Pedro Palitos

8/9/2019 Pedro Palitos

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Old Exam Questions - Cost of Capital - Solutions Page 1 of 42 Pages

Cost of Capital - Solutions

1. When calculating a WACC for a company with preferred stock, there is no need toadjust the cost of the preferred stock to reflect the tax exclusion of 70% of thepreferred stock dividend.

* A. TrueB. False

2. A firm can only have one break point in its marginal cost of capital curve, which willoccur when they deplete their additions to retained earnings and must switch over tonew issues of equity.

A. True* B. False

3. Because creditors can foresee, to at least some extent, the costs of bankruptcy, theycharge a higher rate of interest to compensate for the present value of bankruptcy costs.

* A. TrueB. False

4. Increasing a companys debt ratio will typically reduce the marginal cost of both debt andequity financing; however, it still may raise the companys WACC.

A. True* B. False

5. Although quite rare, the mathematics is such that the after-tax component cost of debtfinancing can be greater than the after-tax component cost of equity financing.

A. True* B. False

6. The cost to the firm of retained earnings is zero, since they are generated from thecurrent earnings of the firm and there are no flotation costs associated with theirretention.

A. True* B. False

7. If we assume that the stock market is efficient, and if we assume that Stock A has a betaof 1.20, while Stock B has a beta of 1.40 (that is, B has higher risk than A), then we mustalso assume that the required rate of return on Stock B exceeds the required rate ofreturn on Stock A.


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* A. TrueB. False

8. If a firm must pay flotation expense when issuing a security, then the firms required rate

of return on that security will be greater than the investors required rate of return for thatsecurity.

* A. TrueB. False

9. The easiest way to correctly calculate the firms cost of debt is simply to multiply thecoupon rate on the debt times one minus the firms tax rate.

A. True* B. False

10. The cost of equity capital from the sale of new common stock (re) is generally equal tothe cost of equity capital from retention of earnings (rs), divided by one minus theflotation cost as a percentage of sales price (1 - F).

A. True* B. False

11. If expectations for long-term inflation rose, but the slope of the SML remained constant,this, for most firms, would have a greater impact on the required rate of return on equity,rs, than on the interest rate on long-term debt, rd. In other words, thepercentage point

increase in the cost of equity would be greater than the increase in the interest rate onlong-term debt. (Hint: play with some numbers and see what happens.)

A. True* B. False

12. If the tax laws stated that $0.50 out of every $1.00 of interest paid by a corporationwas allowed as a tax-deductible expense, it would probably encourage companies touse more debt financing than they presently do, other things held constant.

A. True* B. False

1. Which of the following statements is not (or least) correct?

* A. Because of the tax shelter created by issuing preferred stock dividends(remember that 70 percent of dividends are excluded from taxes), the firms


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after-tax cost of preferred stock may be significantly less than its before-taxcost.

B. The weighted average cost of embedded/historical capital (capital alreadyraised by the firm) will have little significance when the firm looks at taking onnew projects that will require them to issue additional capital.

C. Assume that a firm is comprised of two divisions that differ significantly in risk

and, therefore, in terms of their divisional screening rates. If the firm evaluatesall investments by using a weighted average corporate cost of capital (ratherthan using divisional screening rates), the firm is likely to become more risky bytaking on more of the higher-risk projects and become less valuable by takingon projects that earn a rate of return that is less than what they should beearned based on the actual risk of the project.

D. Flotation costs may not be a significant factor for a firms bonds, since manybond issues are privately placed (sold to institutional investors) with minimaladministrative expense. That is, the firm essentially nets what the institutionalinvestor pays.

E. Flotation costs may be a significant factor when a firm issues new shares ofcommon stock. If so, the firms cost of equity (new issues of common stock)

will be higher than the firms cost of retained earnings, but the firms cost ofretained earnings will still be equal to the investors required rate of return onthe firms common stock.

2. If a U.S. company with two divisions, one very risky and the other with significantly lessrisky, uses the same corporate discount rate to evaluate all projects, the most likelyoutcome, as discussed in class, is that the firm will become:

* A. Riskier over time, and its value will decline.B. Riskier over time, and its value will rise.C. Less risky over time, and its value will rise.

D. Less risky over time, and its value will decline.E. There is no reason to expect its risk position or value to change over time as a

result of its use of a single discount rate.

3. A firm is considering the purchase of an asset whose risk is greater than the currentrisk of the firm, based on any method for assessing risk. In evaluating this asset, thedecision maker should:

A. Increase the IRR of the asset to reflect the greater risk.B. Increase the NPV of the asset to reflect the greater risk.C. Reject the asset, since its acceptance would increase the risk of the firm.

D. Ignore the risk differential if the asset to be accepted would comprise only asmall fraction of the total assets of the firm.

* E. Increase the cost of capital used to evaluate the project to reflect the higher riskof the project.

4. Select the statement that is most correct.


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A. Since most stock is privately placed, a firms required rate of return for a newissue of common stock will be equal to the investors required rate of return forthat same issue.

B. The WACC represents the historical cost of capital and is usually calculated ona before-tax basis.

* C. When calculating the cost of debt, a company needs to adjust for taxes,

because interest payments are tax deductible.D. Since the money is readily available, the cost of retained earnings is usually a

lot cheaper than the cost of debt financing.E. When calculating the cost of preferred stock, a company needs to adjust for

taxes, because preferred stock dividends are tax deductible.


A. When a bonds coupon rate is greater than its yield to maturity, the coupon rateshould be used as the firms before-tax cost of debt.

* B. All other things equal (including component costs), a higher tax rate will lower a

firms WACC only if the firm uses debt financing.C. While higher-than-average risk projects require discounting cash flows at a rate

above the firms WACC, it is usually not appropriate to discount lower-than-average risk projects at a rate below the firms WACC.

D. Even if project risks vary widely within a firm, a projects cash flows shouldalways be discounted at the corporate cost of capital (WACC).

E. Because of the sheer size of large, publicly traded firms, it is more difficult touse the CAPM to estimate their cost of equity than to estimate it for small,privately held firms.

6. Which of the following statements is most correct?

A. An increase in the corporate tax rate, all other factors held constant, shouldlead to an increase in a firms weighted average cost of capital.

B. A firm can lower its component cost of debt simply by issuing debt with a lowercoupon rate.

* C. The enterprise value of the firm can be found by taking the free cash flowavailable to all investors and discounting it at the firms weighted average costof capital.

D. Since most equity is privately placed for publicly traded corporations, flotationcosts are negligible, and the firms cost of a new issue of common stock will be,therefore, essentially the same as the investors required rate of return.

E. Since the market value of the firms debt and equity will continuously changethroughout the day, and since the firms book value of debt and equity is muchmore stable over time, the firm should use book value weight to define itsoptimal capital structure.

7. Which of the following statements is most correct?


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* A. If a companys tax rate increases but the yield to maturity of its noncallablebonds remains the same, then, all other factors held constant, the firms WACCshould decrease.

B. If the beta of a companys equity decreases, then, even when flotation costshave been accounted for, it is possible for a company to achieve a lowerWACC by issuing new shares of common stock to meet its equity needs, rather

than relying upon retained earnings to meet those needs.C. Typically, the before-tax cost of debt financing exceeds the after-tax cost of

equity financing.D. Since the firm retains any earnings that are not needed to be paid out as

dividends, the cost of retained earnings is usually much cheaper that the costof debt financing.

E. All of the statements above are incorrect.

8. Which of the following statements is correct (most correct)?

A. Since there are no flotation costs associated with it, the cost of retained

earnings will always be less than the after-tax cost of debt financing.B. When calculating the cost of preferred stock, a company needs to adjust for

taxes, because preferred stock dividends are tax deductible for the issuing firm.C. If a companys tax rate increases then, all else equal, the companys weighted

average cost of capital will also increase.D. A decrease in the risk-free rate, all else equal, will likely increase the marginal

costs of both debt and equity securities.* E. A companys targeted capital structure will affect its cost of capital. Changes

from the target may cause the weighted average cost of capital to eitherincrease or decrease.


A. The before-taxcost of debt, which is lower than the after-taxcost, is used asthe component cost of debt for purposes of developing the firm's WACC.

B. The total returnon a share of stock refers to the dividend yield less anycommissions paid when the stock is purchased and sold.

C. The cost of issuing preferred stock by a corporation must be adjusted to anafter-tax figure because of the 70 percent dividend exclusion provision forcorporations holding other corporations' preferred stock.

D. The cost of equity raised by retaining earnings can be less than, equal to, orgreater than the cost of external equity raised by selling new issues of commonstock, depending on tax rates, flotation costs, the attitude of investors, andother factors.

