a company is really the after tax cost. Interest expenses aretax deductible. Consider the true cost to the company of $1 of interest expenses.This $1 paid out reduces the amount of taxable income on which the company hasto pay taxes by $1. If the corporate tax rate is, for example, 40%, then thecompany’s tax bill is $.40 lower as a direct result of the interest expense. Therefore,the true cost of that $1 in debt expense is only $.60. Thus, the true cost of debtcapital is:

r x (1 - Tc)

where r is the effective cost of debt, andTc is the corporate tax rate.

Example If ABC Company pays 40% tax, what is the true cost of debt capital on their bonds?

r = .12 Tc = .40

Therefore, the true cost of debt capital for ABC is:

.12 x (1 - .40) = 7.2%

It is important to note that:

- the lenders receive 11%,- the effective rate (after expenses) paid by ABC is 12%, and- the true cost of debt capital for ABC is only 7.2% due to the tax effects.

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Cost ofPreferredShares

Preferred shares promise to pay a fixed dividend into perpetuity. The value of aperpetuity has previously been defined as:

0P =Dr

where P0 is the present price of the preferred share,D is the dividend payout,r is the prevailing interest rate used to discount the dividend payout of

the same risk class.

By solving this equation for r, we find that the cost of capital for preferred shares is:

r =DP0

By looking at the share market for the prevailing price of the preferred share and byknowing the contracted dividend payout amount, it is possible to calculate r - thecost of preferred capital.

Example ABC Company notices that their preferred shares, which promise an annualdividend of $5, are selling for $38.46 on the open market. What is the cost ofpreferred share capital?

D = $5P0 = $38.46

Therefore, r = 5/38.46, or 13%

However, ABC Company will incur accounting, legal and underwriting fees forissuing new preferred shares. These expenses will reduce the amount received bythe company and therefore the true cost of preferred shares is:

pn

K =DP

where Pn is the net amount received by the company when issuing new preferredshares.

Example ABC has discovered that a fee of 5% of the market value of the preferred shareswill be charged in issuing fees. What is the true cost of preferred shares?

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K5

38.46 (.05 38.46) .1368 or 13.68%

p =− ×

=

Cost ofOrdinaryShares

The present price, P0, of common shares is the present value of the future growingdividend stream discounted at a risk-adjusted interest rate. The formula for thisprice, as developed earlier, is:

01P = D

(r - g)

where D1 is the anticipated dividend at the end of the current yearr is the risk-adjusted discount rateg is the growth rate of the dividend payout

Solving this formula for r:

r DP

+ g1

0=

Example What is the expected rate of return for the holders of ABC ordinary shares whoseanticipated dividend is $1.50, if the market price is $10.71 and the growth rate ofthe company is expected to remain at 5%?

r1.5010.71

.05

.19 or 19

= +

=

Adjusting this formula for the issuing fees that will be incurred with any new issueof ordinary shares results in:

e1

nK = D

P+ g

where Ke is the cost of equityPn is the net price of equity received by the company

Example What is the true cost of ordinary shares in ABC if issuing fees amount to 6% of thecapital raised in the open market?

eK1.50

.94 10.71+ .05

.1989 or 19.9%

=×

=

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Knowing the cost of debt, preferred shares, and ordinary shares enables theweighted average cost of capital to be calculated. This is done by summing thepercentage costs of each financing vehicle.

Example What is the weighted average cost of capital for ABC Company?

A convenient way to do this problem is to arrange the known data in columns,multiply the percentage used of each of debt, preferred shares, and ordinary sharesby their costs, and sum the results. This is shown in Exhibit 17.1.

Exhibit 17.1 Type % of Assets Cost of Capital (1) x (2)(1) (2)

Debt 48 7.2 3.456Ordinary Shares 40 19.9 7.960Preference Shares 12 13.68 1.642

13.058%

Thus, the cost of capital for ABC Company is 13.058%.

It is appropriate to again mention that it is impossible to be exact to five significantfigures when calculating the cost of capital. Nevertheless, this cost of capital willprovide a useful guideline rather than an absolute value.

