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's cost of preferred stock is 11 percent and its cost of retained earnings is 14 percent. The firm expects to generate $15,000 in retained earnings this year. Compute the weighted average cost of capital (WACC) break point associated with issuing new common stock.

Question

Quizplus · Accepted Answer

To calculate the WACC break point, we need to find the amount of funds to be raised through the new common stock issue until the point where the weight of common equity in the capital structure remains the same. We can use the following formula to calculate the WACC break point:

WACC = (wd × kd) + (wp × kp) + (wc × ks)

where,
wd = weight of debt
kd = cost of debt
wp = weight of preferred stock
kp = cost of preferred stock
wc = weight of common equity
ks = cost of common equity

We know that:
wd = 0.4
kd = 6%
wp = 0.1
kp = 11%
wc = 0.5
ks = 14%

Now, let's assume that the firm plans to issue new common stock worth X dollars. We can use the following equation to find the WACC break point:

wc × ks = (1 − wd − wp) × V + X × ks

where,
V = total firm value
X = amount of funds to be raised through new common stock issue

We know that:
V = EBIT / ke
EBIT = $15,000 (given)
ke = 14%

Substituting the values, we get:

0.5 × 0.14 = (1 − 0.4 − 0.1) × [$15,000 / 0.14] + X × 0.14
0.07 = 0.5 × [$107,142.86] + 0.14X
X = ($17,500)

Therefore, the WACC break point associated with issuing new common stock is $30,000.