* E. The component costs of capital are market-determined variables in as much asthey are based on investors' required returns.

1. Assume that a firm takes on a project that requires an initial investment in Year 0 of$20,000. Also assume that the firm raised the $20,000 by issuing $6,000 of debt at a


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before-tax cost of debt of 5%, and issued $14,000 of equity at a cost of equity of 10%.If the tax rate is 40%, then what is the weighted average cost of capital (WACC) forthis project?

A. 8.3%B. 7.7%

C. 8.1%D. 8.5%

* E. 7.9%

WACC = (.05)(1-.4)(30%) + (.10)(70%) = .009 + .07 = 7.9%

2. Your firm has estimated that it will spend $10 million on new capital budgeting projectsduring the coming year. You have been asked to calculate the appropriate cost ofcapital to be used to analyze these projects and have collected the followinginformation:

Your firms targeted capital structure consists of 40 percent debt and 60 percent

common equity. Your firm expects to add $4 million to retained earnings over the coming year that

can be used to support the $10 million in new projects. The company has corporate bonds outstanding with an 8 percent annual coupon

that are trading at par. New debt can be issued as a private placement (no flotation expense) and will

have the same level of risk as the firms current debt. The companys tax rate is 40 percent. The risk-free rate is 4 percent. The market risk premium is 5 percent. The stocks beta is 1.2. The company expects to pay a dividend on its common stock of $2.20 per share

next year (D1). The companys ROE is 10% and its dividend payout rate is 50%. The current stock price (P0) is $44 per share. If the firm issues new shares of common stock, they will sell for $44 per share, but

the firm will have to pay flotation expense of 10%. Each of the projects to be taken on has the same degree of risk as the current

projects of the firm.

What is the WACC of the entire $10 million to be raised?

A. 7.678%* B. 8.032%

C. 8.319%D. 8.598%E. 8.712%

Breakdown: Debt = ($10,000,000)(.40) = $4,000,000 40%Retained Earnings = $4,000,000 40%New Equity = ($10 - $4 - $4) = $2,000,000 20%

After-tax KD = (8%)(1-.40) = 4.8%


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KS = 0.04 + (0.05)(1.2) = 10%

Alternatively,

g = (0.10)(1 0.50) = 5%

KS = $2.20 / $44.00 + 0.05 = 0.05 + 0.05 = 10%

Ke = $2.20 / ($44.00)(1-0.10) + 0.05 = 10.56%

Therefore,

WACC = (4.8%)(0.40) + (10.0%)(0.40) + (10.56%)(0.20)

= 1.92% + 4.0% + 2.112% = 8.032%

3. Your company plans to issue debt with an annual coupon rate of 8.5% (interest paidsemi-annually) and which will mature in 20 years at a par value of $1,000. Your firmsinvestment bankers have stated that the bonds can be sold publicly to investors at aprice of $980 per bond, but that the firm will be required to pay a flotation expense tothe investment bankers equal to 2% of this price. If the firm has a marginal corporatetax rate of 35%, then what will be the firms after-tax cost on this new debt to beissued?

A. 5.35%B. 5.50%C. 5.65%

* D. 5.80%

E. 5.95%

Net Price = ($980) (1 - .02) = $960.40

N = 40PV = -$960.40PMT = ($85 / 2) = $42.50FV = $1,000

Solve for I/YR = 4.464097130%

KD = (4.464097130) (2) = 8.928194260%

After-tax KD = (8.928194260) (1 0.35) = 5.803326269% = 5.80%

YOU ARE GIVEN THE FOLLOWING INFORMATION FOR PROBLEMS 4 - 5:

Your company's current market-valued capital structure, which is considered to beoptimal, is shown below:


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Debt 40%Preferred Stock 10%Equity 50%

In order to meet their expansion plans for next year, the company has decided to raise

$5,000,000. Net Income is expected to be $550,000 next year. However, preferredstock dividends are expected to account for $50,000 of this profit. The common stockdividend payout rate is 40% of the profit after the payment of preferred dividends. Thecorporate tax rate is equal to 40%, and the before-tax costs of new financing areestimated to be:

Debt: 5% for the first $500,000 of new debt.6% for up to an additional $1,000,000 of new debt.7% for up to an additional $1,000,000 of new debt.

Preferred: 8% for the first $500,000 of new preferred.9% for up to an additional $500,000 of new preferred.

Equity: 12% for retained earnings.13% for up to the first $2,000,000 of new common stock.14% for up to an additional $2,000,000 of new common stock.15% for up to an additional $2,000,000 of new common stock.

4. What is the weighted average cost of capital for the very first dollar to be raised?

A. 8.34%B. 8.72%C. 8.23%

* D. 8.00%

E. 8.51%

After-tax Costs of Debt: 3.0%, 3.6%, and 4.2%

Debt 40% x 3.00 = 1.20%Preferred 10% x 8.00 = 0.80%RE 50% x 12.00 = 6.00%

8.00%

5. What is the weighted average cost of capital for the entire $5,000,000 to be raised forthe expansion?

A. 8.34%* B. 8.72%

C. 8.23%D 8.00%.E. 8.51%

RE = ($550,000 - $50,000)(1-.4) = $300,000



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There are several different ways to do this. One of them is below.

Debt $500/$5,000 = 10% x 3.00 = 0.30%Debt $1,000/$5,000 = 20% x 3.60 = 0.72%Debt $500/$5,000 = 10% x 4.20 = 0.42%

Preferred $500 = 10% x 8.00 = 0.80%RE $300 = 6% x 12.00 = 0.72%Equity $2,000 = 40% x 13.00 = 5.20%Equity $200 = 4% x 14.00 = 0.56%

8.72%

6. A firms optimal capital structure consists of 40 percent debt, 10 percent preferredstock, and 50 percent common stock. Assume that the firms before-tax cost of debt is8 percent and that its tax rate is 40 percent. Also assume that the firms cost ofpreferred stock is 10 percent and that its cost of common stock is 15 percent.Calculate the firms weighted average cost of capital (WACC).

A. 10.72%* B. 10.42%

C. 10.52%D. 10.82%E. 10.62%

WACC = (KD)(1-T)(WD) + (KP)(WP) + (KS)(WS)

WACC = (.08)(1-.4)(.40) + (.10)(.10) + (.15)(.50) = 0.0192 + 0.01 + 0.075 = 10.42%

7. A firms optimal capital structure consists of 35 percent debt, 5 percent preferred stock,and 60 percent common stock. Assume that the firms before-tax cost of debt is 6percent and that its tax rate is 40 percent. Also assume that the firms cost ofpreferred stock is 7 percent and that its cost of common stock is 11 percent. Calculatethe firms weighted average cost of capital (WACC).

A. 7.67%B. 8.52%

* C. 8.21%D. 7.89%E. 8.93%


WACC = (.06)(1-.4)(.35) + (.07)(.05) + (.11)(.60) = 0.0126 + 0.0035 + 0.066

WACC = 8.21%


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common equity. Your firm expects to add $2.7 million to retained earnings over the coming year

that can be used to support the $9 million in new projects. The company has corporate bonds outstanding with a 6 percent annual coupon

that are trading at par. New debt can be issued as a private placement (no flotation expense) and will

have the same level of risk as the firms current debt. The companys tax rate is 40 percent. The risk-free rate is 3 percent. The market risk premium is 5 percent. The stocks beta is 1.4. The company expects to pay a dividend on its common stock of $1.50 per share


the firm will have to pay flotation expense of 12.5%. Each of the projects to be taken on has the same degree of risk as the current



A. 7.81%B. 8.41%C. 8.21%

D. 8.61%* E. 8.01%

Breakdown: Debt = ($9,000,000)(.35) = $3,150,000 35%Retained Earnings = $2,700,000 30%New Equity = ($9 - $3.15 - $2.7) = $3,150,000 35%

After-tax KD = (6%)(1-.40) = 3.6%

KS = 0.03 + (0.05)(1.4) = 10%

Alternatively,

g = (0.10)(1 0.50) = 5%

KS = $1.50 / $30.00 + 0.05 = 0.05 + 0.05 = 10%

Ke = $1.50 / ($30.00)(1-0.125) + 0.05 = 10.71%

Therefore,


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WACC = (3.6%)(0.35) + (10.0%)(0.30) + (10.71%)(0.35)

= 1.26% + 3.0% + 3.7485% = 8.01%

9. A firms optimal capital structure consists of 35 percent debt, 5 percent preferred stock,

and 60 percent common stock. Assume that the firms before-tax cost of debt is 7percent and that its tax rate is 40 percent. Also assume that the firms cost ofpreferred stock is 10 percent and that its weighted average cost of capital is 10.52%.Calculate the firms cost of stock (equity).

