Question

Alpha Products maintains a capital structure of 40 percent debt and 60 percent common equity. To finance its capital budget for next year, the firm will sell $50 million of 11 percent bonds at par value (assume no flotation costs). The firm will finance the rest of its $125 million in capital expenditures with retained earnings. Next year, Alpha expects net income to grow 7 percent to $140 million, and dividends also are expected to increase 7 percent to $1.40 per share and to continue growing at that rate for the foreseeable future. The current market value of Alpha's common stock is $30 per share. If the firm has a marginal tax rate of 40 percent, what is its weighted cost of capital for next year

Answer 1

The weighted cost of capital for next year can be calculated using the formula: WACC = (E/V) * Ke + (D/V) * Kd * (1 - T).

Step-by-step explanation:

The weighted cost of capital for next year can be calculated using the formula: WACC = (E/V) * Ke + (D/V) * Kd * (1 - T)

Where:

WACC = weighted average cost of capital

E = market value of equity

V = total market value of equity and debt

Ke = cost of equity

D = market value of debt

Kd = cost of debt

T = tax rate

In this case, we need to determine the cost of equity and the cost of debt. The cost of equity can be calculated using the dividend growth model: Ke = (D1 / P0) + g

Where:

D1 = expected dividend per share

P0 = current market price per share

g = expected growth rate of dividends

The cost of debt can be calculated using the yield to maturity on the bonds. Since the bonds are sold at par value, the yield to maturity is equal to the coupon rate of 11%.

After calculating the cost of equity and the cost of debt, we can substitute these values into the WACC formula to find the weighted cost of capital for next year.

Answer 2

To calculate the weighted cost of capital, we need to determine the cost of debt, cost of equity, and the weights of each component. The cost of debt is 6.6% and the cost of equity is 3.73%. The weighted cost of capital for next year is 3.4345%.

Step-by-step explanation:

Weighted Cost of Capital Calculation:

To calculate the weighted cost of capital, we need to determine the cost of debt, cost of equity, and the weights of each component. In this case, the firm's capital structure consists of 40% debt and 60% common equity.

The cost of debt is the yield on the bonds, which is 11%. Since the interest expense is tax deductible, we need to adjust for taxes by multiplying the yield by (1 - tax rate). So the after-tax cost of debt is 11% * (1 - 0.40) = 6.6%.

The cost of equity can be calculated using the dividend growth model. The firm's expected growth rate is 7%, and the dividend per share is $1.40. The current market value per share is $30. Using these values, we can calculate the cost of equity to be 7% / ($30 / $1.40) = 3.73%.

Next, we calculate the weights of debt and equity by multiplying the respective percentages by the capital budget. The weight of debt is 40% * $50 million = $20 million, and the weight of equity is 60% * ($125 million - $50 million) = $45 million.

Finally, we can calculate the weighted cost of capital by multiplying the cost of debt by the weight of debt, and the cost of equity by the weight of equity. Adding these two values together gives us the weighted cost of capital for next year.

Calculation:

Weighted Cost of Capital = (6.6% * $20 million + 3.73% * $45 million) / ($20 million + $45 million)

Weighted Cost of Capital = 1.32% + 2.1145% = 3.4345%