Mr. Long runs a chain of outlet stores called Cheap Ware (CW). Currently CW uses

Question

Mr. Long runs a chain of outlet stores called Cheap Ware (CW). Currently CW uses only equity capital.
Mr. Long was approached by representatives from Lenders Inc. who have pointed out to him that his cost
of unlevered equity capital is 11% and the cost of debt capital is only 7%. The reps said his company
(which produces after-tax operating cash flows of $1.2 million per year) would benefit from using some
debt. They recommend that he issues $2 million worth of bonds and use the entire proceeds to repurchase
$2 million worth of its own stocks. Assume that both the firm’s cash flows and the debt are perpetual,
and Cheap Ware’s marginal corporate tax rate is 35%.
a) What is the current value of the firm without debt?
b) If Mr. Long follows Lenders Inc.’s plan, what will be the cost of equity capital, the after-tax WACC,
and the total value of the firm?
c) What would be the value of the firm under the proposal from Lenders if interest expenses were not
tax deductible? What would be the cost of equity capital in that case (i.e., what would be the cost of
equity if Mr. Long followed Lenders’ advice even though interest expenses were not tax deductible)?

Explanation / Answer

a)current value of the firm without debt

=after-tax operating cash flows/unlevered equity capital

=$1.2 million/.11

=$ 10.91 million

b)Value of Debt issued=D=$2 million

Value of Equity after Debt issued=E=$ 10.91 million-$2 million=$8.91 million

after-tax WACC=(D/D+E)*After tax cost of Debt+(E/D+E)*cost of equity capital

after-tax WACC=(2/10.91)*.07*(1-.35)+(8.91 /10.91)*.11=0.0982

after-tax WACC=9.82%

the total value of the firm

=after-tax operating cash flows/after-tax Wacc

=$1.2 million/0.0982

=$12.22 million

c) the value of the firm under the proposal from Lenders if interest expenses were not
tax deductible

WACC=(D/D+E)*cost of Debt+(E/D+E)*cost of equity capital

WACC=(2/10.91)*.07+(8.91 /10.91)*.11=0.1027=10.27%

the total value of the firm

=after-tax operating cash flows/Wacc

=$1.2 million/0.1027

=$ 11.69 million

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