Chapter 9
The Cost of Capital
ANSWERS TO END-OF-CHAPTER QUESTIONS


9-1 a. The weighted average cost of capital, WACC, is the weighted average of the after-tax component costs of capital—-debt, preferred stock, and common equity. Each weighting factor is the proportion of that type of capital in the optimal, or target, capital structure. The after-tax cost of debt, rd(1 - T), is the relevant cost to the firm of new debt financing. Since interest is deductible from taxable income, the after-tax cost of debt to the firm is less than the before-tax cost. Thus, rd(1 - T) is the appropriate component cost of debt (in the weighted average cost of capital).

b. The cost of preferred stock, rps, is the cost to the firm of issuing new preferred stock. For perpetual preferred, it is the preferred dividend, Dps, divided by the net issuing price, Pn. Note that no tax adjustments are made when calculating the component cost of preferred stock because, unlike interest payments on debt, dividend payments on preferred stock are not tax deductible. The cost of new common equity, re, is the cost to the firm of equity obtained by selling new common stock. It is, essentially, the cost of retained earnings adjusted for flotation costs. Flotation costs are the costs that the firm incurs when it issues new securities. The amount actually available to the firm for capital investment from the sale of new securities is the sales price of the securities less flotation costs. Note that flotation costs consist of (1) direct expenses such as printing costs and brokerage commissions, (2) any price reduction due to increasing the supply of stock, and (3) any drop in price due to informational asymmetries.

c. The target capital structure is the relative amount of debt, preferred stock, and common equity that the firm desires. The WACC should be based on these target weights.

d. There are considerable costs when a company issues a new security, including fees to an investment banker and legal fees. These costs are called flotation costs. The cost of new common equity is higher than that of common equity raised internally by reinvesting earnings. Project’s financed with external equity must earn a higher rate of return, since they project must cover the flotation costs.

9-2 The WACC is an average cost because it is a weighted average of the firm's component costs of capital. However, each component cost is a marginal cost; that is, the cost of new capital. Thus, the WACC is the weighted average marginal cost of capital.




9-3 Probable Effect on
rd(1 - T) rs WACC

a. The corporate tax rate is lowered. + 0 +

b. The Federal Reserve tightens credit. + + +

c. The firm uses more debt; that is, it
increases its debt/assets ratio. + + 0

d. The firm doubles the amount of capital
it raises during the year. 0 or + 0 or + 0 or +

e. The firm expands into a risky
new area. + + +

f. Investors become more risk averse. + + +

9-4 Stand-alone risk views a project’s risk in isolation, hence without regard to portfolio effects; within-firm risk, also called corporate risk, views project risk within the context of the firm’s portfolio of assets; and market risk (beta) recognizes that the firm’s stockholders hold diversified portfolios of stocks. In theory, market risk should be most relevant because of its direct effect on stock prices.

9-5 If a company’s composite WACC estimate were 10 percent, its managers might use 10 percent to evaluate average-risk projects, 12 percent for those with high-risk, and 8 percent for low-risk projects. Unfortunately, given the data, there is no completely satisfactory way to specify exactly how much higher or lower we should go in setting risk-adjusted costs of capital.




SOLUTIONS TO END-OF-CHAPTER PROBLEMS



9-1 40% Debt; 60% Equity; rd = 9%; T = 40%; WACC = 9.96%; rs = ?

WACC = (wd)(rd)(1 - T) + (wce)(rs)
9.96% = (0.4)(9%)(1 - 0.4) + (0.6)rs
9.96% = 2.16% + 0.6rs
7.8% = 0.6rs
rs = 13%.


9-2 Vps = $50; Dps = $3.80; F = 5%; rps = ?

rps =
=
= = 8%.


9-3 P0 = $30; D1 = $3.00; g = 5%; rs = ?

rs = + g = + 0.05 = 15%.


9-4 a. rd(1 - T) = 13%(1 - 0) = 13.00%.

b. rd(1 - T) = 13%(0.80) = 10.40%.

c. rd(1 - T) = 13%(0.65) = 8.45%.


9-5 rd(1 - T) = 0.12(0.65) = 7.80%.


9-6 rps = = = = 11.94%.


