Question

Cunningham Inc. has a target debt-equity ratio of .41, its WACC is 9.6 percent, and the tax rate is 22 percent.

a. If the company's cost of equity is 12 percent, what is its pretax cost of debt?

b. If instead, you know that the aftertax cost of debt is 6.1 percent, what is the cost of equity?

Answer 1

Let the weight of equity be x

weight of debt = (1-x)

target debt-equity ratio = Debt / equity

0.41 = x(/1-x)

0.41 * (1-x) = x

0.41 - 0.41x = x

0.41 = x+ 0.41x

0.41 = 1.41x

x = 0.41 / 1.41

= 29.07801418%

Hence equity = 29.07801418%

Debt = 1-29.07801418%

= 70.92198582%

a. WACC = (Cost of debt * weight of debt) + (cost of equity*weight of equity)

9.6% = (Cost of debt *70.92198582%)+(12%*29.07801418%)

9.6% = Cost of debt *70.92198582% + 3.4893617016%

(9.6%-3.4893617016%)/70.92198582% = Cost of debt

Cost of debt = 8.616%

After tax cost of debt = Pre Tax Cost of debt * (1-tax rate)

8.616%/(1-22%) = Pre Tax Cost of debt

Pre Tax Cost of debt = 11.04615385%

= 11.05%

Answer = 11.05%

b.

WACC = (Cost of debt * weight of debt) + (cost of equity*weight of equity)

9.6% = (6.1% *70.92198582%)+(cost of equity *29.07801418%)

9.6% = 4.32624113502% + (cost of equity *29.07801418%)

9.6 % - 4.32624113502% = (cost of equity *29.07801418%)

5.2737588650%/29.07801418% = Cost of Equity

Cost of Equity = 18.14%

Answer = 18.14%