Question

Shadow Corp. has no debt but can borrow at 6.3 percent. The firm’s WACC is currently 8.1 percent, and the tax rate is 35 percent.

a. What is the firm’s cost of equity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Cost of equity            %

b. If the firm converts to 30 percent debt, what will its cost of equity be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Cost of equity            %

c. If the firm converts to 50 percent debt, what will its cost of equity be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Cost of equity            %

d-1 If the firm converts to 30 percent debt, what will the company's WACC be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

WACC            %

d-2 If the firm converts to 50 percent debt, what will the company's WACC be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

WACC            %

Answer 1

WACC = (w(d) * k(d) * (1 - tax rate)) + (w(e) * k(e))

where,

w(d) and w(e) = weight of debt and equity

k(d) and k(e) = cost of debt and equity

a. Cost of equity when no debt

Since the firm has no debt, equity is its sole means of financing and therefore, WACC shall be the k(e) = 8.1%

b. k(e) with 30% debt

Assumption for ques b: WACC remains constant

WACC = (w(d) * k(d) * (1 - tax rate)) + (w(e) * k(e))

where,

WACC = 8.1%

w(d) = 30%

w(e) = 1 - 30% = 70%

k(d) = 6.3%

Tax rate = 35%

Therefore,

0.081 = (0.3 * 0.063 * (1 - 0.35)) + (0.7 * k(e))

0.081 = 0.0123 + (0.7 * k(e))

k(e) = (0.081 - 0.0123) / 0.7

k(e) = 0.0982 = 9.82%

c. k(e) with 50% debt

Assumption for ques c: WACC remains constant

WACC = (w(d) * k(d) * (1 - tax rate)) + (w(e) * k(e))

where,

WACC = 8.1%

w(d) = 50%

w(e) = 1 - 50% = 50%

k(d) = 6.3%

Tax rate = 35%

Therefore,

0.081 = (0.5 * 0.063 * (1 - 0.35)) + (0.5 * k(e))

0.081 = 0.0205 + (0.5 * k(e))

k(e) = (0.081 - 0.0205) / 0.5

k(e) = 0.1211 = 12.11%

d-1. WACC when debt is 30%

Assumption for ques d-1: Cost of equity (k(e)) is kept constant at 0 debt levels = 8.1%

WACC = (w(d) * k(d) * (1 - tax rate)) + (w(e) * k(e))

where,

w(d) = 30%

w(e) = 1 - 30% = 70%

k(d) = 6.3%

k(e) = 8.1%

Tax rate = 35%

Therefore,

WACC = (0.3 * 0.063 * (1 - 0.35)) + (0.7 * 0.081)

WACC = 0.0123 + 0.0567

WACC = 0.069 = 6.9%

d-2. WACC when debt is 50%

Assumption for ques d-2: Cost of equity (k(e)) is kept constant at 0 debt levels = 8.1%

WACC = (w(d) * k(d) * (1 - tax rate)) + (w(e) * k(e))

where,

w(d) = 50%

w(e) = 1 - 50% = 50%

k(d) = 6.3%

k(e) = 8.1%

Tax rate = 35%

Therefore,

WACC = (0.5 * 0.063 * (1 - 0.35)) + (0.5 * 0.081)

WACC = 0.0205 + 0.0405

WACC = 0.061 = 6.1%