Reading 45: Cost of Capital - LOS a ～ Q11-15

答案和详解如下：

11.Hatch Corporation's target capital structure is 40 percent debt, 50 percent common stock, and 10 percent preferred stock. Information regarding the company's cost of capital can be summarized as follows:

§       The company's bonds have a nominal yield to maturity of 7 percent.

§       The company's preferred stock sells for $40 a share and pays an annual dividend of $4 a share.

§       The company's common stock sells for $25 a share and is expected to pay a dividend of $2 a share at the end of the year (i.e., D₁=$2.00). The dividend is expected to grow at a constant rate of 7 percent a year.

§       The company has no retained earnings.

§       The company's tax rate is 40 percent.

What is the company's weighted average cost of capital (WACC)?

A)   10.03%.

B)   10.59%.

C)   11.30%.

D)   10.18%.

The correct answer was D)

WACC = (w_d)(k_d)(1-t) + (w_ps)(k_ps) + (w_ce)(k_ce)

where: w_d = .40    w_ce = .50    w_ps = .10    k_d = .07

k_ps = D_ps / P = 4.00 / 40.00 = 0.10

k_ce = D₁ / P₀ + g = 2.00 / 25.00 + 0.07 = 0.08 + 0.07 = 0.15

WACC = (0.4)(0.07)(1 - 0.4)+ (0.1)(0.10) + (0.5)(0.15)

= 0.0168 + 0.01 + .075

= 0.1018   or  10.18%

12.The following data is regarding the Link Company:

§       A target debt/equity ratio of .5

§       Bonds are currently yielding 10%

§       Link is a constant growth firm that just paid a dividend of $3.00

§       Stock sells for $31.50 per share, and has a growth rate of 5%

§       Marginal tax rate is 40%

What is Link's after-tax cost of capital?

A)   12.0%.

B)   12.5%.

C)   11.0%.

D)   10.5%.

The correct answer was A)

Use the revised form of the constant growth model to determine the cost of equity. Use algebra to determine the weights for the target capital structure realizing that debt is 50% of equity. Substitute 0.5E for D in the formula below.

k_s = D₁/P₀ + growth = (3)(1.05)/(31.50) + .05 = .15 or 15%

V = debt + equity = .5 + 1 = 1.5

WACC = (E/V)(k_s) + (D/V)(k_debt)(1 - t)

WACC = (1/1.5)(.15) + (.5/1.5)(.10)(1 - .4) = .1 + .02 = .12 or 12%

13.Helmut Humm, manager at a large U.S. firm, has just been assigned to the capital budgeting area to replace a person who left suddenly. One of Humm’s first tasks is to calculate the company’s weighted average cost of capital (WACC) – and fast! The CEO is scheduled to present to the board in half an hour and needs the WACC – now! Luckily, Humm finds clear notes on the target capital component weights. Unfortunately, all he can find for the cost of capital components is some handwritten notes. He can make out the numbers, but not the corresponding capital component.  As time runs out, he has to guess.

Here is what Humm deciphered:

§       Target weights: w_d = 30%, w_ps = 20%, w_ce = 50%, where w_d, w_ps, and w_ce are the weights used for debt, preferred stock, and common equity.

§       Cost of components (in no particular order): 6.0%, 15.0%, and 8.5%.

§       The cost of debt is the after-tax cost.

If Humm guesses correctly, the WACC is:

A)   9.2%.

B)   11.0%.

C)   9.0%.

D)   8.6%.

The correct answer was B)

If Humm remembers to order the capital components from cheapest to most expensive, he can calculate WACC. The order from cheapest to most expensive is: debt, preferred stock (which acts like a hybrid of debt and equity), and common equity.

 Then, using the formula for WACC = (w_d)(k_d) + (w_ps)(k_ps) + (w_ce)(k_ce)

where w_d, w_ps, and w_e are the weights used for debt, preferred stock, and common equity.

 WACC =  (0.30 * 6.0%) + (0.20 * 8.5%) + (0.50 * 15.00%) = 11.0%.

14.A company has the following capital structure:

§       Target weightings: 30% debt, 20% preferred stock, 50% common equity.

§       Tax Rate: 35%.

§       The firm can issue $1,000 face value, 7.00% semi-annual coupon debt with a 15-year maturity for a price of $1,047.46.

§       An 8.0% dividend preferred stock issue has a value of $35 per share.

§       The company’s growth rate is estimated at 6.0%.

§       The company's common shares have a value of $40 and a dividend in year 0 of D₀ = $3.00.

The company's weighted average cost of capital is closest to:

A)   9.84%.

B)   9.28%.

C)   9.21%.

D)   10.53%.

The correct answer was A)

Step 1: Determine the after-tax cost of debt:

The after-tax cost of debt [k_d (1 – t)] is used to compute the weighted average cost of capital. It is the interest rate on new debt (k_d) less the tax savings due to the deductibility of interest (k_dt).

Here, we are given the inputs needed to calculate k_d: n = 15*2 = 30, PMT = (1000*0.07)/2 = 35, FV = 1000, PV = -1047.46, compute I = 3.25, multiply by 2 = 6.50%.

Thus, k_d (1 – t) = 6.50% * (1 – 0.35) = 4.22%

Step 2: Determine the cost of preferred stock:

Preferred stock is a perpetuity that pays a fixed dividend (D_ps) forever. The cost of preferred stock (k_ps) = D_ps / P

Here, D_ps = 0.08 * $35.00 = $2.80, so k_ps = D_ps / P = $2.80 / $35 = 0.08, or 8.0%.

Step 3: Determine the cost of common equity:

k_ce = (D₁ / P₀) + g

Here, D₁ = D₀ * (1 + g) = $3.00 * ( 1 + 0.06) = $3.18.

k_ce = (3.18 / 40) + 0.06 = 0.1395 or 13.95%.

Step 4: Calculate WACC:

WACC = (w_d)(k_d) + (w_ps)(k_ps) + (w_ce)(k_ce)

where w_d, w_ps, and w_ce are the weights used for debt, preferred stock, and common equity.

Here, WACC = (0.30 * 4.22%) + (0.20 * 8.0%) + (0.50 * 13.95%) = 9.84%.

Note: Your calculation may differ slightly, depending on whether you carry all calculations in your calculator, or round to two decimals and then calculate.

15.Ravencroft Supplies is estimating its weighted average cost of capital (WACC). Ravencroft’s optimal capital structure includes 10 percent preferred stock, 30 percent debt, and 60 percent equity. They can sell additional bonds at a rate of 8 percent. The cost of issuing new preferred stock is 12 percent. The firm can issue new shares of common stock at a cost of 14.5 percent. The firm’s marginal tax rate is 35 percent. Ravencroft’s WACC is closest to:

A)   12.3%.

B)   13.3%.

C)   11.1%.

D)   11.5%.

The correct answer was D)

0.10(12%) + 0.30(8%)(1 – 0.35) + 0.6(14.5%) = 11.46%.