9-7 Enter these values: N = 60, PV = -515.16, PMT = 30, and FV = 1000, to get I = 6% = periodic rate. The nominal rate is 6%(2) = 12%, and the after-tax component cost of debt is 12%(0.6) = 7.2%.

9-8 a. rs = + g = + 7% = 9.3% + 7% = 16.3%.

b. rs = rRF + (rM - rRF)b
= 9% + (13% - 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% = 15.4%.

c. rs = Bond rate + Risk premium = 12% + 4% = 16%.

d. The bond-yield-plus-risk-premium approach and the CAPM method both resulted in lower cost of equity values than the DCF method. The firm's cost of equity should be estimated to be about 15.9 percent, which is the average of the three methods.

9-9 a. $6.50 = $4.42(1+g)5
(1+g)5 = 6.50/4.42 = 1.471
(1+g) = 1.471(1/5) = 1.080
g = 8%.

Alternatively, with a financial calculator, input N = 5, PV = -4.42, PMT = 0, FV = 6.50, and then solve for I = 8.02% » 8%.

b. D1 = D0(1 + g) = $2.60(1.08) = $2.81.

c. rs = D1/P0 + g = $2.81/$36.00 + 8% = 15.81%.

9-10 a. rs = + g
0.09 = + g
0.09 = 0.06 + g
g = 3%.

b. Current EPS $5.400
Less: Dividends per share 3.600
Retained earnings per share $1.800
Rate of return ? 0.090
Increase in EPS $0.162
Current EPS 5.400
Next year's EPS $5.562

Alternatively, EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562.


9-11 a. Common equity needed:

0.5($30,000,000) = $15,000,000.

b. Cost using rs:

After-Tax
Percent ? Cost = Product
Debt 0.50 4.8%* 2.4%
Common equity 0.50 12.0 6.0
WACC = 8.4%

*8%(1 - T) = 8%(0.6) = 4.8%.

c. rs and the WACC will increase due to the flotation costs of new equity.


9-12 The book and market value of the current liabilities are both $10,000,000.

The bonds have a value of

V = $60(PVIFA10%,20) + $1,000(PVIF10%,20)
= $60([1/0.10]-[1/(0.1*(1+0.10)20)]) + $1,000((1+0.10)-20)
= $60(8.5136) + $1,000(0.1486)
= $510.82 + $148.60 = $659.42.

Alternatively, using a financial calculator, input N = 20, I = 10, PMT = 60, and FV = 1000 to arrive at a PV = $659.46.
The total market value of the long-term debt is 30,000($659.46) = $19,783,800.
There are 1 million shares of stock outstanding, and the stock sells for $60 per share. Therefore, the market value of the equity is $60,000,000.
The market value capital structure is thus:

Short-term debt $10,000,000 11.14%
Long-term debt 19,783,800 22.03
Common equity 60,000,000 66.83
$89,783,800 100.00%


9-13 Several steps are involved in the solution of this problem. Our solution follows:

Step 1.

Establish a set of market value capital structure weights. In this case, A/P and accruals, and also short-term debt, may be disregarded because the firm does not use these as a source of permanent financing.

Debt:

The long-term debt has a market value found as follows:

V0 = = $699,

or 0.699($30,000,000) = $20,970,000 in total.
Preferred Stock:

The preferred has a value of

Pps = = $72.73.

There are $5,000,000/$100 = 50,000 shares of preferred outstanding, so the total market value of the preferred is

50,000($72.73) = $3,636,500.

Common Stock:

The market value of the common stock is

4,000,000($20) = $80,000,000.

Therefore, here is the firm's market value capital structure, which we assume to be optimal:

Long-term debt $ 20,970,000 20.05%
Preferred stock 3,636,500 3.48
Common equity 80,000,000 76.47
$104,606,500 100.00%

We would round these weights to 20 percent debt, 4 percent preferred, and 76 percent common equity.
Step 2.

Establish cost rates for the various capital structure components.

Debt cost:

rd(1 - T) = 12%(0.6) = 7.2%.

Preferred cost:

Annual dividend on new preferred = 11%($100) = $11. Therefore,

rps = $11/$100(1 - 0.05) = $11/$95 = 11.6%.