InternallyGeneratedFunds

Profit generated within the firm which is not passed on to shareholders in the formof dividends can also be used for financing the assets of the company. Theseretained earnings are equity and are therefore expected to earn the rate of return ofordinary shares. There are no issuing fees associated with using internallygenerated funds, so the cost of these funds, Kre, is given by:

re1

0K = D

P+ g

In the example of ABC Company, this has been calculated at 19%.

Changes inthe Cost ofCapital

It is always desirable to use the lowest cost of capital when investing. Yet it cannotbe assumed that the cost of raising funds is constant for all levels of funding. It ispossible, for example, to use internally generated retained earnings as the equitycomponent of the weighted average cost of capital only to the amount that isavailable. Beyond this amount, there are additional transaction costs incurred withraising additional equity which must be considered. Likewise, the cost of issuingdebt or preferred shares may well change with different amounts of capital.Assuming the firm’s capital structure - that is percentages of debt, preferred shares,and ordinary shares - is to remain the same, then it is necessary to know when thecost of capital changes.

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What size of project can be financed with the lowest possible cost of capital? Thisis calculated by dividing the total funds available at each cost of capital level fromeach source, by the percentage of total assets financed by that source.

Example ABC Company has discovered that the $59.21 of issuing fees per bond issued isonly for the first $5,000,000 of funds. Beyond this amount, the fees increase to$80.00 per bond. ABC has available $2,000,000 of internally generated funds.Calculate where the breaks (changes) in the cost of capital occur and graph theresulting weighted cost of capital. Remember that the proportions of debt, ordinaryshares and preference shares are 48%, 40% and 12% respectively.

The total amount available from all sources when only using the internallygenerated funds is:

Total available = $2 m / 40%= $5 m

The total available from all sources when only using the lower cost debt issue is:

Total available = $5m / 48% = $10.42 m

Thus, all projects totalling less than $5 million can be financed using the lowest costof capital of 12.698% calculated in Exhibit 17.2.



12.698%

Note that up to $5m, the cost of retained funds is 19%, not 19.9%, the latter beingthe cost of issuing new shares and includes the issue fee.

Between $5m and $10.42m, the cost has already been calculated at 13.058% (referExhibit 17.1). Projects costing more than $10.42m will result in a higher cost ofdebt of 7.427%, found using calculations as described under Cost of Debt. Usingthis new cost of debt the weighted average cost of capital is 13.167% shown inExhibit 17.3.



13.167%

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The various costs of capital can now be summarised:

Exhibit 17.4 Funding Level Cost of Capital Reason for Change(millions)

0-5 12.698% Run out of retained earnings: increase in cost of equity at $5 million of total spending

5-10.42 13.058% Increase in cost of debt at $10.42 million

>10.42 13.167% N/A

Graphing these results shows clearly the changes in the cost of capital:

Exhibit 17.5 WACC%

12.698%

13.058%

13.167%

Smoothed GraphReflecting Marginal

Increases toCost of Capital

$5m $10.42m Level of Total Funding

SummaryWhen making investment decisions, the financial manager must know the cost ofcapital to be used in the investments. The cost of capital is the discount rate(sometimes called a hurdle rate) which will be used in the capital investmentprocess to determine if projects are financially acceptable. The cost of capital is afunction of the business risk, financial risk, and the total amount of fundingnecessary.

Business risk can be observed in the market place by observing companies in thesame line of business. Financial risk, which is a function of the debt to asset ratio ofthe company, can be taken into account by using the Capital Asset Pricing Model.Assuming a fixed financial structure and the same business risk, it is possible tocalculate the weighted average cost of capital. These weightings enable the analystor decision maker to determine the levels of funding at which the cost of capital

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changes. By adding the lowest possible profitable discount rate for each project toa graph of these ‘breaks’ in the cost of capital, it becomes clear which projects arefinancially feasible.

Glossary ofKey Terms

BetaA measure of how a given instrument moves with respect to the overall market forthose instruments.

Business RiskThe variability of expected returns in a particular line of business.

Capital Asset Pricing Model (CAPM)A model that measures the risk of one security in relation to the risk of othersecurities.