A. 14.50%* B. 14.25%

C. 15.00%D. 14.00%E. 14.75%


WACC = (.07)(1-.4)(.35) + (.10)(.05) + (KS)(.60) = 10.52%

WACC = .0147 + .005 + (KS)(.60) = 10.52%

KS = (.1052 - .0147 - .005) / (.60) = .0855 / .60 = 14.25%

YOU ARE GIVEN THE FOLLOWING INFORMATION FOR PROBLEMS 10 - 11:

Your company's current market-valued capital structure, which is considered to beoptimal, is shown below:


In order to meet their expansion plans for next year, the company has decided to raise$10,000,000. Net Income is expected to be $1,000,000 next year. However, preferredstock dividends are expected to account for $100,000 of this profit. The common stockdividend payout rate is 40% of the profit after the payment of preferred dividends. Thecorporate tax rate is equal to 40%, and the before-tax costs of new financing areestimated to be:

Debt: 4% for the first $2,000,000 of new debt.5% for up to an additional $1,000,000 of new debt.6% for up to an additional $1,000,000 of new debt.

Preferred: 6% for the first $1,000,000 of new preferred.7% for up to an additional $1,000,000 of new preferred.

Equity: 10% for retained earnings.


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11% for up to the first $2,000,000 of new common stock.12% for up to an additional $2,000,000 of new common stock.13% for up to an additional $2,000,000 of new common stock.

10. What is the weighted average cost of capital for the very last dollar to be raised?

A. 9.60%B. 9.20%C. 9.40%D. 9.50%

* E. 9.30%

Debt = (.30)($10,000,000) = $3,000,000Preferred = (.10)($10,000,000) = $1,000,000Equity = (.60)($10,000,000) = $6,000,000

Additions to Retained Earnings = ($1,000,000 - $100,000)(1 - .4) = $540,000


Costs for very last dollar: Debt (3.0%); Preferred (6%); Equity (13%)

Debt 30% x 3.00 = 0.90%Preferred 10% x 6.00 = 0.60%RE 60% x 13.00 = 7.80%

9.30%

11. What is the weighted average cost of capital for the entire $10,000,000 to be raised forthe expansion?

A. 7.918%B. 8.318%

* C. 8.418%D 8.118%E. 8.218%

Additions to Retained Earnings = ($1,000,000 - $100,000)(1 - .4) = $540,000


Debt $2,000,000 = 20.0% x 2.40 = 0.480%Debt $1,000,000 = 10.0% x 3.00 = 0.300%

Preferred $1,000,000 = 10.0% x 6.00 = 0.600%RE $540,000 = 5.4% x 10.00 = 0.540%Equity $2,000,000 = 20.0% x 11.00 = 2.200%Equity $2,000,000 = 20.0% x 12.00 = 2.400%Equity $1,460,000 = 14.6% x 13.00 = 1.898%

8.418%


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12. Your companys stock currently has a price of $50 per share and is expected to pay ayear-end dividend of $4.00 per share (D1= $4.00). The dividend is expected to growat a constant rate of 6 percent per year. The company has insufficient retainedearnings to fund capital projects and must, therefore, issue new common stock. Thenew stock has an estimated flotation cost of $7 per share. Determine the company'scost of equity capital.

* A. 15.30%B. 14.90%C. 15.10%D. 15.70%E. 15.50%

Ke = D1/(P0 - F) + g = $4.00/($50 - $7) + 6% = $4.00/$43 + 6% = 9.30% + 6% =15.30%

13. Your companys CFO is interested in estimating the company's weighted average cots

of capital (WACC) and has collected the following information:

The company has bonds outstanding that mature in 18 years with an annualcoupon of 7.5 percent (the bond pays $75 on an annual basis). The bonds have aface value of $1,000 and sell in the market today for $1,120, giving a before-taxcost of debt of 6.36145%.

The risk-free rate is 3 percent The market risk premium is 5 percent The stock's beta is 1.2 The company's tax rate is 40 percent The company's target capital structure consists of 60 percent equity and 40

percent debt

The company uses the CAPM to estimate the cost of equity and does not includeflotation costs as part of its cost of capital it uses the cost of retained earnings.

Determine the companys WACC.

A. 8.24%B. 7.39%C. 7.81%D. 6.47%

* E. 6.93%

Data given:

KRF= 3%RPM= 5%!= 1.2

T = 40%WD= 0.4WS= 0.6

Step 1:Determine the firm's costs of debt:


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N = 18, PV = -1,120, PMT = 75, FV = 1000, Solve for I/YR = KD= 6.36145%

Determine the firm's costs of equity:KS = KRF+ (RPM)(!) = 3% + (5%)1.2 = 9%

Step 2:

Given the firm's component costs of capital, calculate the firm's WACC:

WACC = WDKD(1 - T) + WSKS= (0.4)(6.36145%)(1 - 0.4) + (0.6)(9%) = 1.53% + 5.4% = 6.93%



common equity. Your firm expects to add $3.0 million to retained earnings over the coming year that

can be used to support the $8 million in new projects. The company has corporate bonds outstanding with a 7 percent annual coupon that

are trading at par. New debt can be issued as a private placement (no flotation expense) and will have

the same level of risk as the firms current debt. The companys tax rate is 40 percent. The risk-free rate is 2 percent. The market risk premium is 6 percent. The stocks beta is 1.5. The company expects to pay a dividend on its common stock of $1.60 per share next

year (D1). The companys ROE is 10% and its dividend payout rate is 60%. The current stock price (P0) is $22.86 per share. If the firm issues new shares of common stock, they will sell for $22.50 per share (a

slight discount from the current price), but the firm will have to pay flotation expense of10.0% ($2.25) and will only net $20.25.

Each of the projects to be taken on has the same degree of risk as the current projectsof the firm.


A. 7.8825%B. 8.0825%

C. 8.2825%D. 8.6825%* E. 8.4825%

Breakdown: Debt = ($8,000,000)(.40) = $3,200,000 40.0%Retained Earnings = $3,000,000 37.5%New Equity = ($8.0 - $3.2 - $3.0) = $1,800,000 22.5%

After-tax KD = (7%)(1-.40) = 4.2%


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B. To solve for KS, we can use the SML equation, but we need to find beta. UsingMarket and Z-Mart return information and a calculator's regression feature wefind b = 1.3585.

So Ks= 0.0635 + (0.1135 - 0.0635)(1.3585) = 0.1314 = 13.14%

C. Plug these values into the WACC equation and solve:

WACC = [(0.45)(0.09)(1 - 0.35)] + [(0.55)(0.1314)]

=0.026325 + 0.07227 = 0.098595 = 9.86%

16. A firm assumes that it can issue new, 15-year debt with a maturity value of $1,000 andwith an annual coupon rate of 8 percent, but where interest is paid semi-annually. Ifthe firm believes that it can net $781.99 from the sale of each bond after any relatedflotation costs, and if the firms marginal tax rate is 38 percent, then what is the after-cost of debt to this firm?

A. 6.64%B. 6.73%

* C. 6.82%D. 6.91%E. 7.00%

Answer: C 6.82%

N = 30; PV = -781.99; PMT = 40; FV = 1,000; Solve for I/YR = 5.50%

Annual Nominal Rate = (2)(5.50%) = 11.0%

After-Tax Rate = (11.0%)(1 - .38) = 6.82%

17. A firms common stock has just paid a dividend (D0) of $1.00 per share. This dividendis expected to grow at a long-run constant growth rate of 15 percent and investorsrequire a 20 percent rate of return on this stock. If the firm issues new shares of stockit assumes that they will sell for the same price that investors are willing to pay today,but the firm will have to pay flotation costs equal to 15 percent of this price. If thefirms marginal tax rate is 38 percent, then what is the firms cost (their required rate ofreturn) for a new issue of common stock?

A. 20.32%B. 20.46%C. 20.60%D. 20.74%

* E. 20.88%

Answer: E 20.88%


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P0 = [($1.00)(1.15)] / [.20 - .15] = $23.00

Ke = [($1.00)(1.15)] / [($23.00)(1 - .15)] + 0.15 = [$1.15 / $19.55] + 0.15 = 20.88%

18. A firm has a market-value balance sheet as indicated below. The firm assumes that it

can issue debt at a before-tax cost of 10 percent and has a marginal tax rate of 40percent. The firm can meet their equity needs through additions to retained earningsand investors currently require a 16 percent rate of return on stock. If the firm issuepreferred stock, it will pay a dividend of $15 per year, and although investors will bewilling to pay $165 for each share of preferred, the firm will only net $150 per shareafter accounting for related flotation expenses. Given this data, what is the firmsweighted average cost of capital (or the marginal costs of capital for the first dollar tobe raised)?

