Cost of Capital (Reading 37)  

Exercise Problems:

1.      WV Corporation’s estimated costs of debt, preferred stock, and common stock are 12%, 15%, and 20%, respectively. Assuming equal funding from each source and a 30% tax rate, the weighted average cost of capital is closest to:

A. 13.9%.

B. 14.5%.

C. 16.3%.

Ans: B;

WACC = (1 – t) +  +  = [0.12 × (1 – 0.30) + 0.15 + 0.20] ÷ 3 = 14.47%.

Tips: when you punch your calculator, it is easier if you input only the rates before the %, as [12 × (1 – 0.30) + 15 + 20] ÷ 3 = 14.5. You then can add the % back when you finish calculating.

2.      Which of the following is most likely considered an example of matrix pricing?

A. Debt-rating approach only

B. Yield-to-maturity approach only

C. Both the yield-to-maturity and the debt-rating approaches

Ans: A;

A is correct.  In the fixed-income markets, matrix pricing is to price a security on the basis of valuation-relevant characteristics. The debt-rating approach is an example of matrix pricing. The yield-to-maturity approach is not an example of matrix pricing.

3.      A company expects to fund its capital budget without issuing any additional shares of common stock. An analyst has gathered the following information:

Assume no significant size or timing differences exist among the projects and the projects all have the same risk as the company, which project has an internal rate of return that exceeds 10 percent?

A. All three projects

B. The warehouse project only

C. The warehouse project and the equipment project

Ans: B;

B is correct.  The WACC of the company is calculated as

0.5(6%) + 0.1(10%) + 0.4(15%) = 10%.

To have a positive NPV, a project must have an IRR greater than the WACC used to calculate the NPV. Only the warehouse project has a NPV greater than $0 (at the company’s WACC of 10%), therefore only the warehouse project has an IRR that exceeds 10%. Notice that the Equipment project has an IRR equal to 10 percent.

4.      A fund manager gathers the following data in order to assess a stock’s potential for a possible addition to her portfolio:

Which of the following is the most appropriate decision for the fund manager?

A. Do not invest in the stock.

B. Invest in the stock because the company’s ROE is greater than the required rate of return.

C. Invest in the stock because the required rate of return is greater than the company’s WACC.

 Ans: A;

A is correct. The company’s cost of equity is often used as a proxy for the investors’ minimum required rate of return because it is the minimum expected rate of return that a company must offer its investors to purchase its shares in the market.

Using the CAPM, the company’s cost of equity = 3.50% + 1.80(5.25%) = 12.95%; the fund manager, however, has a required rate of return of 13.60%. Therefore, the fund manager should not add this stock to her portfolio.

5.      Which of the following will most likely result in an increase in a company’s sustainable growth rate?

A. Higher tax burden ratio

B. Lower interest burden ratio

C. Higher dividend payout ratio

Ans: A;

Sustainable growth rate = Retention ratio × ROE.

The higher a company’s ROE and its ability to finance itself from internally generated funds (a higher retention ratio), the greater its sustainable growth rate.

In the five-factor ROE, any factor that increases ROE will increase sustainable growth:

ROE = Tax burden × Interest burden × EBIT margin × Asset turnover × Leverage.

A is correct because a higher tax burden ratio (Net income/Earnings before tax) implies that the company can keep a higher percentage of pretax profits; this implies a lower tax rate and a higher ROE.

B is incorrect because a lower interest burden ratio (earnings before tax to EBIT) means that the company has higher borrowing costs, implying a lower ROE and sustainable growth rate.

C is incorrect because a higher dividend payout ratio (1-retention ratio) means the company retain less funds internally for its growth, implying a lower Retention ratio and  sustainable growth rate.

6.      The following information is available for a company:

? Bonds are priced at par and they have an annual coupon rate of 9.3%

? Preferred stock is priced at $8.18 and it pays an annual dividend of $1.45

? Common equity has a beta of 1.5

? The risk-free rate is 3% and the market premium is 10%

? Capital structure: Debt = 30%; Preferred stock = 15%; Common equity = 55%

? The tax rate is 40%

The weighted average cost of capital (WACC) for the company is closest to:

A. 11.5%.

B. 13.4%.

C. 14.2%.

Ans: C;

The yield to maturity on a par value bond is the coupon rate of the bond, = 9.3%.

= ????/???? = $1.45/$8.18 = 17.7%

= + ??[??()? ] = 3% + 1.5[10%] = 18%

WACC = (1 – t) +  +  

WACC = 30% × 9.3% × (1?40%) + 15% × 17.7% + 55%×18% = 14.2%

7.      The following information is available for a company:

A plan to repurchase $5 million worth of shares using debt will most likely cause the earnings per share to:

A. increase.

B. decrease.

C. remain unchanged.

Ans: A;

A is correct.

?????????????? ???????????????? ?????? ?????????=$6,000,000 ÷4,000,000=$1.50 ???????????????? ??????????=$1.50 ÷$20.00=7.5%

The after-tax cost of debt (10% × [1 – 40%] = 6%) is lower than the earnings yield, implying the average cost of raising capital for the company after this plan is cheaper than before, thus, the earnings per share will increase. 

8.      In finding the cost of debt, the debt-rating approach is most appropriate when market prices for a company’s debt are:

A. stable.

B. unreliable.

C. below par value.

B is correct because the debt-rating approach is used when the market prices for debt are unreliable or non-existent.