Common equity cost:

There are three basic ways of estimating rs: CAPM, DCF, and risk premium over own bonds. None of the methods is very exact.

CAPM:

We would use rRF = T-bond rate = 10%. For RPM, we would use 4.5% to 5.5%. For beta, we would use a beta in the 1.3 to 1.7 range. Combining these values, we obtain this range of values for rs:

Highest: rs = 10% + (5.5)(1.7) = 19.35%.
Lowest: rs = 10% + (4.5)(1.3) = 15.85%.
Midpoint: rs = 10% + (5.0)(1.5) = 17.50%.

DCE:

The company seems to be in a rapid, nonconstant growth situation, but we do not have the inputs necessary to develop a nonconstant rs. Therefore, we will use the constant growth model but temper our growth rate; that is, think of it as a long-term average g that may well be higher in the immediate than in the more distant future.
Data exist that would permit us to calculate historic growth rates, but problems would clearly arise, because the growth rate has been variable and also because gEPS ? gDPS. For the problem at hand, we would simply disregard historic growth rates, except for a discussion about calculating them as an exercise.
We could use as a growth estimator this method:

g = b(r) = 0.5(24%) = 12%.

It would not be appropriate to base g on the 30% ROE, because investors do not expect that rate.
Finally, we could use the analysts' forecasted g range, 10 to 15 percent. The dividend yield is D1/P0. Assuming g = 12%,

= = 5.6%.

One could look at a range of yields, based on P in the range of $17 to $23, but because we believe in efficient markets, we would use P0 = $20. Thus, the DCF model suggests a rs in the range of 15.6 to 20.6 percent:

Highest: rs = 5.6% + 15% = 20.6%.
Lowest: rs = 5.6% + 10% = 15.6%.
Midpoint: rs = 5.6% + 12.5% = 18.1%.

Generalized risk premium.

Highest: rs = 12% + 6% = 18%.
Lowest: rs = 12% + 4% = 16%.
Midpoint: rs = 12% + 5% = 17%.

Based on the three midpoint estimates, we have rs in this range:

CAPM 17.5%
DCF 18.1%
Risk Premium 17.0%

Step 3.

Calculate the WACC:

WACC = (D/V)(rdAT) + (P/V)(rps) + (S/V)(rs or re)
= 0.20(rdAT) + 0.04(rps) + 0.76(rs or re).

It would be appropriate to calculate a range of WACCs based on the ranges of component costs, but to save time, we shall assume rdAT = 7.2%, rps = 11.6%, and rs = 17.5%. With these cost rates, here is the WACC calculation:

WACC = 0.2(7.2%) + 0.04(11.6%) + 0.76(17.5%) = 15.2%.




9-14 P0 = $30; D1 = $3.00; g = 5%; F = 10%; rs = ?

rs = [D1/(1-F) P0] + g = [3/(1-0.10)(30)] + 0.05 = 16.1%.


9-15 Enter these values: N = 20, PV =1000(1-0.02)=980, PMT = -90(1-.4)=-54, and
FV = -1000, to get I = 5.57%, which is the after-tax component cost of debt.





SPREADSHEET PROBLEM



9-16 The detailed solution for the problem is available both on the instructor’s resource CD-ROM (in the file Solution for FM11 Ch 09 P16 Build a Model.xls) and on the instructor’s side of the web site, http://brigham.swcollege.com.




MINI CASE



During the last few years, Harry Davis Industries has been too constrained by the high cost of capital to make many capital investments. Recently, though, capital costs have been declining, and the company has decided to look seriously at a major expansion program that had been proposed by the marketing department. Assume that you are an assistant to Leigh Jones, the financial vice-president. Your first task is to estimate Harry Davis’ cost of capital. Jones has provided you with the following data, which she believes may be relevant to your task:

1. The firm's tax rate is 40 percent.

2. The current price of Harry Davis’ 12 percent coupon, semiannual payment, noncallable bonds with 15 years remaining to maturity is $1,153.72. Harry Davis does not use short-term interest-bearing debt on a permanent basis. New bonds would be privately placed with no flotation cost.

3. The current price of the firm's 10 percent, $100 par value, quarterly dividend, perpetual preferred stock is $113.10. Harry Davis would incur flotation costs of $2.00 per share on a new issue.

