Question

Homework #4 Cost of Capital 2. Vo = So + Bo, where V. is the firm value in period 0, S, is the stockholder's equity in period 0, and B, is the value of the firm's debt in period 0. The same notations apply to the firm value in period 1, V1, and the firm's equity, S1, and debt, B1 A. (5 points) Vo = $100, V1 = $110, what is the rate of return for the firm from period 0 to period 1? B. (5) Bo = $15, B1 = $17, what is the rate of return for the debt? C. (10) What is the equity's value in period 0 and period 1, S, and Sy? D. (10) What is the rate of return for the equity? E. (20) Please use this example to verify that the rate of return for the firm is a weighted average of the returns on its equity and its debt: Rp = Rs (Equity Ratio) + RB (Debt Ratio).

Answer 1

A. Rate of return for the firm = (V1-V0)/V0

=(110-100)/100 =10%

B. Rate of Return for the debt = (B1-B0)/B0

=(17-15)/15 =13.33%

C. S0 = V0- B0 = 100-15 =85

S1= V1- B1 = 110-17 = 93

D. Rate of return for equity = (S1-S0)/S0

= (93-85)/85 =9.412%

E. Return for the firm =10%

Return for the firm on weighted average basis

= [(1/3)×13.33]+[(2/3)×9.412] =10% (Rounded off)