Question

Boxcars, Inc. has a capital structure consisting of $100MM in equity and $150MM in debt. With this capital structure, the expected return to its equity is 18 percent, the expected return to its debt is 7 percent, and the market beta of Boxcars enterprise value is 1.68. The risk-free rate is 3 percent. The firm unexpectedly issues $110MM in new shares, using the cash to repurchase $110MM of its debt. After the repurchase, the remaining $40MM in debt is risk-free because there is no chance the firm will default on the debt.

What is the expected return to Boxcars’s equity after the change in capital structure?

Answer 1

Expected return to Boxcars’s equity (X) after the change in capital structure is 13%.

Solution given below.

Old capital structure:

Equity : $100 (40%)

Debt : $150 (60%)

Total : $250

Return to its equity is 18% and return to its debt is 7%.

So, overall return to capital is 0.4(18%)+0.6(7%) = 7.2%+4.2%=11.4%

After unexpected issue of $110

New capital structure:

Equity : $210 (84%)

Debt : $40 (16%)

Total : $250

Expected return to Boxcars’s equity (X) after the change in capital structure is calculated assuming overall return to capital is unchanged. Hence i.e, 11.4%.

and after the repurchase, the remaining $40 in debt is risk-free 3% because there is no chance the firm will default on the debt.

11.4% = 0.84(X%)+0.16(3%) -----> find X

11.4%= .84(X%)+0.48%

X = (11.4%-0.48%)/0.84

X= 13%

Therefore Expected return to Boxcars’s equity (X) after the change in capital structure is 13%.