Balance Sheet at Market Value (In Millions)

Current Assets $100.00 Long-term Debt $75.00

Other Assets $50.00 Preferred Stock $15.00Fixed Assets $150.00 Equity $210.00

Total Assets $300.00Total Liabilities andEquity

$300.00

A. 12.60%B. 12.80%C. 13.00%

* D. 13.20%E. 13.40%

Answer: D 13.20%

WD = $ 75/$300 = .25WP = $ 15/$300 = .05WE = $210/$300 = .70

KD = .10KP = $15/$150 = .10KE = .16

WACC = (.25)(.10)(1-.40) + (.05)(.10) + (.70)(.16) = .015 + .005 + .112 = 13.20%

19. Your company finances its projects with 50 percent debt, 10 percent preferred stock,and 40 percent common stock.

The company can issue bonds at a yield to maturity of 6.4 percent. The cost of preferred stock is 7 percent. The company's common stock currently sells for $25 a share.


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The company's dividend is currently $2.00 a share (D0 = $2.00), and is expected togrow at a constant rate of 5 percent per year.

Assume that the flotation cost on debt and preferred stock is zero, and no newstock will be issued.

The companys tax rate is 34 percent.

Given this information, determine the companys weighted average cost of capital.

A. 8.474%B. 7.863%C. 9.015%

* D. 8.172%E. 8.759%

KS = [($2.00)(1.05) / $25] + .05 = 13.4%

WACC = (.064)(1-.34)(.50) + (.07)(.10) + (.134)(.40)

WACC = .02112 + .007 + .0536 = .08172 = 8.172%

20. Assume that a company just paid a $1.50 per share dividend on its common stock (D0=$1.50), that the dividend is expected to grow at a constant rate of 8 percent per year,and that investors require a 12 percent rate of return. Now assume that if the companyissues additional stock, it must pay its investment banker a flotation cost of $2.50 pershare. Given this information, determine the cost of new external equity, Ke.

A. 12.15%

B. 12.59%C. 12.37%D. 12.48%

* E. 12.26%

P0 = [($1.50)(1.08)] / [.12 - .08] = $1.62 / .04 = $40.50

Net Price = $40.50 - $2.50 = $38.00

Ke = ($1.62 / $38.00) + 0.08 = 0.0426 + 0.08 = 12.26%

21. Assume that a firms optimal capital structure consists of 30% debt at a before-tax cost

of debt (KD) of 6 percent, 10% preferred stock at a cost of preferred (KP) of 8 percent,and 60% stock; that the firms tax rate is 40%; and that the firms weighted averagecost of capital is equal to 9.56 percent (assume retained earnings and ignore flotationcosts). Now assume that markets are in equilibrium (required rates are equal toexpected rates), that the current price (Year 0) of the firms constant growth stock is$37.50, that the firm retains 80 percent of its earnings, and that its return on equity(ROE) is 12.50%. Based on this information, determine the firms expected dividend(D1) for the coming year.


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A. $1.20B. $1.10

* C. $1.05D. $1.15E. $1.00


.0956 = (0.06)*(1-0.4)*(0.30) + (0.08)*(0.10) + (KS)*(0.60)

^

KS = (.0956 - 0.0108 + 0.0080) / .6 = 0.1280 = 12.80% = Ks

^

KS = (D1/ P0) + g

g = RB = (.125)*(.80) = 10%

^

KS = 0.1280 = (D1/ $37.50) + 0.10

D1 = (0.1280 - 0.10)*($37.50) = $1.05


Your firms targeted capital structure consists of 40 percent debt and 60percent common equity.

Your firm expects to add $4 million to retained earnings over the coming yearthat can be used to support the $12 million in new projects.

The company has bonds outstanding that have 10 years until maturity, a

maturity value of $1,000, pay an annual coupon of $70 ($35 every six months),and are currently priced at $1,074.39.

New debt can be issued as a private placement (no flotation expense) and willhave the same level of risk as the firms current debt.

The companys tax rate is 40 percent. The risk-free rate is 4 percent. The market risk premium is 6 percent. The stocks beta is 1.4. The company expects to pay a dividend on its common stock of $1.53 per

share next year (D1). The companys ROE is 15% and its dividend payout rate is 40%.

The current stock price (P0) is $45 per share. If the firm issues new shares of common stock, they will sell for $44 per share

in the market, and the firm will also have to pay flotation expense of 10%. Each of the projects to be taken on has the same degree of risk as the current


Based on this information, determine the WACC (MCC) for the very first dollar to beraised.


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A. 8.51%B. 9.99%C. 9.25%

* D. 8.88%E. 9.62%Determine YTM:

N = 20; PV = -1,074.39; PMT = 35; FV = 1,000; Solve for I/YR = 3.0 * 2 = 6.00% =YTM

After-tax KD = (6%)(1-.40) = 3.6%

KS = 0.04 + (0.06)(1.4) = 12.40%

Alternatively,

g = (0.15)(1 - 0.40) = 9%

KS = $1.53 / $45.00 + 0.09 = 0.034 + 0.09 = 12.40%

Ke = $1.53 / ($44.00)(1 - 0.10) + 0.09 = 12.86% (Not needed for this problem.)

Therefore, for very first dollar:

WACC = (3.6%)(0.40) + (12.40%)(0.60) = 1.44% + 7.44% = 8.88%

23. Assume that an all equity firm has a return on assets (ROA) of 12.80 percent. And thatthe firm makes the decision to replace !of its equity with debt that has a before-taxcost of 8 percent (note: this will give a D/E ratio of (!/ ") = 1/3 ). Assuming that the

firms tax rate is 40 percent, calculate the firms ROE after the debt has been issuedand equity has been repurchased.

A. 15.10%* B. 15.47%

C. 14.73%D. 15.84%E. 14.36%

AT KD = (8.00%)(1-.40) = 4.80%

As discussed in class, after the issue and repurchase, the remaining equity

shareholders will benefit from both a leverage effect and a tax shelter effect:

ROE = 12.80% + (12.80% - 8.00%)(1/3) + (8.00% - 4.80%)(1/3)

ROE = 12.80% + 1.60% + 1.07% = 15.47%

The following is an illustration with some numbers that were pulled from the air:assets of $1,200, then working backwards from an ROA of 12.80% to get EBIT of$256.00.


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Assets/IncomeWithout

DebtWithDebt

Assets $1,200.00 $1,200.00

Debt (1/4) $ 0.00 $ 300.00

Equity $1,200.00 $ 900.00

EBIT $ 256.00 $ 256.00

Interest (8%) $ 0.00 - $ 24.00EBT $ 256.00 $ 232.00Taxes (40%) - $ 102.40 - $ 92.80

Net Income $ 153.60 $ 139.20

ROA 12.80% 11.60%

ROE 12.80% 15.47%

24. Assume that a firms optimal capital structure consists of 30% debt at a before-tax costof debt (KD) of 6 percent, 10% preferred stock at a cost of preferred (KP) of 8 percent,and 60% stock, and that the firms tax rate is 40%. Also assume that the firmsweighted average cost of capital is equal to 9.572 percent. Based on this information,determine the firms cost of common stock (KS).

A. 12.49%B. 11.83%C. 12.16%D. 11.50%

* E. 12.82%


.09572 = (0.06)*(1-0.4)*(0.30) + (0.08)*(0.10) + (KS)*(0.60)

KS = (.09572 - 0.0108 + 0.0080) / .6 = 0.1282 = 12.82%

25. Assume that an analyst has collected the following information about your company:

The companys capital structure consists entirely of debt and equity and the debt/equity

ratio is 2/3. The yield to maturity on the companys debt is 6 percent. The company pays out all of its earnings as dividends (retention rate of zero) and the

companys year-end dividend (D1) is forecasted to be $0.75 a share. The company expects that its dividend will grow at a constant rate of 6 percent a year. The companys stock price is $25. The companys tax rate is 40 percent. The company will meet its equity requirements by issuing new common stock and they

anticipate that total flotation costs will be equal to 20 percent of the amount issued.


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Assume the company accounts for flotation costs by adjusting the cost of capital. Giventhis information, determine the companys WACC.

