Question

A firm has a debt-to-equity ratio of 1/4. The WACC is 18.6%, and the pretax cost of debt is 9.4%. What is the cost of common equity if the tax rate is 21%?

Answer 1

The cost of common equity is 20.9%.

Step-by-step explanation:

The cost of common equity can be calculated using the WACC formula:

WACC = (Weight of Debt x Cost of Debt) + (Weight of Equity x Cost of Equity)

Given that the debt-to-equity ratio is 1/4, the weight of debt would be 1/5 (1 divided by 1 + 4) and the weight of equity would be 4/5 (4 divided by 1 + 4).

Let's assume the cost of common equity is x. Plugging in the values:

0.186 = (1/5 x 0.094) + (4/5 x x)

Simplifying the equation:

0.186 = 0.0188 + 0.8x

0.8x = 0.186 - 0.0188

0.8x = 0.1672

x = 0.209

Therefore, the cost of common equity is 20.9%.

Answer 2

The cost of common equity is 22.32%.

Step-by-step explanation:

This can be calculated using the weighted average cost of capital (WACC) formula as follows:

WACC = (WS * CE) + (WD * CD * (1 - T)) ……………… (1)

Where;

WACC = Weighted average cost of capital = 18.6%, or 0.186

WS = Weight of Market value of common shares outstanding = 1 - WD = 1 - 0.25 = 0.75

WD = Weight of debt = Debt-to-equity ratio = 1/4 = 0.25

CE = cost of common equity = ?

CD = Pretax cost of debt = 9.4%, or 0.094

T = Tax rate = 21%, or 0.21

Substituting the values into equation (1) and solve for CE, we have:

0.186 = (0.75 * CE) + (0.25 * 0.094 * (1 - 0.21))

0.186 = (0.75 * CE) + 0.018565

0.75 * CE = 0.186 - 0.018565

0.75 * CE = 0.167435

CE = 0.167435 / 0.75

CE = 0.223246666666667, or 22.3246666666667%

Rounding to two decimal places, we have:

CE = 22.32%

Therefore, the cost of common equity is 22.32%.