4. Harry Davis’ common stock is currently selling at $50 per share. Its last dividend (d0) was $4.19, and dividends are expected to grow at a constant rate of 5 percent in the foreseeable future. Harry Davis’ beta is 1.2; the yield on t-bonds is 7 percent; and the market risk premium is estimated to be 6 percent. For the bond-yield-plus-risk-premium approach, the firm uses a 4 percentage point risk premium.

5. Harry Davis’ target capital structure is 30 percent long-term debt, 10 percent preferred stock, and 60 percent common equity.

To structure the task somewhat, Jones has asked you to answer the following questions.

a. 1. What sources of capital should be included when you estimate Harry Davis’ weighted average cost of capital (WACC)?

Answer: The WACC is used primarily for making long-term capital investment decisions, i.e., for capital budgeting. Thus, the WACC should include the types of capital used to pay for long-term assets, and this is typically long-term debt, preferred stock (if used), and common stock. Short-term sources of capital consist of (1) spontaneous, noninterest-bearing liabilities such as accounts payable and accruals and (2) short-term interest-bearing debt, such as notes payable. If the firm uses short-term interest-bearing debt to acquire fixed assets rather than just to finance working capital needs, then the WACC should include a short-term debt component. Noninterest-bearing debt is generally not included in the cost of capital estimate because these funds are netted out when determining investment needs, that is, net rather than gross working capital is included in capital expenditures.


a. 2. Should the component costs be figured on a before-tax or an after-tax basis?

Answer: Stockholders are concerned primarily with those corporate cash flows that are available for their use, namely, those cash flows available to pay dividends or for reinvestment. Since dividends are paid from and reinvestment is made with after-tax dollars, all cash flow and rate of return calculations should be done on an after-tax basis.


a. 3. Should the costs be historical (embedded) costs or new (marginal) costs?

Answer: In financial management, the cost of capital is used primarily to make decisions which involve raising new capital. Thus, the relevant component costs are today's marginal costs rather than historical costs.


b. What is the market interest rate on Harry Davis’ debt and its component cost of debt?

Answer: Harry Davis’ 12 percent bond with 15 years to maturity is currently selling for $1,153.72. Thus, its yield to maturity is 10 percent:

0 1 2 3 29 30
| | | | · · · | |
-1,153.72 60 60 60 60 60
1,000

Enter n = 30, PV = -1153.72, pmt = 60, and FV = 1000, and then press the i button to find rd/2 = i = 5.0%. Since this is a semiannual rate, multiply by 2 to find the annual rate, rd = 10%, the pre-tax cost of debt.
Since interest is tax deductible, Uncle Sam, in effect, pays part of the cost, and Harry Davis’ relevant component cost of debt is the after-tax cost:

rd(1 - T) = 10.0%(1 - 0.40) = 10.0%(0.60) = 6.0%.


Optional Question

Should flotation costs be included in the estimate?

Answer: The actual component cost of new debt will be somewhat higher than 6 percent because the firm will incur flotation costs in selling the new issue. However, flotation costs are typically small on public debt issues, and, more important, most debt is placed directly with banks, insurance companies, and the like, and in this case flotation costs are almost nonexistent.


Optional Question

Should you use the nominal cost of debt or the effective annual cost?

Answer: Our 10 percent pre-tax estimate is the nominal cost of debt. Since the firm's debt has semiannual coupons, its effective annual rate is 10.25 percent:

(1.05)2 - 1.0 = 1.1025 - 1.0 = 0.1025 = 10.25%.

However, nominal rates are generally used. The reason is that the cost of capital is used in capital budgeting, and capital budgeting cash flows are generally assumed to occur at year-end. Therefore, using nominal rates makes the treatment of the capital budgeting discount rate and cash flows consistent.


c. 1. What is the firm's cost of preferred stock?

Answer: Since the preferred issue is perpetual, its cost is estimated as follows:

rps = = = = 0.090 = 9.0%.

