978-0134730417 Chapter 11 Part 3

Chapter 11 ◼ The Cost of Capital 397

Re = 3% + 1.3 (8%) = 13.4%

If Bonds sell for $43 million, the firm can retire 1 million shares, $43,000,000 / $43 = 1,000,000

The market value of equity is now $43 × 1,000,000 = $43,000,000

The market value of debt is $43,000,000

E/V = $43,000,000 / ($43,000,000 + $43,000,000) = 0.5

D/V = $43,000,000 / ($43,000,000 + $43,000,000) = 0.5

Adjusted WACC = 0.5 × 13.4% + 0.5 × 9% × (1 – 0.35) = 6.7% + 2.925% = 9.625%

18. Adjusted WACC. Thorpe and Company is currently an all-equity firm. It has 3 million shares

selling for $28 per share. Its beta is 0.85, and the current risk-free rate is 2.5%. The expected

return on the market for the coming year is 13%. Thorpe will sell corporate bonds for

$28,000,000 and retire common stock with the proceeds. The bonds are twenty-year

semiannual bonds with a 10% coupon rate and $1,000 par value. The bonds are currently

selling for $1,143.08 per bond. When the bonds sell, the company’s beta will increase to

0.95. What was Thorpe and Company’s WACC before the bond sale? What is its adjusted

WACC after the bond sale if the corporate tax rate is 40%? Hint: The weight of equity before

selling the bond is 100%.

ANSWER

Before the sale of bonds the weighted average cost of capital is the cost of equity.

398 Brooks ◼ Financial Management: Core Concepts, 4e

If Bonds sell for $28 million the firm can retire 1 million shares, $28,000,000 / $28 = 1,000,000

The market value of equity is now $28 × 2,000,000 = $56,000,000

The market value of debt is $28,000,000

E/V = $56,000,000 / ($56,000,000 + $28,000,000) = 0.6667

D/V = $28,000,000 / ($56,000,000 + $28,000,000) = 0.3333

Adjusted WACC = 0.667 × 12.475% + 0.3333 × 8.5% × (1 – 0.40) = 8.3167% + 1.7%

= 10.0167%

19. Adjusted WACC. Hollydale’s is a clothing store in East Park. It paid an annual dividend of

$2.50 last year to its shareholders and plans to increase the dividend annually at 2%. It has

500,000 shares outstanding. The shares currently sell for $21.25 per share. Hollydale’s has

10,000 semiannual bonds outstanding with a coupon rate of 7.5%, a maturity of sixteen

years, and a par value of $1,000. The bonds are currently selling for $874.08 per bond. What

is the adjusted WACC for Hollydale’s if the corporate tax rate is 35%?

ANSWER

Find the cost of equity via the dividend growth model.

Chapter 11 ◼ The Cost of Capital 399

Adjusted WACC = 0.5487 × 14% + 0.4513 × 9% × (1 – 0.35) = 7.6812% + 2.6404% = 10.3216%

Chapter 11 ◼ The Cost of Capital 401

E = 500,000 × $21.25 = $10,625,000

D1 = 10,000 × $874.04 = $8,740,800

D2 = 5,000 × $817.7856 = $4,088,928

E/V = $10,625,000 / ($10,625,000 + $8,740,800 + $4,088,928) = 0.453

D1/V = $8,740,800 / ($10,625,000 + $8,740,800 + $4,088,928) = 0.373

D2/V = $4,088,928 / ($10,625,000 + $8,740,800 + $4,088,928) = 0.174

Adjusted WACC = 0.453 × 14% + 0.3713 × 9% × (0.65) + 0.1754 × 9.91% × (0.65) = 6.34%

+ 2.18% + 1.12 = 9.64%

Chapter 11 ◼ The Cost of Capital 403

Projects A, C, D, and F – NPV is $13,000 Total Cost = $168,000

Projects A, C, E, and F – NPV is $15,000 Total Cost = $183,000

Projects A, D, E, and F – NPV is $16,000 Total Cost = $186,000

Projects B, C, D, and F – NPV is $15,000 Total Cost = $186,000

Projects B, C, and E – NPV is $15,000 Total Cost = $172,000

Projects B, D, and E – NPV is $16,000 Total Cost = $175,000

Projects C, D, E, and F – NPV is $15,000 Total Cost = $164,000

Pick Projects A, C, D, and E, highest NPV, while using almost all $200,000.

24. Constraints on borrowing. Runway Fashions, Inc. is considering the following potential

projects for the company but has only $1,000,000 in the capital budget. Which projects

should it choose?