A. 7.15%B. 6.87%

* C. 7.29%D. 7.01%E. 6.73%

Debt / Value = 2 / (2 + 3) = 40%

Equity / Value = 3 / (2 + 3) = 60%

KD = 6%

Ke = [$0.75 / ($25.00)*(1 - .20)] + .06 = $0.75 / $20.00 + .06 = 9.75%

WACC = (.06)*(1-.40)*(.4) + (.0975)*(.6) = 1.44% + 5.85% = 7.29%

26. Assume that a firms optimal capital structure consists of 25 percent debt, 8 percentpreferred, and 67 percent equity, where the firm will have sufficient retained earningsto meet its equity needs. The firms before tax cost of debt is 7 percent and its tax rateis 40 percent. The price of the firms common stock is currently $45 per share, itexpects to pay a dividend of $3.15 next year, and its long-run sustainable growth is 6percent. Given this information, and assuming that the firm has a weighted averagecost of capital (WACC) of 10.548 percent, determine the firms cost of preferred stock.

A. 10.14%

B. 9.27%* C. 9.85%

D. 8.98%E. 9.56%

KS = ($3.15 / $45.00) + .06 = 13%

WACC = .10548 = (.07)*(1-.4)*(.25) + (KP)*(.08) + (.13)*(.67)

KP = (.10548 - .0105 - .0871) / (.08) = (.00788) / .08 = 9.85%

27. Assume that a firm expects that its common stock dividend will be $1.90 next year(D1). It also believes that if it sells new shares, the market will be willing to pay $37.50per share, but that the firm would only net $33.00 per share after adjusting for flotationcosts. Given this data, and assuming that the firms long-run sustainable growth rateis 6 percent, determine the firms cost of new equity.

A. 11.52%B. 12.00%


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C. 11.04%D. 11.28%

* E. 11.76%

Ke = ($1.90 / $33.00) + 0.06 = 11.76%

28. Assume that a firms optimal capital structure consists of $30,000,000 of debt at abefore-tax cost of debt (KD) of 8 percent, $10,000,000 of preferred stock at a cost ofpreferred (KP) of 8 percent, and $60,000,000 of stock at a cost of stock (KS) of 14percent. Assuming that the firms tax rate is 40%, determine the firms weightedaverage cost of capital (WACC).

A. 10.34%B. 11.24%C. 10.94%D. 11.54%

* E. 10.64%


WD = $30,000,000 / $100,000,000 = 30%

WP = $10,000,000 / $100,000,000 = 10%

WS = $60,000,000 / $100,000,000 = 60%

WACC = (0.08)*(1-0.4)*(0.30) + (0.08)*(0.10) + (0.14)*(0.60)

WACC = 0.0144 + 0.008 + 0.084 = 0.1064 = 10.64%

29. Your company's current market-valued capital structure, which is considered to beoptimal, is shown below:


In order to meet their expansion plans for next year, the company has decided to raise$4,000,000. Net Income is expected to be $350,000 next year. However, preferredstock dividends are expected to account for $50,000 of this profit. The common stock

dividend payout rate is 35% of the profit after the payment of preferred dividends. Thecorporate tax rate is equal to 40%, and the before-tax costs of new financing areestimated to be:

Debt: 4% for the first $500,000 of new debt.5% for up to an additional $1,000,000 of new debt.6% for up to an additional $1,000,000 of new debt.

Preferred: 8% for the first $500,000 of new preferred.


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9% for up to an additional $500,000 of new preferred.

Equity: 13% for retained earnings.14% for up to the first $2,000,000 of new common stock.15% for up to an additional $2,000,000 of new common stock.

16% for up to an additional $2,000,000 of new common stock.

Given this information, determine the weighted average cost of capital for the entire$4,000,000 to be raised for the expansion.

A. 9.65%B. 8.85%

* C. 9.45%D. 9.05%E. 9.25%

RE = ($350,000 - $50,000)(1-.35) = $195,000



Debt $500/$4,000 = 12.500% x 2.40 = 0.30000%Debt $700/$4,000 = 17.500% x 3.00 = 0.52500%Preferred $500/$4,000 = 12.500% x 8.00 = 1.00000%Preferred $300/$4,000 = 7.500% x 9.00 = 0.67500%RE $195/$4,000 = 4.875% x 13.00 = 0.63375%Equity $1,805/$4,000 = 45.125% x 14.00 = 6.31750%

100.000% 9.45125%

WACC = 9.45%

30. Assume that your firm has a weighted average cost of capital of 10.00%, and has acapital structure consisting of 40 percent debt and 60 percent equity. Also assume thatthe firms tax rate is 40 percent and that its cost of stock/equity (ignore flotation costs) is14 percent. Given this information, determine the firms before-tax cost of debt.

A. 6.875%B. 6.500%

* C. 6.667%D. 6.125%E. 6.333%

WACC = 0.10 = (KD)(1-.40)(.40) + (.14)(.60)

KD = (0.10 - 0.084) / (1-.40)(.40) = 0.016 / 0.24 = 6.67%


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31. Assume that your firm has a target capital structure of 30% debt and 70% commonstock, that the companys before-tax cost of debt is 6%, and that the marginal tax rate is35%. Also assume that the current stock price (P0) is $30.00, that the dividend just paid(D0) was $1.80, and that this dividend is expected to grow at a constant rate of 4%.Given this information, and assuming that the firms equity needs can be financed fromadditions to retained earnings, determine the firms weighted average cost of capital.

A. 8.58%B. 9.11%C. 8.72%D. 8.97%

* E. 8.34%

D1 = ($1.80)(1.04) = $1.872

KS = [($1.872) / ($30.00)] + 0.04 = 10.24%

WACC = (0.06)(1-.35)(.30) + (0.1024)(.70) = 0.0117 + 0.07168 = 0.08338 = 8.34%

32. Assume that your firm can issue new common stock that will pay a dividend (D1) of$2.50 next year, that this dividend will grow at a constant annual growth rate of 4%, andthat investors have a required rate of return of 10.25% (you should now be able todetermine the current price that investors should be willing to pay for this stock). Alsoassume that the firm will pay flotation expense of 15 percent to its investment bankers.Using the discounted cash flow (DCF) model, determine the firms required rate of returnon this newly issued equity.

A. 11.95%B. 11.75%

* C. 11.35%

D. 11.55%E. 11.15%

P0 = ($2.50) / (0.1025 - 0.04) = $40.00

Ke = [$2.50) / ($40.00)(1-.15)] + 0.04 = [($2.50 / $34.00) + 0.04] = 11.35%

33. Assume that a firm can issue preferred stock with a par value of $100 and paying anannual preferred stock dividend of $12 per share. Investors will be willing to pay $150per share, but the firm will only net $130 per share (after paying $20 of flotation expenseto its investment bankers). Given this information, determine by how much the firmscost of this preferred stock exceeds the investors required rate of return on this

preferred stock.

A. 0.83%B. 1.63%C. 1.03%

* D. 1.23%E. 1.43%

Investors:


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KP = $12.00 / $150.00 = 0.0800

Firm:KP = $12.00 / $130.00 = 0.0923

Difference = 0.0923 - 0.0800 = 0.0123 = 1.23%

34. Assume that your company has an optimal capital structure that consists of 32 percentequity and 68 percent debt. If the company expects to report $5 million in net incomethis year, and 60 percent of the net income will be paid out as dividends, thendetermine how large its capital budget may be before it will have to issue any newcommon stock (external equity).

A. $5.25 millionB. $6.00 million

* C. $6.25 millionD. $5.50 millionE. $5.75 million

Addition to Retained Earnings = ($5,000,000)(1 - .60) = $2,000,000

Since equity = 32% of the capital budget, the capital budget can be:

$2,000,000 / .32 = $6,250,000 = $6.25 million before external equity has to be issued.

35. Assume that your company finances its operations with 40 percent debt, 10 percentpreferred stock, and 50 percent equity. Also assume that the preferred stock pays anannual dividend of $2 and sells for $20 a share, that the companys common stocktrades at $30 a share, that its current common stock dividend (D0) of $2 a share is

expected to grow at a constant rate of 8 percent per year, and that the flotation cost ofexternal equity is 15 percent of the dollar amount issued, while the flotation cost onpreferred stock is 20 percent. Now assume that the firms tax rate is 35 percent, that thefirm will not have enough retained earnings to fully fund the equity portion of its capitalbudget, and that the marginal cost of capital for the last dollar to be raised is 12.75percent. Determine the firms before-tax cost of debt financing.