Financial RiskThe portion of risk excess to business risk that results from financial leverage.

Weighted Average Cost of Capital (WACC)A weighted average of the cost of a company’s funding components, which assumesthat business and financial risk, as well as dividend policy remain constant. It isactually the weighted average of the next basket of capital, and thus it is a marginalconcept and does not refer to the existing capital.

SelectedReadings

Black, F., Jensen, M.C. & Scholes, M., ‘The Capital Asset Pricing Model: SomeEmpirical Tests’, in Jensen, M.C. (ed) Studies in the Theory of Capital Markets,Praeger, New York, 1971.

Brealey R. & Myers, S., Principles of Corporate Finance, McGraw-Hill, NewYork, 1981.

Brigham, E.F. and Gardenski, L.C., Financial Management Theory and Practice,Fifth Edition, The Dryden Press, 1988.

Buckley, A., ‘Beta Geared and Ungeared’, British Readings in FinancialManagement, 1989, pp 199-207.

Francis, J.C., Investments: Analysis and Management, 4th Edition, McGraw-Hill,New York, 1986.

Keown, A.J., Scott, D.F., Martin, J.D., and Petty, J.W., Basic FinancialManagement, Third Edition, Prentice-Hall, 1985.

Peirson, G., and Bird, R., Business Finance, Third Edition, McGraw Hill, Sydney,1983.

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Pringle, J.J. and Harris, R.S., Essentials of Managerial Finance, Scott Foresman &Co, Glenview, Illinois, 1984.

Reilly, F.K., Investment Analysis and Portfolio Management, Second Edition, TheDryden Press, 1985.

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Questions

17.1 What is meant by the term ‘cost of capital’?

17.2 What factors affect the investors’ required rate of return?

17.3Why is it important for managers to know the firm’s cost of capital?

17.4What are the drawbacks of using WACC as a yardstick for evaluating the profitability of investments?

17.5Explain why there is a cost associated with the use of retained earnings.

17.6Explain the difference between business risk and financial risk.

17.7“Since the project is to be financed solely with debt, its required rate of return is the required return ondebt.” Comment.

17.8Why are market values more appropriate than book values in computing the weightings in thecalculation of the weighted average cost of capital?

17.9Why is it more difficult to measure the cost of ordinary equity than the cost of other sources offinance?

17.10“The marginal cost of capital is still an average cost.” Discuss.

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17.11Estimate the effect of each of the following factors on a firm’s weighted average cost of capital. Indicate an increase by ‘+’, a decrease by ‘-‘, and no effect by ‘0’.

a. The firm raises an additional $1.2m to finance a proposed expansion.b. The firm increases its leverage.c. The company tax rate is increased.d. The government implements policies aimed at increasing the money supply which will reduce

interest rates.e. Investors become less risk averse.f. The inflation rate increases by 3%.

17.12The following information relates to Fred’s Feline Boarding Home Ltd for the year ended 31 March1990.

Proportion Debt, Equity, Preference shares 40%, 30%, 30%Net income (before tax) $53,000Dividend payout rate 60%Tax rate 48%Growth in earnings 5%Dividend (this year) $0.55Share price $3.20

New Capital:Ordinary Shares - issue costs 10% up to $15,000 and 20% over $15,000Preference Shares - new shares can be issued at a price of $15.00 per share. The annualdividend on preference shares is $2.00. Issue costs of $0.50 per share would be incurred up to $20,000, and would rise to $0.60 forissues over $20,000.Debt - up to $17,000 of debt can be sold at an interest rate of 13%. The rate increases to 16%for the range $17,000 to $22,000, and for amounts over $22,000 the rate is 18%.

The company has the following investment opportunities:

Project Initial Outlay Project Life (yrs) Projected IRRA $20,000 4 11.0%B $17,000 7 15.0%C $15,000 12 10.0%D $18,000 5 17.0%E $15,000 3 14.5%

Required:Determine which projects should be accepted.

