Question 1

Explain the conditions under which the constant-growth dividend formula for the cost of ordinary shares can be used to find the cost of equity capital for the company.

Accepted Answer

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Question 2

Using the WACC in practice: Maloney's, Ltd., has found that its cost of equity capital is 17 percent and its cost of debt capital is 6 percent. If the company is financed with $3,000,000 of ordinary shares (market value) and $2,000,000 of debt, then what is the after-tax weighted average cost of capital for Maloney's if it is subject to a 40 percent company tax rate?

Accepted Answer

First, we need to calculate the weighted average cost of capital (WACC) before tax:

WACC before tax = [($3,000,000 / $5,000,000) x 0.17] + [($2,000,000 / $5,000,000) x 0.06]
WACC before tax = 0.116 = 11.6%

Next, we can calculate the after-tax WACC by adjusting the cost of debt capital to reflect the tax shield gained from interest expenses:

Cost of debt after tax = Cost of debt before tax x (1 - tax rate)
Cost of debt after tax = 0.06 x (1 - 0.4) = 0.036 = 3.6%

After-tax WACC = [($3,000,000 / $5,000,000) x 0.17] + [($2,000,000 / $5,000,000) x 0.036]
After-tax WACC = 0.116 - 0.0048 = 0.1116 = 11.16%

Therefore, the best choice is C, which is the after-tax WACC calculated above.

Question 3

Using the WACC in practice: Marley's Pipe Shops has found that its equity capital shares have a beta equal to 1.5 while the risk-free return is 8 percent and the expected return on the market is 14 percent. Its cost of debt financing is 12 percent. If the company is financed with $120,000,000 of ordinary shares (market value) and $80,000,000 of debt, then what is the after-tax weighted average cost of capital for Marley's if it is subject to a 35 percent company tax rate?

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Question 4

The cost of preference shares: Billy's Goat Coats has a preference share issue outstanding with a current price of $38.89. The company last paid a dividend on the issue of $3.50 per share. What is the company's cost of preference shares?

Accepted Answer

The cost of preference shares is calculated as the dividend divided by the current price. Here, $3.50 / $38.89 = 0.09 or 9%.

Question 5

Overall cost of capital: If the market risk premium is currently 6 percent and the risk-free rate of return is 4 percent, then what is the expected return on a common share with a beta equal to 2?

Accepted Answer

First, we need to use the Capital Asset Pricing Model (CAPM) to calculate the expected return on the common share.

Expected Return = Risk-Free Rate + (Beta x Market Risk Premium)
Expected Return = 4% + (2 x 6%) 
Expected Return = 4% + 12% 
Expected Return = 16%

Therefore, the answer is D) 16.0%.

Question 6

How companies estimate their cost of capital: You are analysing the cost of capital for a company that is financed with 65 percent equity and 35 percent debt. The cost of debt capital is 8 percent, while the cost of equity capital is 20 percent for the company. What is the overall cost of capital for the company?

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Question 7

How companies estimate their cost of capital: The Diverse Co. has invested 40 percent of the company's assets in a project with a beta of 0.4 and the remaining assets in a project with a beta of 1.8. What is the beta of the company?

Accepted Answer

The beta of the company can be calculated as the weighted average of the betas of its projects, where the weights are based on the proportion of assets invested in each project.

Beta of the project with beta 0.4 = 0.4
Beta of the project with beta 1.8 = 1.8

Weight of the project with beta 0.4 = 40%
Weight of the project with beta 1.8 = 60% (100% - 40%)

Beta of the company = (0.4)(40%) + (1.8)(60%)
= 0.16 + 1.08
= 1.24

Therefore, the answer is B) 1.24.

Question 8

Using the WACC in practice: Swirlpool Ltd has found that its cost of equity capital is 18 percent, and its cost of debt capital is 8 percent. If the company is financed with 60 percent ordinary shares and 40 percent debt, then what is the after-tax weighted average cost of capital for Swirlpool if it is subject to a 40 percent company tax rate?

Accepted Answer

To find the after-tax weighted average cost of capital (WACC), we first need to calculate the weighted average cost of capital (WACC) using the formula:

WACC = (E/V) x Re + (D/V) x Rd x (1 - T)

Where:
E = Market value of equity
D = Market value of debt
V = Total value of the firm (E + D)
Re = Cost of equity
Rd = Cost of debt
T = Tax rate

Given:
Re = 18%
Rd = 8%
D/V = 40%
E/V = 60%
T = 40%

We can calculate WACC as follows:

WACC = (0.60 x 0.18) + (0.40 x 0.08 x (1 - 0.4))
WACC = 0.108 + 0.024
WACC = 0.132 or 13.2%

However, this is the pre-tax WACC. To get the after-tax WACC, we need to multiply this by (1 - T):

After-tax WACC = 0.132 x (1 - 0.4)
After-tax WACC = 0.132 x 0.6
After-tax WACC = 0.0792 or 7.92%

Therefore, the answer is C) 12.72%.

Question 9

The cost of equity: Wally's War Duds has a preference share issue outstanding with a current price of $26.57. The company is expected to pay a dividend of $1.86 per share a year from today. What is the company's cost of preference shares?

Accepted Answer

The cost of preference shares is the dividend yield, which is calculated by dividing the annual dividend by the market price of the preference share: $1.86/$26.57 = 7.00%. Therefore, the answer is B.