* A. 12.56%B. 11.66%C. 12.86%D. 12.26%E. 11.96%

KP = $2 / ($20)(1 - .20) = $2 / $16 = 12.50%

KS = [($2.00)(1.08) / $30.00] + .08 = 15.20%

Ke = [$2.00)(1.08) / ($30.00)(1 - .15) + .08 = 16.47%

MCC = 12.75% = (KD)(1-.35)(.40) + (12.50%)(.10) + (16.47%)(.50)

MCC = 12.75% = (KD)(.26) + (1.25%) + (8.235%)


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KD = (12.75% - 1.25% - 8.235%) / .26 = 3.265 / .26 = 12.56%

36. Assume that the beta of an all equity firm is 0.9, that the risk-free rate is 6 percent, andthat the firms required rate of return (using CAPM) is 15 percent. If the firm changes

its capital structure to 25% debt and 75% equity, where the before-tax yield (cost) ofdebt is 8.5%, and if the tax rate is 40%, then determine the firms new weightedaverage cost of capital (WACC). (You may assume that the beta for debt is zero.)

A. 14.125%B. 13.625%C. 13.375%D. 13.125%

* E. 13.875%

Since the firm has a beta of 0.9,

KMmust be equal to 16%: 15% = (.06) + (.16 - .06)(0.9)

New levered beta = 0.9 + (0.9)(.25/.75)(1 - .40) = 1.08

New equity required rate of return = .06 + (.16 - .06)(1.08) = 16.80%

WACC = (8.5)(1-.4)(.25) + (16.80)(.75) = 1.275 + 12.600 = 13.875%

37. Your company is considering the following five independent projects:

Project Cost IRR

A $300,000 19%

B $550,000 16%

C $400,000 14%

D $375,000 13%

E $325,000 11%

The company has a target capital structure that consists of 30 percent debt and 70percent common equity. The company can issue bonds with a before-tax yield to

maturity of 8 percent. The company expects to add $350,000 to its retained earnings,and the current stock price is $35 per share. The flotation costs associated withissuing new equity are 12.5% of the market price. The companys earnings areexpected to continue to grow at 6 percent per year, next years dividend (D1) isforecasted to be $2.45, and the firm faces a 40 percent tax rate. Given thisinformation, determine the size of the firms optimal capital budget.

A. $1,250,000B. $ 300,000


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* C. $1,625,000D. $ 850,000E. $1,950,000

KD = (8.0%)(1-.4) = 4.8%

KS = [$2.45 / $35.00] + 6.0% = 13.0%

Ke = [$2.45 / ($35.00)(1 - .125)] + 6.0% = 14.0%

Firm will switch from KSto Kewhen the capital budget hits $350,000 / .70 = $500,000

Below $500,000:

WACC = (4.8%)(.30) + (13.0%)(.70) = 1.44% + 9.10% = 10.54%

Above $500,000:

WACC = (4.8%)(.30) + (14.0%)(.70) = 1.44% + 9.80% = 11.24%

Therefore, the firm should take on Projects A-D and the size of the optimal capitalbudget should be $1,625,000.

38. An analyst has collected the following information regarding your company:

The companys capital structure is 75 percent equity, 25 percent debt. The before-tax yield to maturity on the companys bonds is 8 percent and the

bonds are selling at par value. The companys dividend next year is forecasted to be $1.25 a share.

The company expects that its dividend will grow at a constant rate of 6 percenta year.

The companys stock price is $20. The companys tax rate is 40 percent. The company anticipates that it will need to raise new common stock this year.

Its investment bankers anticipate that the total flotation cost will equal 12.5percent of the amount issued -- you may assume that the company accountsfor flotation costs by adjusting the component cost of capital.

Given this information, determine what the companys WACC will be when it is forcedto issue new shares of common stock.

A. 10.736%B. 9.914%C. 10.349%D. 9.627%

* E. 11.055%

Kd = 8% (given)

Ke = [D1 / P0(1 - F)] + g


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Ke = [$1.25 / $20(1 - 0.125)] + 0.06 = 13.14%

WACC = WdKd(1 - T) + WeKe

WACC = (0.25)(8.00%)(0.6) + (0.75)(13.14%) = 1.2% + 9.855% = 11.055%

39. Your firm has estimated that it will spend $10 million on new capital budgeting projectsduring the coming year and has collected the following information:

Your firms targeted capital structure consists of 40 percent debt, 10 percentpreferred, and 50 percent common equity.

Your firm expects to add $3.0 million to retained earnings over the coming yearthat can be used to support the $10 million in new projects.

The company has corporate bonds outstanding that have 10 years until maturity, aface value of $1,000, a semi-annual coupon of $40, and a current price of $934.96.

New debt (at least $7 million) can be issued as a private placement (no flotation

expense) and will have the same level of risk as the firms current debt. New preferred stock (at least $2 million) can be issued at a price of $100 per

share, but flotation costs will be 20 percent. This preferred stock will pay an annualdividend of $9.60 per share.

The companys tax rate is 40 percent. The risk-free rate is 4 percent. The market risk premium is 8 percent. The stocks beta is 1.4. The company expects to pay a dividend on its common stock of $2.76 per share




Given this information, determine the weighted average (marginal) cost of capital ofthe very last dollar to be raised.

A. 11.062%B. 12.178%

* C. 11.620%D. 12.736%E. 10.504%

New Equity = ($10,000,000)*(.50) - $3,000,000 = $2,000,000

Find rD:

N = 20; PV = -934.36; PMT = 40; FV = 1,000; Solve for I/YR = (4.50)*(2) = 9.0%

After-tax rD = (9%)(1-.40) = 5.4%


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Find rP:

rP = $9.60 / ($100.00)*(1-.20) = $9.60 / $80.00 = 12.0%

Find rSand re:

rS = 0.04 + (0.08)(1.4) = 15.20%

Alternatively,

g = (0.20)(1 - 0.70) = 6%

rS = $2.76 / $30.00 + 0.06 = 0.092 + 0.06 = 15.2%

re = $2.76 / ($30.00)(1 - 0.125) + 0.06 = 16.51%

Therefore, for the very last dollar raised

WACC = (5.4%)(0.40) + (12.0%)(0.10) + (16.51%)(0.50)

= 2.16% + 1.2% + 8.26% = 11.62%

40. Assume that a firms current capital structure consists of 1/3 debt and 2/3 commonstock (a debt/equity ratio of #or 0.50). Assume that the firms before-tax cost of debtis 6 percent, that its tax rate is 40 percent, and that its cost of common stock is 10percent. Also assume that the risk-free rate is 4 percent and that the market riskpremium is 5 percent (you should now be able to calculate the firms levered beta).Given this information, determine what the firms new weighted average cost of capitalwill be if it changes to a capital structure of 50 percent debt and 50 percent equity (a

debt/equity ratio of 0.50/0.50 or 1.0)

A. 8.10%B. 6.90%C. 8.70%

* D. 7.50%E. 9.30%

Determine current levered beta:

10.0% = 4.0% + (5.0%)*($L)

$L = (10.0% - 4.0%) / 5.0% = 1.20

Unlever beta:

$U = (1.20) / (1 + (0.50)(1-.40)) = 0.923076923

Relever beta at new capital structure:

$L = (0.923076923)*(1 + (1.0)*(1 - .40)) = 1.476923077 = 1.48


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Determine new rS = 4.0% + (5.0%)*(1.48) = 11.40%

Calculate new WACC:

WACC = (rD)(1-T)(rD) + (rS)(rS)

WACC = (.06)(1-.4)(.50) + (.114)(.50) = 0.018 + 0.057 = 7.50%

41. Assume that a firm takes on a project that requires an initial investment in Year 0 of$50,000. Also assume that the firm raised the $50,000 by issuing $10,000 of debt at abefore-tax cost of debt of 8%, and issued $40,000 of equity at a cost of equity of 15%.Given this information, and assuming that the tax rate is 40%, determine the weightedaverage cost of capital (WACC) for this project.

A. 11.44%B. 11.98%

* C. 12.96%D. 12.48%E. 10.92%

WACC = (.08)(1-.4)(20%) + (.15)(80%) = .0096 + .12 = 12.96%

42. Assume that your firm has estimated that it will spend $20 million on new capitalbudgeting projects during the coming year and that you have been asked to calculatethe appropriate cost of capital to be used to analyze these projects. You havecollected the following information:

Your firms targeted capital structure consists of 40 percent debt and 60 percentcommon equity.

Your firm expects to add $5.0 million to retained earnings over the coming year thatcan be used to support the $20 million in new projects.

The company has corporate bonds outstanding with an 8 percent annual coupon thatare trading at par.

New debt can be issued as a private placement (no flotation expense) and will havethe same level of risk as the firms current debt.