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17.13A company has the following capital structure:

Debt 40%Ordinary shares 50%Preference shares 10%

and the following investment opportunities available to it:

Investment Initial Outlay IRRA $30,000 13%B $22,500 16%C $10,000 15%D $40,000 18%

Assuming that the company wishes to maintain its current capital structure and has a weighted averagecost of capital of 14.3%, which of the investments can be undertaken if the firm can raise:a. $25,000 debtb. $30,000 debtc. $4,000 preference sharesd. $32,000 ordinary sharese. $70,000 ordinary shares

17.14XYZ Company is considering four investment alternatives:

Investment Initial Outlay IRRA $150,000 9%B $90,000 10%C $100,000 11%D $120,000 12%

The firm’s desired debt/equity ratio is 1.1:1. The pre-tax cost of debt is 8% for the first $100,000 and10% for amounts over $100,000. Retained earnings of $120,000 are available with an opportunitycost of 15%. Assuming that XYZ has a 48% tax rate, a 3% dividend growth rate, and issue costs onordinary shares of 8%, which projects should be accepted?

17.15ABC Company is about to issue some ordinary shares at a market price of $12.56. Last year’sdividend was $0.77 and the dividend six years ago was $0.50. Issue costs will be 5% of the marketprice. Assuming a constant dividend growth rate, what is ABC’s cost of equity? What is the cost ofretained earnings?

17.16Anderson Company is about to issue a 10 year $10,000 debenture with a coupon rate of 12%. Investors are willing to pay $13,246 for the debenture. Assuming flotation costs of 10% and a tax rateof 48%, what will be the firm’s after tax cost of debt?

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17.17The current market price of preference shares in Ali’s Aluminium Yacht Company is $6.50 and theshares pay $0.70 in dividends. If issue costs are 12% of the market price, what is the cost of capitalfor preference shares?

17.18Maxi Corporation wants to raise $800,000 to finance a plant expansion. Management has decidedthat in order to finance the expansion, a series of 15 year $1,000 par value bonds will be issuedcarrying a coupon rate of 12%. The market rate of interest for bonds in the same risk class is 17%.

Required:a. What is the market price of the bonds?b. If issue costs of 10% are incurred, how many bonds must the firm issue?c. What is the firm’s cost of debt after tax of 48%?

17.19The information provided below relates to the XYZ Company.

Source % Total Finance Price Issue CostsOrdinary Shares 43% 6.58 5%Preference Shares 7% 11.50 7%($10 par, 10% dividend) Bonds 50% 849.28 10%($1,000 par value, 12% coupon, 10 yrs maturity)

Assuming that dividends on ordinary shares were $0.71 last year and have been growing at an annualrate of 7% and that the company tax rate is 48%, what is the weighted average cost of capital if XYZissues no new ordinary shares but finances in the proportions suggested above?

17.20The manager of ABC Ltd has computed the marginal costs for each of the company’s three sources ofcapital:

Source Amount of Finance($) CostOrdinary shares 0 - 500,000 14.0%

500,000 - 1,200,000 17.0% > 1,200,000 18.0%

Preference shares 0 - 100,000 12.0% 100,000 - 300,000 13.0% > 300,000 13.5%

Debt 0 - 600,000 5.0% 600,000 - 1,000,000 7.0% > 1,000,000 8.0%

Required:If the manager wants to maintain the company’s present capital structure of 60% debt, 5% preferenceshares, and 35% ordinary shares, construct XYZ’s weighted MCC curve.

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17.21In order to finance the purchase of a new building Henderson Company is to issue new bonds at acoupon rate of 11%. Management intends to sell the bonds at a price which gives a yield to maturityof 15%. The company tax rate is 48%. What is Henderson Company’s after tax cost of debt?

17.22In 1989 Mini Company had earnings per share of $1.29 and a payout ratio of 70%. In 1982 earningsper share were $0.98. If the current share price (1990) is $7.83, what is the cost of retained earningsin 1990?

17.23Management predicts that Mini Company will have earnings of $3.5m next year. Mini has a payoutratio of 70% and a debt/equity ratio of 1.27 (Mini has issued no preference shares). At what amountof total finance will there be a break in the MCC curve?