Note (1) that flotation costs for preferred are significant, so they are included here, (2) that since preferred dividends are not deductible to the issuer, there is no need for a tax adjustment, and (3) that we could have estimated the effective annual cost of the preferred, but as in the case of debt, the nominal cost is generally used.


c. 2. Harry Davis’ preferred stock is riskier to investors than its debt, yet the preferred's yield to investors is lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? (Hint: think about taxes.)

Answer: Corporate investors own most preferred stock, because 70 percent of preferred dividends received by corporations are nontaxable. Therefore, preferred often has a lower before-tax yield than the before-tax yield on debt issued by the same company. Note, though, that the after-tax yield to a corporate investor, and the after-tax cost to the issuer, are higher on preferred stock than on debt.


d. 1. What are the two primary ways companies raise common equity?

Answer: A firm can raise common equity in two ways: (1) by retaining earnings and (2) by issuing new common stock.


d. 2. Why is there a cost associated with reinvested earnings?

Answer: Management may either pay out earnings in the form of dividends or else retain earnings for reinvestment in the business. If part of the earnings is retained, an opportunity cost is incurred: stockholders could have received those earnings as dividends and then invested that money in stocks, bonds, real estate, and so on.


d. 3. Harry Davis doesn’t plan to issue new shares of common stock. Using the CAPM approach, what is Harry Davis’ estimated cost of equity?

Answer: rs = 0.07 + (0.06)1.2 = 14.2%.


e. 1. What is the estimated cost of equity using the discounted cash flow (DCF) approach?

Answer: = = = = 13.8%.


e. 2. Suppose the firm has historically earned 15 percent on equity (ROE) and retained 35 percent of earnings, and investors expect this situation to continue in the future. How could you use this information to estimate the future dividend growth rate, and what growth rate would you get? Is this consistent with the 5 percent growth rate given earlier?

Answer: Another method for estimating the growth rate is to use the retention growth model:

g = (1 - Payout Ratio)ROE

In this case g = (0.35)0.15 = 5.25%. This is consistent with the 5% rate given earlier.


e. 3. Could the DCF method be applied if the growth rate was not constant? How?

Answer: yes, you could use the DCF using nonconstant growth. You would find the PV of the dividends during the nonconstant growth period and add this value to the PV of the series of inflows when growth is assumed to become constant.


f. What is the cost of equity based on the bond-yield-plus-risk-premium method?

Answer: rs = company’s own bond yield + risk premium.

First find the YTM of the bond:

Enter n = 30, PV = -1153.72, pmt = 60, and FV = 1000, and then press the i button to find r/2 = i = 5%. Since this is a semiannual rate, multiply by 2 to find the annual rate, r = 10%.
The assumed risk premium is 4%, thus

rs = 0.10 + 0.04 = 14%.


g. What is your final estimate for the cost of equity, rs?

Answer: The final estimate for the cost of equity would simply be the average of the values found using the above three methods.

CAPM 14.2%
DCF 13.8
BOND YIELD + R.P. 14.0
AVERAGE 14.0%


h. What is Harry Davis’ weighted average cost of capital (WACC)?

Answer: WACC= wdrd(1 - T) + wpsrps + wce(rs)
= 0.3(0.10)(0.6) + 0.1(0.09) + 0.6(0.14)
= 0.111 = 11.1%.


i. What factors influence Harry Davis’ composite WACC?

Answer: There are factors that the firm cannot control and those that they can control that influence WACC.

Factors The Firm Cannot Control:
Level Of Interest Rates
Tax Rates

Factors The Firm Can Control:
Capital Structure Policy
Dividend Policy
Investment Policy


j. Should the company use the composite WACC as the hurdle rate for each of its projects?

Answer: No. The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk. Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.


k. What procedures are used to determine the risk-adjusted cost of capital for a particular division? What approaches are used to measure a division’s beta?

Answer: The following procedures can be used to determine a division’s risk-adjusted cost of capital:

(1) Subjective adjustments to the firm’s composite WACC.

(2) Attempt to estimate what the cost of capital would be if the division were a stand-alone firm. This requires estimating the division’s beta.

The following approaches can be used to measure a division’s beta:

(1) Pure play approach. Find several publicly traded companies exclusively in the project’s business. Then, use the average of their betas as a proxy for the project’s beta. (It’s hard to find such companies.)

