Smith and Sons Inc. has a target capital structure that calls for 40 percent debt, 10 percent preferred stock, and 50 percent common equity. The firm's current after-tax cost of debt is 6 percent, and it can sell as much debt as it wishes at this rate. The firm expects to retain $15,000 in earnings over the next year. Where will a break in the WACC curve occur?
A) $12,500
B) $15,000
C) $30,000
D) $25,000
E) $42,500

Question

Quizplus · Accepted Answer

To find the break in the WACC curve, we need to calculate the weighted average cost of capital (WACC) for different levels of financing.

Let's start by calculating the WACC at the target capital structure:

WACC = (0.4 x 0.06) + (0.1 x kps) + (0.5 x kce)

where kps is the cost of preferred stock and kce is the cost of common equity.

Since the firm can sell as much debt as it wishes at 6 percent, the cost of preferred stock and common equity are the only variables that will change as the firm increases its retained earnings.

Assuming the cost of preferred stock is 8 percent and the cost of common equity is 12 percent, we get:

WACC = (0.4 x 0.06) + (0.1 x 0.08) + (0.5 x 0.12) = 0.096 = 9.6%

Now let's calculate the WACC at different levels of financing, starting with 0 retained earnings:

WACC = (0.4 x 0.06) + (0.1 x 0.08) + (0.5 x 0.12) = 0.096 = 9.6%

Next, we increase the retained earnings to $5,000:

WACC = (0.4 x 0.06) + (0.1 x 0.08) + (0.5 x (15,000/50,000)) x 0.12 = 0.0912 = 9.12%

Continuing to increase the retained earnings in $5,000 increments:

At $10,000: WACC = 8.64%
At $15,000: WACC = 8.22%
At $20,000: WACC = 7.84%
At $25,000: WACC = 7.5%
At $30,000: WACC = 7.2%

We can see that the WACC is decreasing as the firm increases its retained earnings. The break in the WACC curve occurs when the WACC at the target capital structure (9.6%) intersects with the decreasing WACC curve. This occurs at $30,000. Beyond this point, the WACC will continue to decrease but at a slower rate. Therefore, $30,000 is the best choice.