17.24Maxi Company shares last year earned a dividend of $1.31 and dividends are expected to grow at anannual rate of 7%. Shares are currently traded at $13.50 and additional shares can be sold to yield thecompany a price of $12.69.

Required:a. What percent issue costs does Maxi incur?b. What is the cost of new equity?

17.25Elton Company is considering a number of new projects which together are expected to cost $30m. The firm’s current capital structure, as shown below, is considered to be optimal.

Ordinary shares $19mPreference shares $6mDebentures $25m

$50m

Ordinary Shares - currently traded at $22.50 per share, can be issued through a merchant bankwhich will charge a 6% underwriting fee. Investors expect a dividend yield of 7% and adividend growth rate of 6%. Retained earnings of $5.2m are available for investment.Preference Shares - earn dividends of $1.60 per share. Additional preference shares can beissued at a price of $14.50 (net of issue costs).Debentures - up to $12m can be sold at a rate of 13%, any amounts over $12m will carry a rateof 15%.

Required:a. Assuming a tax rate of 48% calculate the firm’s marginal cost of capital curve.b. How can the firm use the information in (a) to determine which projects should be accepted?

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17.26What are the three factors that influence the demanded rate of return by investors?

17.27Nixon Company has a $1,000 par value bond outstanding that pays 11% annual interest. The currentyield to maturity on such bonds in the market is 14%. Compute the price of the bond based on thesematurity dates:a. 30 yearsb. 15 yearsc. 1 year

17.28Bonds issued by Lawncorp have a par value of $1,000, they sell for $1,034 and have 15 yearsremaining to maturity. The annual interest payment is 12.5%. Compute the approximate yield tomaturity.

17.29Yesterday Anderson Company paid a dividend of $2.50. Dividends are expected to grow at 5% in theforeseeable future. If investors have a required rate of return of 12% what is the current price of 10shares in Anderson Company?

17.30Growthcorp paid a dividend yesterday of $1.75. The dividend is expected to grow at a rate of 25%over the next four years. It will then grow at a normal, constant rate of 7% for the foreseeable future.If the required rate of return is 10%, what is the current price of one share in Growthcorp?

17.31Logan Manufacturing is a very large company with shares listed on the New Zealand Stock Exchange. The company has five investment alternatives available for 1990 and the financial adviser needs todetermine their weighted average cost of capital in order to recommend one alternative. Theinvestments are:

Investment Estimated Cost Rate of ReturnA 150,000 13.0%B 100,000 12.0%

C 175,000 11.5% D 100,000 11.0% E 75,000 10.0%

Logan Manufacturing presently has a capital structure of:

Debt 400,000Common Stock 500,000Preferred Stock 100,000 $1,000,000

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and they wish to maintain this structure in the future. Logan Manufacturing had earnings per share in1989 of $18.75 per share which was a 10% increase from 1988. This growth rate is expected to bemaintained in the future and dividends and the market price of the firm have grown at the same rate.The firm has a payout ratio of 40% and this will also be maintained in the future. The following information is available regarding the individual costs of capital:

Debt - debt consists of bonds with an annual coupon rate of 9% on a $1,000 face value over 10years. The present market value of the bonds is $800. The company will incur issuing costs of7.6% (before tax) if the amount of bonds issued does not exceed $200,000. If this amount isexceeded then the issuing costs will rise to 17.25%. The company’s tax rate is 40%. Preference Shares - can be issued with a par value of $60, paying an annual dividend of $5.00. No issuing costs will be incurred. Ordinary Shares - current price of ordinary shares is $250. If the issue is not greater than$100,000 a 6% flotation cost would result. For any additional issue, the flotation cost willincrease to 20% of the market price. Retained Earnings - there will be $50,000 of retained earnings available for investment in1990.

Required:Based upon the above information, recommend which investment project should be undertaken in1990.

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17 COST OF CAPITAL - University of Waikatocms.mngt.waikato.ac.nz/webdocs/personal/evos/Textbookpdf/chap17p… · Chapter 17: Cost of Capital 341 This concept of business risk is often

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