Question 10

Using the WACC in practice: Ronnie's Comics has found that its cost of equity capital is 15 percent and its cost of debt capital is 12 percent. If the company is financed with $250,000,000 of ordinary shares (market value) and $750,000,000 of debt, then what is the after-tax weighted average cost of capital for Ronnie's if it is subject to a 35 percent company tax rate?

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Question 11

The cost of equity: Oasis Ltd has common shares with a price of $21.12 per share. The company is expected to pay a dividend of $1.75 one year from today, and dividends are expected to grow at 10 percent for two years after that and then at 5 percent thereafter. What is the implied cost of ordinary shares for Oasis?

Accepted Answer

First, we need to calculate the expected dividends for the next three years:

- Year 1: $1.75
- Year 2: $1.75 x 1.1 = $1.925
- Year 3: $1.925 x 1.1 = $2.1175

After year 3, dividends are expected to grow at a rate of 5%. We can use the Gordon growth model to calculate the cost of equity:

Cost of equity = (next year's dividend / current stock price) + growth rate

Cost of equity = ($2.1175 / $21.12) + 0.05

Cost of equity = 0.1 or 10%

Therefore, the best answer is B) 14%.

Question 12

Using the WACC in practice: Poly's Parrot Shops has found that its cost of equity capital is 17 percent. It has 7-year maturity bonds outstanding with a price of $767.03 that have a coupon rate of 7 percent. If the company is financed with $120,000,000 of ordinary shares (market value) and $80,000,000 of debt, then what is the after-tax weighted average cost of capital for Poly's if it is subject to a 35 percent company tax rate?

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Question 13

Overall cost of capital: Stryder Ltd has 3 million shares outstanding at a current price of $15 per share. The book value of the shares is $10 per share. The company also has $30 million in par value of bonds outstanding. The bonds are selling at a price equal to 101 percent of par. What is the market value of the company?

Accepted Answer

The market value of equity = current price per share x number of shares outstanding = $15 x 3 million = $45 million
The market value of bonds = selling price per bond x par value of bonds outstanding = 101% x $30 million = $30.3 million
Therefore, the total market value of the company = market value of equity + market value of bonds
= $45 million + $30.3 million
= $75.3 million. 
Hence, the correct option is D.

Question 14

Using the WACC in practice: Droz's Hiking Gear Ltd has found that its equity capital shares have a beta equal to 1.5 while the risk-free return is 8 percent and the expected return on the market is 14 percent. It has 7-year maturity bonds outstanding with a price of $767.03 that have a coupon rate of 7 percent. If the company is financed with $120,000,000 of ordinary shares (market value) and $80,000,000 of debt, then what is the after-tax weighted average cost of capital for Droz's if it is subject to a 35 percent company tax rate?

Accepted Answer

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Question 15

How companies estimate their cost of capital: The WACC for a company is 13.00 percent. You know that the company's cost of debt capital is 10 percent and the cost of equity capital is 20%. What proportion of the company is financed with debt?

Accepted Answer

The WACC formula is WACC = (E/V) * Re + (D/V) * Rd, where E is equity, D is debt, V is total value (E+D), Re is cost of equity, and Rd is cost of debt. Solving 13% = (E/V)*20% + (D/V)*10% with E/V + D/V = 1, we find D/V = 50%.

Question 16

The cost of equity: Melba's Toast has a preference share issue outstanding with a current price of $19.50. The company is expected to pay a dividend of $2.34 per share a year from today. What is the company's cost of preference shares?

Accepted Answer

The cost of preference shares is calculated as the dividend divided by the current price: $2.34 / $19.50 = 0.12 or 12.00%.

Question 17

Briefly explain why the book value of debt might not reflect the current cost of debt for the company, with respect to a single issuance of debt?

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Question 18

How companies estimate their cost of capital: The WACC for a company is 19.75 percent. You know that the company is financed with $75 million of equity and $25 million of debt. The cost of debt capital is 7 percent. What is the cost of equity for the company?

Accepted Answer

The cost of equity can be calculated using the following formula:Cost of equity = (WACC - (Cost of debt * Debt ratio)) / Equity ratioCost of equity = (19.75% - (7% * 25%) / 75%)= (19.75% - 1.75%) / 75%= 18% / 75%= 24%

Question 19

How companies estimate their cost of capital: You are analysing the cost of capital for a company that is financed with $300 million of equity and $200 million of debt. The cost of debt capital for the company is 9 percent, while the cost of equity capital is 19 percent. What is the overall cost of capital for the company?

Accepted Answer

To calculate the overall cost of capital, we need to use the weighted average cost of capital (WACC) formula: WACC = (E/V x Re) + (D/V x Rd) x (1 - T), where E = equity, D = debt, V = total value (equity + debt), Re = cost of equity, Rd = cost of debt, and T = corporate tax rate.

Plugging in the given values, we get:

WACC = (0.6 x 0.19) + (0.4 x 0.09) x (1 - 0)
WACC = 0.114 + 0.036
WACC = 0.15 or 15.0%

Therefore, the best choice is C) 15.0%.

Question 20

Overall cost of capital: What is the beta of a company whose equity has an expected return of 21.3 percent when the risk-free rate of return is 7.0 percent and the expected return on the market is 18.0 percent?

Accepted Answer

The formula for calculating beta is:

Beta = (Expected Return on Equity - Risk-Free Rate) / Expected Return on Market - Risk-Free Rate)

Using the numbers given:

Beta = (21.3% - 7.0%) / (18.0% - 7.0%)
Beta = 14.3% / 11.0%
Beta = 1.30

Therefore, the answer is (B) 1.30.

Quiz 13: The Cost of Capital