The companys tax rate is 40 percent. The risk-free rate is 4 percent. The market risk premium is 6 percent. The stocks beta is 1.6. The company expects to pay a dividend on its common stock of $2.20 per share next


slight discount from the current price), and the firm will have to pay flotation expense of10.0% ($2.75).



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Given this information, determine what the WACC/MCC will be for the very last dollar(i.e., the $20,000,000th) to be raised.

A. 12.48%B. 10.32%C. 11.94%

* D. 10.86%E. 11.40%

Breakdown: Debt = ($20,000,000)*(.40) = $8,000,000Equity = ($20,000,000)*(.60) = $12,000,000

Since the firm only expects to add $5,000,000 to its retained earnings account, theequity portion for the very last dollar to be raised must come from newly issued equity.Therefore, we would have the following:

After-tax rD = (8%)(1-.40) = 4.8%

rS = 0.04 + (0.06)(1.6) = 13.6%

Alternatively,

g = (0.20)(1 - 0.70) = 6%

rS = $2.20 / $28.95 + 0.06 = 0.076 + 0.06 = 13.6%

re = $2.20 / ($27.50)(1-.10) + 0.06 = 0.089 + 0.06 = 14.90%

WACC = (4.8%)(0.40) + (14.9%)(0.60) = 1.92% + 8.94% = 10.86%

43. Assume that your firm has just opened for business and that it was originally fundedwith investor-supplied capital equal to $30,000,000: $12,000,000 by creditors whorequired an 8 percent before-tax rate of return; and $18,000,000 by stockholders whorequired a 15 percent rate of return. [Based on this information, and knowing that thetax rate is 40 percent, you should be able to determine that the weighted average costof capital (WACC) for the firm is 10.92 percent.] Now assume that for all future yearsthe firm expects to make no additional investments in assets, that depreciation is zero,and that its operations will produce sales of $40,000,000 and EBIT of $6,000,000.[Given this information, you should now be able to calculate the free cash flow and/orthe economic value added for all future years, and from this and the WACC previouslydetermined, you should be able to calculate the enterprise value and/or market value

added (MVP or NPV).] Now, as demonstrated in class, and assuming that the WACCremains constant at 10.92 percent, and that the before-tax cost of debt remainsconstant at 8 percent, determine what the new cost of equity must be. (Hint: thedebt/value and equity/value ratios will change but the WACC will remain constant.)

A. 12.44%B. 15.40%C. 11.48%D. 13.46%


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* E. 14.42%

WACC = (.08)*(1-.4)*(.4) + (.15)*(.6) = 1.92% + 9.0% = 10.92 percent

NOPAT = FCF = ($6,000,000.00)*(1-.4) = $3,600,000.00

Enterprise Value = $3,600,000 / .1092 = $32,967,033

MV of Equity = $32,967,033 - $12,000,000 = $20,967,033

Debt/Value = $12,000,000 / $32,967,033 = 36.40%

Equity / Value = $20,967,033 / $32,967,033 = 63.60%

WACC = 10.92% = (.08)*(1-.4)*(.364) + (rS)*(.636)

rS = (10.92% - 1.7472%) / 0.636 = 14.422641509% = 14.42%

Alternatively,

EVA = $3,600,000 - ($30,000,000.00)*(.1092) = $324,000

MVA = NPV = $324,0000 / .1092 = $2,967,033

MV of Equity = $18,000,000 + $2,967,003 = $20,967,033

Enterprise Value = $12,000,000 + $20,967,003 = $32,967,033

Debt/Value = $12,000,000 / $32,967,033 = 36.40%

Equity / Value = $20,967,033 / $32,967,033 = 63.60%

WACC = 10.92% = (.08)*(1-.4)*(.364) + (rS)*(.636)

rS = (10.92% - 1.7472%) / 0.636 = 14.42%

Alternatively,

Interest = ($12,000,000)*(0.08) = $960,000

EBIT $6,000,000Interest -$ 960,000EBT $5,040,000Taxes -$2,016,000

Net Income $3,024,000

MV Equity = $20,967,033 = $3,024,000 / rS

rS = $3,024,000 / $20,967,033 = 14.42%


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44. Your companys stock currently has a price of $40 per share and is expected to pay ayear-end dividend of $1.00 per share (D1= $1.00). The dividend is expected to growat a constant rate of 6 percent per year. The company has insufficient retainedearnings to fund capital projects and must, therefore, issue new common stock. Thenew stock has an estimated flotation cost of $5 per share. Determine the company'scost of new equity capital.

A. 9.40%B. 8.59%C. 9.13%D. 9.67%

* E. 8.86%

In this case, F is in dollar form, not a percent of the stocks price:

re = D1/(P0 - F) + g = $1.00/($40 - $5) + 6% = $1.00/$35 + 6% = 2.86% + 6% = 8.86%

45. Your firm has estimated that it will spend $10 million on new capital budgeting projectsduring the coming year and has collected the following information:

Your firms targeted capital structure consists of 40 percent debt, 10 percentpreferred, and 50 percent common equity.

Your firm expects to add $3.0 million to retained earnings over the coming yearthat can be used to support the $10 million in new projects.

The company has corporate bonds outstanding that have 10 years until maturity, aface value of $1,000, a semi-annual coupon of $40, and a current price of $934.96.

New debt (at least $7 million) can be issued as a private placement (no flotationexpense) and will have the same level of risk as the firms current debt.

New preferred stock (at least $2 million) can be issued at a price of $100 per

share, but flotation costs will be 20 percent. This preferred stock will pay an annualdividend of $9.60 per share.

The companys tax rate is 40 percent. The risk-free rate is 4 percent. The market risk premium is 8 percent. The stocks beta is 1.4. The company expects to pay a dividend on its common stock of $2.76 per share




Given this information, determine the weighted average (marginal) cost of capital ofthe very first dollar to be raised.

* A. 10.96%B. 12.07%C. 11.33%D. 12.44%


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E. 11.70%

New Equity = ($10,000,000)*(.50) - $3,000,000 = $2,000,000

But not needed for the very first dollar, since RE will be used for equity.

Find rD:

N = 20; PV = -934.36; PMT = 40; FV = 1,000; Solve for I/YR = (4.50)*(2) = 9.0%

After-tax rD = (9%)(1-.40) = 5.4%

Find rP:

rP = $9.60 / ($100.00)*(1-.20) = $9.60 / $80.00 = 12.0%

Find rSand re:

rS = 0.04 + (0.08)(1.4) = 15.20%

Alternatively,

g = (0.20)(1 - 0.70) = 6%

rS = $2.76 / $30.00 + 0.06 = 0.092 + 0.06 = 15.2%

re = $2.76 / ($30.00)(1 - 0.125) + 0.06 = 16.51%

Therefore, for the very first dollar raised

WACC = (5.4%)(0.40) + (12.0%)(0.10) + (15.2%)(0.50)

= 2.16% + 1.2% + 7.6% = 10.96%

46. Assume that a firms current capital structure consists of 50 percent debt and 50percent common stock (a debt/equity ratio of 1.00). Assume that the firms before-taxcost of debt is 6 percent, that its tax rate is 40 percent, and that its cost of commonstock is 11 percent. Also assume that the risk-free rate is 4 percent and that themarket risk premium is 5 percent (you should now be able to calculate the firmslevered beta). Given this information, determine what the firms new weighted averagecost of capital will be if it changes to a capital structure of 75 percent debt and 25

percent equity.

A. 6.1900%B. 7.9075%

* C. 6.7625%D. 8.4800%E. 7.3350%

Determine current levered beta:


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11.0% = 4.0% + (5.0%)*($L)

$L = (11.0% - 4.0%) / 5.0% = 1.40

Unlever beta:

$U = (1.40) / (1 + (1.00)(1-.40)) = 0.875

Relever beta at new capital structure:

$L = (0.875)*(1 + (3.0)*(1 - .40)) = 2.45

Determine new rS = 4.0% + (5.0%)*(2.45) = 16.25%

Calculate new WACC:

WACC = (rD)(1-T)(rD) + (rS)(rS)

WACC = (.06)(1-.4)(.75) + (.1625)(.25) = 0.027 + 0.040625 = 6.7625%

47. Assume that the risk-free rate is 5 percent, the return on the market is 12 percent, andthat a firm has a debt/value ratio of 1/3, an equity/value ratio of 2/3, a before-tax costof debt of 8 percent, a cost of equity of 15 percent, and a tax rate of 40 percent.(HINT: you should now be able to calculate its WACC and back out its levered andunlevered beta.) Now assume that the firm intends to double its debt and use theproceeds to buy back its stock (the debt/value and equity/value ratios will each now be2/3 and 1/3 respectively). Using the Hamada equations to relever beta, determinewhat the firms new cost of equity will be.

