Table 9.1
A firm has determined its optimal capital structure which is composed of the following sources and target market value proportions. Debt: The firm can sell a 12-year, $1,000 par value, 7 percent bond for $960. A flotation cost of
2 percent of the face value would be required in addition to the discount of $40.
Preferred Stock: The firm has determined it can issue preferred stock at $75 per share par value. The stock will pay a $10 annual dividend. The cost of issuing and selling the stock is $3 per share.
Common Stock: A firm's common stock is currently selling for $18 per share. The dividend expected to be paid at the end of the coming year is $1.74. Its dividend payments have been growing at a constant rate for the last four years. Four years ago, the dividend was $1.50. It is expected that to sell, a new common stock issue must be underpriced $1 per share in floatation costs. Additionally, the firm's marginal tax rate is 40 percent.
-If the target market proportion is reduced to 15 percent, what will be the revised weighted average cost of capital? (See Table 9.1)
A) 13.6 percent
B) 11.0 percent
C) 12.34 percent
D) 10.4 percent

Question

Table 9.1
A firm has determined its optimal capital structure which is composed of the following sources and target market value proportions.  Debt: The firm can sell a 12-year, $1,000 par value, 7 percent bond for $960. A flotation cost of
2 percent of the face value would be required in addition to the discount of $40.
Preferred Stock: The firm has determined it can issue preferred stock at $75 per share par value. The stock will pay a $10 annual dividend. The cost of issuing and selling the stock is $3 per share.
Common Stock: A firm's common stock is currently selling for $18 per share. The dividend expected to be paid at the end of the coming year is $1.74. Its dividend payments have been growing at a constant rate for the last four years. Four years ago, the dividend was $1.50. It is expected that to sell, a new common stock issue must be underpriced $1 per share in floatation costs. Additionally, the firm's marginal tax rate is 40 percent.
-If the target market proportion is reduced to 15 percent, what will be the revised weighted average cost of capital? (See Table 9.1)
A) 13.6 percent 
B) 11.0 percent 
C) 12.34 percent 
D) 10.4 percent

Quizplus · Accepted Answer

To calculate the weighted average cost of capital (WACC), we need the cost of each source of capital and its target market value proportion. 
Using the information given in the problem:

- Debt: 
The cost of debt is calculated as follows:

Cost of debt = (annual interest payment ÷ net proceeds) + flotation cost

Annual interest payment = $1,000 x 7% = $70 
Net proceeds = selling price - flotation cost - par value 
Net proceeds = $960 - ($1,000 x 2%) - $1,000 = $940 
Cost of debt = ($70 ÷ $940) + 0.02 = 0.0894 or 8.94%

The target market value proportion for debt is 30%. Therefore, the contribution of debt to the WACC is:

Weight of debt = 0.3

After-tax cost of debt = Cost of debt x (1 - marginal tax rate) 
After-tax cost of debt = 8.94% x (1 - 0.4) = 5.364%

Contribution of debt to WACC = Weight of debt x After-tax cost of debt 
Contribution of debt to WACC = 0.3 x 5.364% = 1.6092%

- Preferred stock: 
The cost of preferred stock is calculated as follows:

Cost of preferred stock = (annual dividend ÷ net proceeds) + flotation cost

Annual dividend = $10 per share 
Net proceeds = selling price - flotation cost - par value 
Net proceeds = $75 - $3 = $72 
Cost of preferred stock = ($10 ÷ $72) + ($3 ÷ $75) = 0.1528 or 15.28%

The target market value proportion for preferred stock is 10%. Therefore, the contribution of preferred stock to the WACC is:

Weight of preferred stock = 0.1

Contribution of preferred stock to WACC = Weight of preferred stock x Cost of preferred stock 
Contribution of preferred stock to WACC = 0.1 x 15.28% = 1.528%

- Common stock: 
The cost of common stock is calculated using the dividend growth model:

Cost of common stock = (expected dividend ÷ current price) + growth rate - underpricing cost

Expected dividend = $1.74 
Current price = $18 
Growth rate = (new dividend - old dividend) ÷ old dividend 
Growth rate = ($1.74 - $1.50) ÷ $1.50 = 0.16 or 16% 
Underpricing cost = $1

Cost of common stock = ($1.74 ÷ $18) + 0.16 - 0.056 (underpricing cost ÷ current price) 
Cost of common stock = 0.2689 or 26.89%

The target market value proportion for common stock is 60%. Therefore, the contribution of common stock to the WACC is:

Weight of common stock = 0.6

Contribution of common stock to WACC = Weight of common stock x Cost of common stock 
Contribution of common stock to WACC = 0.6 x 26.89% = 16.134%

Now, we can calculate the WACC as follows:

WACC = Contribution of debt to WACC + Contribution of preferred stock to WACC + Contribution of common stock to WACC 
WACC = 1.6092% + 1.528% + 16.134% = 19.2712%

If the target market proportion of common stock is reduced to 15%, the new market value proportions will be:

- Debt: 30% 
- Preferred stock: 10% 
- Common stock: 15%

The contributions of debt, preferred stock, and common stock to the WACC will be:

- Contribution of debt to WACC = 0.3 x 5.364% = 1.6092% 
- Contribution of preferred stock to WACC = 0.1 x 15.28% = 1.528% 
- Contribution of common stock to WACC = 0.15 x 26.89% = 4.0335%

The new WACC will be:

WACC = Contribution of debt to WACC + Contribution of preferred stock to WACC + Contribution of common stock to WACC 
WACC = 1.6092% + 1.528% + 4.0335% = 7.1717%

Therefore, the revised WACC will be 7.1717%, which is closest to option C (12.34%).

Table 9.1 A Firm Has Determined Its Optimal Capital Structure Which Is