Question

The Goodtread Rubber Company has the following two divisions.

1. (i) Tire Division -- which manufactures tires for new autos

2. (ii) Recap Division -- which manufactures recapping materials that are sold to independent recapping shops.

Since auto manufacturing moves up and down with the general economy, the Tire Division's earnings contribution to Goodtread's stock price is highly correlated with the returns on most other stocks. If the Tire Division was operated as a separate company the beta of its assets would be 1.90. The sales and earnings of the Recap Division, on the other hand, are not as cyclical since recap sales are high when people cannot afford to buy new tires. The beta of Recap's assets is 0.60. Approximately 70% of Goodtread's corporate assets are in the Tire Division and 30% in the Recap Division. Goodtread has a debt/equity ratio of 0.5. Its debt is risk free. Currently, the risk free rate is 5% and the expected return on the market portfolio is 12%. There are no taxes and the assumptions of the CAPM are satisfied.

1. (a) What is the required rate of return on Goodtread's stock?

2. (b) What discount rate should Goodtread use to evaluate capital budgeting projects? Explain your answer.

Answer 1

Part (i)

Goodtread's beta will be = 70% x tire division beta + 30% x recap division beta = 70% x 1.9 + 30% x 0.6 = 1.51

the required rate of return on Goodtread's stock = Ke = Rf + beta x (Rm - Rf) = 5% + 1.51 x (12% - 5%) = 15.57%

Part (ii)

D/E = 0.5; hence Wd = D / (D + E) = 0.5 / (1 + 0.5) = 1/3; We = 1 - Wd = 1 - 1/3 = 2/3; Kd = 5%; Ke = 15.57%

Hence,  discount rate should Goodtread use to evaluate capital budgeting projects = WACC = Wd x Kd + We x Ke = 1/3 x 5% + 2/3 x 15.57% = 12.05%

The correct discount rate should be the blended WACC which takes into account the capital structure, and component cost of individual sources of finance.