ANSWER

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Solutions for Advanced Problems for Spreadsheet Application

1. Changing WACC and optimal choice. Lowest D/E ratio ➔1.27; Lowest WACC➔9.61%

WACC

Company Value 50,000,000.00$

Tax Rate 40.00%

EQUITY: ALL EQUITY Lowest WACC

Number of Shares 2,000,000.00 1,840,000.00 1,680,000.00 1,040,000.00 880,000.00 720,000.00 560,000.00

Value of Shares 50,000,000.00$ 46,000,000.00$ 42,000,000.00$ 26,000,000.00$ 22,000,000.00$ 18,000,000.00$ 14,000,000.00$

Cost of Equity:

Beta 0.85 0.88 0.90 1.00 1.03 1.05 1.08

Market return 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00%

Risk-free rate 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% 3.00%

Cost of Equity 10.65% 10.88% 11.10% 12.00% 12.23% 12.45% 12.68%

DEBT:

Value of Debt/Unit 4,000,000.00$

Units of Debt 0 1 2 6 78 9

Value of Debt –$ 4,000,000.00$ 8,000,000.00$ 24,000,000.00$ 28,000,000.00$ 32,000,000.00$ 36,000,000.00$

Cost of Debt 7.50% 7.50% 8.35% 11.75% 12.60% 13.45% 14.30%

DEBT – EQUITY:

Equity to Value 100.00% 92.00% 84.00% 52.00% 44.00% 36.00% 28.00%

Debt to Value 0.00% 8.00% 16.00% 48.00% 56.00% 64.00% 72.00%

WACC 10.65% 10.37% 10.13% 9.62% 9.61% 9.65% 9.73%

406 Brooks ◼ Financial Management: Core Concepts, 4e

CAPM approach:

Re = 3% + 1.2(12% – 3%) = 13.8%

Average:

(13.57% + 13.8%)/2 = 13.69%

4. Compute BioCom’s weighted average cost of capital. Should you use book values or

market values for this computation?

5. BioCom could sell new bonds with maturities of fifteen to twenty years at approximately

the same yield as bond 2. It would, however, incur flotation costs of $20.00 per $1,000 of

par value. Estimate the effective interest rate BioCom would have to pay on a new issue of

long-term debt.

BioCom would most likely issue bonds with coupon rates to reflect investors current

6. Some of BioCom’s projects are low risk, some average risk, and some high risk. Should

BioCom use the cost of capital to evaluate all of its projects, or adjust the discount rate to

reflect different levels of risk?

Additional Problems with Solutions

1. Cost of debt for a firm. You have been assigned the task of estimating the after-tax cost of

debt for a firm as part of the process in determining the firm’s cost of capital. After doing

some checking, you find out that the firm’s original twenty-year 9.5% coupon bonds (paid

semiannually), currently have fourteen years until they mature and are selling at a price of

$1,100 each. You are also told that the investment bankers charge a commission of $25 per

bond when new bonds are sold. If these bonds are the only debt outstanding for the firm,

what is the after-tax cost of debt for this firm if the marginal tax rate for the firm is 34

percent?

Chapter 11 ◼ The Cost of Capital 407

ANSWER (Slides 11-42 to 11-43)

Calculate the YTM on the currently outstanding bonds, after adjusting the price for the $25

commission.

2. Cost of Equity for a firm. R.K. Boats Inc. is in the process of making some major investments

for growth and is interested in calculating their cost of equity so as to be able to correctly

estimate their adjusted WACC. The firm’s common stock is currently trading for $43.25 and

their annual dividend, which was paid last year, was $2.25 and should continue to grow at

6% per year. Moreover, the company’s beta is 1.35, the risk-free rate is at 3%, and the

market risk premium is 9%. Calculate a realistic estimate of RKBIs cost of equity. (Ignore

floatation costs)

ANSWER (Slides 11-44 to 11-45)

Using the SML Approach:

3. Calculating capital component weights. T.J. Enterprises is trying to determine the weights

to be used in estimating their cost of capital. The firm’s current balance sheet and market

information regarding the price and number of securities outstanding are listed below.

TJ Enterprises

Balance Sheet

(in thousands)

Current Assets: $50,000 Current Liabilities: $ 0

Long-Term Assets: $60,000 Long-Term Liabilities

Bonds Payable $48,000

408 Brooks ◼ Financial Management: Core Concepts, 4e

Owner’s Equity

Preferred Stock $15,000

Common Stock $47,000

Total Assets: $110,000 Total L & OE $110,000

Market Information

Debt Preferred Stock Common Stock

Outstanding 48,000 102,000 1,300,000

Market Price $850 $95.40 $40

Calculate the firm’s capital component weights using book values as well as market values.

ANSWER (Slides 11-49 to 11-53)

Based on book values:

4. Computing WACC. New Ideas Inc. currently has 30,000 of its 9% semiannual coupon bonds

outstanding (Par value = 1,000). The bonds will mature in fifteen years and are currently

priced at $1,340 per bond. The firm also has an issue of 1 million preferred shares

outstanding with a market price of $11.00. The preferred shares offer an annual dividend of

$1.20. New Ideas Inc. also has 2 million shares of common stock outstanding with a price of

$30.00 per share. The firm is expected to pay a $3.20 common dividend one year from

today, and that dividend is expected to increase by 7% per year forever. The firm typically

pays floatation costs of 2% of the price on all newly issued securities. If the firm is subject to

a 35% marginal tax rate, then what is the firm’s weighted average cost of capital?

Chapter 11 ◼ The Cost of Capital 409

ANSWER (Slides 11-47 to 11-50)

1. Determine the component costs

Cost of Debt:

2. Determine the market value weights of the components:

Market value of bonds = $1340*30,000➔ $40,200,000