9.      A ten-year $1,000 fixed rate non-callable bond with 8% annual coupons currently sells for $1,070.24.  If marginal tax rate is 30% and additional risk premium for equity relative to debt is 6%, the cost of equity using the bond-yield-plus-risk-premium approach is closest to:

A. 8.9%.

B. 11.0%.

C. 13.0%.

Ans: C;

First, determine the yield-to-maturity, which is the discount rate that sets the bond price to $1,070.24 This can be done using a financial calculator:

FV = 1,000, PV = -1,070.24, N = 10, PMT = 80, solve for I, which will equal 7%.

The bond-yield-plus-risk-premium approach is calculated by adding a risk premium to the cost of debt (i.e. the yield-to-maturity for the debt): the cost of equity = 7% +6% = 13.00%

10.  Which method of calculating the firm’s cost of equity is most likely to incorporate the long-run return relationship between the firm's stock and the market portfolio?

A. Dividend discount model

B. Bond-yield-plus risk-premium

C. Capital asset pricing model

Ans: C;

C is correct because the capital asset pricing model uses the firm’s equity beta.  The firm’s equity beta is computed from a regression of the company's stock returns against market returns.

11.  A firm is considering a project and gathers the following information of a comparable firm:

The firm’s unlevered beta is closest to:

A. 1.05.

B. 1.20.

C. 0.50.

Ans: C;

First you want to find the comparable firm’s beta:

(11.4% - 3.0%) ÷ 7.0% = 1.20.

Second, un-lever the comparable firm’s beta:

 ÷ (1 + (1 – t)   ) = 1.20 ÷ (1 + (1 – 30%) x 2.0)

= 0.5.

12.  WV Corporation has recently issued a 10-year, 6 percent semi-annual coupon bond for $864. The bond has a maturity value of $1,000. If the marginal tax rate is 40 percent, the cost of debt (%) is closest to:

A. 2.6.

B. 3.9.

C. 4.8.

Ans: C;

Because the bond pays coupons semi-annually, there are 20 periods (N=20) and the periodic coupon payment is $30 (6% of $1,000 per year paid in two equal payments every six months).

Using a financial calculator, enter N=20, PV=-864, PMT=30, and FV=1,000. Compute I/Y. The result (4%) is the semi-annual rate; The annual rate is 4% x 2 = 8%.

Multiplying the pre-tax cost of debt by (1 – tax rate) gives the result 4.8% (8  0.6 = 4.8). 

13.  Which of the following is least likely to be a component of a developing country’s equity premium?

A. Sovereign yield spread

B. Annualized standard deviation of the sovereign bond market in terms of the developing country’s currency

C. Annualized standard deviation of the developing country’s equity index 

Ans: B;

Country equity premium = sovereign yield spread * (annualized standard deviation of equity index ÷ annualized standard deviation of the sovereign bond market in terms of the developed market currency)

The annualized standard deviation of the sovereign bond market in terms of the developing country’s currency is not part of the equity premium calculation.

14.  WV Corporation wants to determine the cost of equity using the bond-yield-plus-risk-premium approach. The company has gathered the following information:

the cost of equity (%) for the company is closest to:

A. 12.0.

B. 15.3.

C. 16.3.

Ans: C;

Per the bond-yield-plus-risk-premium approach, the cost of equity equal to the before-tax cost of debt plus the risk premium of equity over debt.

The before-tax cost of debt is the after-tax cost of debt divided by (1- tax rate). 8.0/ (1 – 0.4) = 13.3%.

Adding the risk premium results in a cost of equity of 13.3% + 3% = 16.3%.

15.  An analyst gathers the following information about the cost and availability of raising various amounts of new debt and equity capital for a company:

The company’s target capital structure is 60 percent equity and 40 percent debt. If the

company raises €8 million in new financing, the marginal cost of capital is closest to:

A. 9.8%.

B. 10.6%.

C. 9.4%.

Ans: C;

The break-points for debt and equity are €10 million (€4.0 million / 0.40) and €8.33 million (€5.0 million / 0.60), respectively.

The cost of debt and equity if the firm raises €8 million in new financing will be 4% and 13%, respectively, because €8 million is below the debt breakpoint and the equity breakpoint.

The marginal cost of capital = 0.40 × 4% + 0.60 × 13% = 9.4%.

16.  A firm’s optimal capital budget is best described as the amount of new capital required to undertake all projects with:  

A. a weighted average cost of capital greater than the cost of new debt capital.

B. an internal rate of return greater than the marginal cost of capital.

C. an internal rate of return greater than the weighted average cost of capital.

Ans: B;

The optimal capital budget is the amount of new capital required to undertake all investment projects with an IRR greater than the marginal cost of capital.

17.  An analyst gathers the following information about a company:

The company’s marginal tax rate is 40 percent. Its weighted average cost of capital (WACC) is closest to:

A. 8.55%.

B. 9.95%.

C. 10.62%.

Notes: because the target capital weights are not given, market value weights are used to compute the WACC.

The market value weights for debt, preferred stock and equity are 0.2667 ($80/$300), 0.0667 ($20/$300), and 0.6667 ($200/$300) respectively.

WACC = (1 – t) +  +  = 0.2667 × 8% × (1 – 0.4) + 0.0667 × 10% + 0.6667 × 13% = 10.62%

18.  An analyst gathers the following information about a company and the market:

Using the dividend discount model approach, the cost of common equity for the company is closest to:

A. 16.1%.

B. 16.5%.

C. 17.2%.

Ans: A;

According to the dividend discount model approach, the cost of common equity is equal to the dividend yield plus the growth rate.

In this case, the growth rate is the earnings retention rate times the expected ROE or (1 – dividend payout rate) × expected ROE = (1 – 0.3) × 12% = 8.4%.

The expected dividend = 2.50 × (1 + 0.084) = 2.71. The expected dividend yield = 2.71 / 35 = 7.743%.

The cost of common equity = 7.743% + 8.4% ≈ 16.14%.