Goodtread Rubber Company has two divisions: the tire division, which manufacture

Question

Goodtread Rubber Company has two divisions: the tire division, which manufactures tires for new autos, and the recap division, which manufactures recapping materials that are sold to independent tire recapping shops throughout the United States. Since auto manufacturing fluctuates with the general economy, the tire division%u2019s earnings contribution to Goodtread%u2019s stockprice is highly correlated with returns on most other stocks. If the tire division were operated as a separate company, its beta coefficient would be about 1.50. The sales and profits of the recap division, on the other hand, tend to be countercyclical, because recap sales boom when people cannot afford to buy new tires. The recap division%u2019s beta is estimated to be 0.5. Approximately 75 percent of Goodtread%u2019s corporate assets are invested in the tire division and 25 percent are invested in the recap division. Currently, the rate of interest on Treasury securities is 9 percent, and the expected rate of return on an average share of stock is 13 percent. Goodtread uses only common equity capital, so it has no debt outstanding.

Required

a.            What is the new corporate beta?

b.            What is the required rate of return on Goodtread%u2019s stock?

c.             What is the cost of capital for projects in each division?

Explanation / Answer

this is a very easy quetion let me explain

a) corporate beta calculation

corporate beta will be = 75% * tire division beta + 25% * recap dvision beta

corporate beta will be =75% *1.5 + 25% *0.5

corporate beta =1.125 +0.125

corporate beta =1.25

B) required rate of return on stock

which can be calculated by capital asset pricing model

CAPM =risk free rate +beta (expected return on maket - risk free rate )

required rate on stock= 9 +1.25 (13-9)

required rate of return =14 %

C)

As company dont have any debt so cost of capital will also be same as required rate of return on stock

cost of capital for company =14 %

however to calculate for seperate division

this can be done by apply capm

for tire division

cost of capital =9 +1.5(13-9)

cost of capital = 16

for recap

cost of capital =9 +0.5(13-9)

cost of capital =9+2=11 %

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