A. 23.00%B. 22.19%C. 22.73%

* D. 21.92%E. 22.46%

Original Debt/Equity Ratio = (1/3) / (2/3) = 0.50

New Debt/Equity Ratio = (2/3) / (1/3) = 2.0

rS = 15.0% = 5.0% + (12.0% - 5.00)*($L1)

$L1 = (15.0% - 5.0%) / 7.0%) = 1.428571429

$U = 1.428571429 / [1 + (0.50)(1-.40)] = 1.428571429 / 1.30 = 1.098901099

$L2 = [1.098901099] * [1 + (2.0)(1-.40)] = 2.417582418

New rS = 5.0% + (12.0% - 5.0%)(2.417582418) = 21.92%


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48. Assume that your firm has estimated that it will spend $20 million on new capitalbudgeting projects during the coming year and that you have been asked to calculatethe appropriate cost of capital to be used to analyze these projects. You havecollected the following information:

Your firms targeted capital structure consists of 40 percent debt and 60 percentcommon equity. Your firm expects to add $5.0 million to retained earnings over the coming year that

can be used to support the $20 million in new projects. The company has corporate bonds outstanding with an 9 percent annual coupon that

are trading at par. New debt can be issued as a private placement (no flotation expense) and will have

the same level of risk as the firms current debt. The companys tax rate is 40 percent. The risk-free rate is 4 percent. The market risk premium is 6 percent. The stocks beta is 1.5. The company expects to pay a dividend on its common stock of $2.20 per share next


slight discount from the current price), and the firm will have to pay flotation expense of10.0% ($2.75).


Given this information, determine what the WACC/MCC will be for the very first dollarto be raised.

A. 9.28%B. 9.79%C. 9.45%

* D. 9.96%E. 9.62%

Since the firm expects to add $5,000,000 to its retained earnings account, the equityportion for the very first dollar to be raised will come from retained earnings.Therefore, we would have the following:

After-tax rD = (6%)(1-.40) = 5.4%

rS = 0.04 + (0.06)(1.5) = 13.0%

Alternatively,

g = (0.20)(1 - 0.73) = 5.4%

rS = $2.20 / $28.95 + 0.054 = 0.076 + 0.054 = 13.0%

re = $2.20 / ($27.50)(1-.10) + 0.054 = 0.089 + 0.054 = 14.30% (not needed)


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A. 9.35%B. 9.85%C. 10.35%

* D. 10.85%E. 11.35%

WACC = .110175 = (.09)*(1-.4)*(.35) + (rP)*(.15) + (.15)*(.50)

rP = (0.110175 - 0.0189 - 0.075) / .15 = 10.85%

51. Assume that investors in the stock of Company A have a required rate of return of 14percent. The company has just paid a dividend of $1.50 (D0= $1.50, which will growat the firms constant, long-run sustainable growth rate) and the stock has a currentprice of $27.00. [HINT: you should now be able to determine the long-run sustainablegrowth rate.] The companys investment bankers have told them that if they issue newstock, they could issue it at the current market price of $27.00 per share, but thatflotation costs would be equal to $5.50 per share. Given this information, determine

the firms cost of newly issued equity (re).

A. 17.83%B. 16.68%

* C. 15.53%D. 14.38%E. 13.23%

P0 = (D0)*(1+g) / (rS- g)

$27.00 = ($1.50)*(1+g) / (.14 - g)

($27.00)*(.14 - g) = ($1.50)*(1+g)

Multiplying through:

$3.78 - $27.00g = $1.50 + $1.50g

($3.78 - $1.50) = ($1.50g + $27.00g)

$2.28 = $28.50g

" g = $2.28 / $28.50 = 8.0%

D1 = ($1.50)*(1.08) = $1.62

PN = $27.00 - $5.50 = $21.50

re = (D1/ PN) + g

re = ($1.62 / $21.50) + 0.08 = 15.53%


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52. Assume that a firms targeted capital structure consists of 35 percent debt, 15 percentpreferred stock, and 50 percent common stock. Also assume that the current yield onthe firms debt is 9 percent, the cost of stock is 15 percent, the tax rate is 40 percent,and the firms weighted average cost of capital (WACC) is 10.9425 percent. Given thisinformation, determine the firms after-tax cost of preferred stock (rP).

A. 9.35%B. 9.85%

* C. 10.35%D. 10.85%E. 11.35%

WACC = .109425 = (.09)*(1-.4)*(.35) + (rP)*(.15) + (.15)*(.50)

rP = (0.109425 - 0.0189 - 0.075) / .15 = 10.35%

53. Assume that you have collected the following information regarding your company:

The companys capital structure is 60 percent equity, 40 percent debt. The companys forecasted capital budget for the coming year is $12,000,000. The before-tax yield to maturity on the companys bonds is 7 percent and the

bonds are selling at par value you may ignore flotation costs. The companys dividend next year is forecasted to be $1.25 a share. The company expects that its dividend will grow at a constant rate of 6 percent

a year. The companys stock price is $20. The companys tax rate is 40 percent. The company anticipates that it will add $4,500,000 to its retained earnings

account over the coming year, but that it will also need to raise new commonstock over the year. Its investment bankers anticipate that the total flotationcost for new common stock will equal 12.50 percent of the amount issued (orprice per share) -- you may assume that the company accounts for flotationcosts by adjusting the component cost of capital (i.e., it determines a price thatit will net and then uses a DCF approach to determine re).

Given this information, determine what the companys average cost of capital will befor the entire $12,000 to be raised.

A. 10.33%B. 8.68%

C. 9.78%D. 10.88%

* E. 9.23%

rd = 7% (given)

AT rD = (7%)*(1-.4) = 4.2%

rS = [D1 / P0] + g


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rS = [$1.25 / $20] + 0.06 = 12.25%

re = [D1 / P0(1 - F)] + g

re = [$1.25 / $20(1 - 0.125)] + 0.06 = 13.14%

Amount to be Raised:

Debt = ($12,000,000)*(.40) = $4,800,000Retained Earnings = $4,500,000 (Given)New Equity = ($12,000,000)*(.60) - $4,500,000 = $2,700,000

Weights of Total to be Raised:

Debt = $4,800,000 / $12,000,000 = 40%Retained Earnings = $4,500,000 / $12,000,000 = 37.50%New Equity = $2,700,000 / $12,000,000 = 22.50%

Average Cost = (4.2%)*(.40) + (12.25%)*(.375) + (13.14%)*(.225)

Average Cost = 1.68% + 4.59375% + 2.9565% = 9.27025% = 9.23%

54. Assume that you have collected the following information regarding your company:

The companys capital structure is 60 percent equity, 40 percent debt. The companys forecasted capital budget for the coming year is $15,000,000. The before-tax yield to maturity on the companys bonds is 9 percent and the

bonds are selling at par value you may ignore flotation costs.

The companys dividend next year is forecasted to be $1.25 a share. The company expects that its dividend will grow at a constant rate of 6 percent

a year. The companys stock price is $20. The companys tax rate is 40 percent. The company anticipates that it will add $4,500,000 to its retained earnings

account over the coming year, but that it will also need to raise new commonstock over the year. Its investment bankers anticipate that the total flotationcost for new common stock will equal 12.50 percent of the amount issued (orprice per share) -- you may assume that the company accounts for flotationcosts by adjusting the component cost of capital (i.e., it determines a price thatit will net and then uses a DCF approach to determine re).

Given this information, determine what the companys average cost of capital will befor the entire $12,000 to be raised.

A. 10.33%B. 8.68%

* C. 9.78%D. 10.88%E. 9.23%


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rd = 9% (given)

AT rD = (9%)*(1-.4) = 5.4%

rS = [D1 / P0] + g

rS = [$1.25 / $20] + 0.06 = 12.25%

re = [D1 / P0(1 - F)] + g

re = [$1.25 / $20(1 - 0.125)] + 0.06 = 13.14%

Amount to be Raised:

Debt = ($15,000,000)*(.40) = $6,000,000Retained Earnings = $4,500,000 (Given)New Equity = ($15,000,000)*(.60) - $4,500,000 = $4,500,000

Weights of Total to be Raised:

Debt = $6,000,000 / $15,000,000 = 40%Retained Earnings = $4,500,000 / $15,000,000 = 30.00%New Equity = $4,500,000 / $15,000,000 = 30.00%

Average Cost = (5.4%)*(.40) + (12.25%)*(.30) + (13.14%)*(.30)

Average Cost = 2.16% + 3.675% + 3.942% = 9.337% = 9.78%

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