Reading 45: Cost of Capital - LOS a ～ Q11-13 corporate, increase, average, capital, company

mayanfang1

Q11. Assume that a company has equal amounts of debt, common stock, and preferred stock. An increase in the corporate tax rate of a firm will cause its weighted average cost of capital (WACC) to:

A)   rise.

B)   fall.

C)   more information is needed.

Q12. 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% semi-annual coupon debt with a 15-year maturity for a price of $1,047.46.

• An 8% dividend preferred stock issue has a value of $35 per share.

• The company’s growth rate is estimated at 6%.

• 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)   10.53%.

Q13. 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)   11.0%.

B)   9.2%.

C)   9.0%.

mayanfang1

答案和详解如下：

Q11. Assume that a company has equal amounts of debt, common stock, and preferred stock. An increase in the corporate tax rate of a firm will cause its weighted average cost of capital (WACC) to:

A)   rise.

B)   fall.

C)   more information is needed.

Correct answer is B)

Recall the WACC equation:

WACC = [w_d × k_d × (1 − t)] + (w_ps × k_ps) + (w_ce × k_s)

The increase in the corporate tax rate will result in a lower cost of debt, resulting in a lower WACC for the company.

Q12. 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% semi-annual coupon debt with a 15-year maturity for a price of $1,047.46.

• An 8% dividend preferred stock issue has a value of $35 per share.

• The company’s growth rate is estimated at 6%.

• 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)   10.53%.

Correct answer is 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 = (1,000 × 0.07) / 2 = 35; FV = 1,000; PV = -1,047.46; CPT → 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

where:	Dps = preferred dividends.
	P = price

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

where:	D1 = Dividend in next year
	P0 = Current stock price
	g = Dividend growth rate

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.

Q13. 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)   11.0%.

B)   9.2%.

C)   9.0%.

Correct answer is A)

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%.

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