The Granite Paving Co. wants to be levered at a debt equity ratio of 1.5. The before-tax cost of debt is 11% and the cost of equity for an all equity firm is 14%. What will be the firm's cost of levered equity? (Assume a tax rate of 33%.)

Question

Quizplus · Accepted Answer

First, we need to calculate the proportion of debt and equity in the firm based on the desired debt equity ratio of 1.5:

Debt/Equity = 1.5 = Debt / (Total assets - Debt)
1.5 = Debt / (1 - Equity)
1.5(1 - Equity) = Debt
Debt = 1.5 - 1.5Equity

Next, we can use the weighted average cost of capital (WACC) formula to calculate the cost of levered equity:

WACC = (E/V) x Re + (D/V) x Rd x (1 - T)

Where:
E = market value of equity
D = market value of debt
V = total value of the firm
Re = cost of equity
Rd = cost of debt
T = tax rate

Since the firm is currently all equity, the market value of equity is equal to the total value of the firm. Therefore:

V = E + D
E = V - D
E = 1(1.5 - 1.5Equity) = 1.5 - 1.5Equity

Next, we can plug in the values:

WACC = [(1.5 - 1.5Equity) / 1.5] x 0.14 + [1.5Equity / 1.5] x 0.11 x (1 - 0.33)
WACC = (1 - Equity) x 0.14 + 0.0777(2Equity)
WACC = 0.14 - 0.06215Equity + 0.0777(2Equity)
WACC = 0.29525Equity + 0.14

To find the cost of levered equity, we need to solve for the value of Equity that gives us the WACC that matches the desired debt equity ratio:

0.29525Equity + 0.14 = 0.15
0.29525Equity = 0.15 - 0.14
Equity = 0.036 / 0.29525
Equity = 0.122
Debt = 1.5 - 1.5(0.122) = 1.269

Now that we have the proportion of debt and equity in the firm, we can calculate the cost of levered equity:

Re(L) = Re + (Re - Rd)(D/E)(1 - T)
Re(L) = 0.14 + (0.14 - 0.11)(1.269 / 0.122) (1 - 0.33)
Re(L) = 0.17

Therefore, the firm's cost of levered equity is 17%.