(2) Accounting beta approach. Run a regression between the project’s ROA and the S&P index ROA. Accounting betas are correlated (0.5 - 0.6) with market betas. However, you normally can’t get data on new project ROAs before the capital budgeting decision has been made.


l. Harry Davis is interested in establishing a new division, which will focus primarily on developing new internet-based projects. In trying to determine the cost of capital for this new division, you discover that stand-alone firms involved in similar projects have on average the following characteristics:
· Their capital structure is 10 percent debt and 90 percent common equity.
· Their cost of debt is typically 12 percent.
· The beta is 1.7.
given this information, what would your estimate be for the division’s cost of capital?

Answer:
rs DIV. = rRF + (rM - rRF)bDIV.
= 7% + (6%)1.7 = 17.2%.

WACCDIV. = Wdrd(1 - T) + Wcrs
= 0.1(12%)(0.6) + 0.9(17.2%)
= 16.2%.

The division’s WACC = 16.2% vs. The corporate WACC = 11.1%. The division’s market risk is greater than the firm’s average projects. Typical projects within this division would be accepted if their returns are above 16.2 percent.

m. What are three types of project risk? How is each type of risk used?

Answer: The three types of project risk are:

Stand-Alone Risk
Corporate Risk
Market Risk

Market risk is theoretically best in most situations. However, creditors, customers, suppliers, and employees are more affected by corporate risk. Therefore, corporate risk is also relevant. Stand-alone risk is the easiest type of risk to measure.
Taking on a project with a high degree of either stand-alone or corporate risk will not necessarily affect the firm’s market risk. However, if the project has highly uncertain returns, and if those returns are highly correlated with returns on the firm’s other assets and with most other assets in the economy, the project will have a high degree of all types of risk.


n. Explain in words why new common stock that is raised externally has a higher percentage cost than equity that is raised internally by reivesting earnings.

Answer: The company is raising money in order to make an investment. The money has a cost, and this cost is based primarily on the investors’ required rate of return, considering risk and alternative investment opportunities. So, the new investment must provide a return at least equal to the investors’ opportunity cost.
If the company raises capital by selling stock, the company doesn’t get all of the money that investors put up. For example, if investors put up $100,000, and if they expect a 15 percent return on that $100,000, then $15,000 of profits must be generated. But if flotation costs are 20 percent ($20,000), then the company will receive only $80,000 of the $100,000 investors put up. That $80,000 must then produce a $15,000 profit, or a 15/80 = 18.75% rate of return versus a 15 percent return on equity raised as retained earnings.


o. 1. Harry Davis estimates that if it issues new common stock, the flotation cost will be 15 percent. Harry Davis incorporates the flotation costs into the DCF approach. What is the estimated cost of newly issued common stock, taking into account the flotation cost?

Answer:



o. 2. Suppose Harry Davis issues 30-year debt with a par value of $1,000 and a coupon rate of 10%, paid annually. If flotation costs are 2 percent, what is the after-tax cost of debt for the new bond?

Answer: Using a financial calculator, n = 30, PV = (1-0.02)(1000) = 980, pmt = -(1-0.40)(100) = -60, FV = -1000. The resulting i is 6.15%, which is the after-tax cost of debt.



p. What four common mistakes in estimating the WACC should Harry Davis avoid?

Answer: 1. Don’t use the coupon rate on a firm’s existing debt as the pre-tax cost of debt. Use the current cost of debt.

2. When estimating the risk premium for the CAPM approach, don’t subtract the current long-term t-bond rate from the historical average return on stocks.
For example, the historical average return on stocks has been about 12.7%. If inflation has driven the current risk-free rate up to 10%, it would be wrong to conclude that the current market risk premium is 12.7% - 10% = 2.7%. In all likelihood, inflation would also have driven up the expected return on the market. Therefore, the historical return on the market would not be a good estimate of the current expected return on the market.

3. Don’t use book weights to estimte the weights for the capital structure. Use the target capital structure to determine the weights for the WACC. If you don’t have the target weights, then use market value rather than book value to obtain the weights. Use the book value of debt only as a last resort.

4. Always remember that capital components are sources of funding that come from investors. If it’s not a source of funding from an investor, then it’s not a capital component.