Question

Far West inc. manufactures telecommunication equipment and communication software. The equipment division is asking the finance department of Far West for an estimate of its cost of capital. Far West can borrow long term at 7%: its corporate tax rate is 1.05. The rate of interest on government bonds is currently 5.2%, and the market risk premium is 5%. The finance department has identified three single business companies with activities that are similar to those of the equipment division of the Far West inc. Their beta coefficient and debt to equity ratio are as follows: A B C

Equity beta	0.70	1.00	1.02
Debt to equity ratio beta	1.00	0.80	0.70

hOW WOULD IT ESTIMATE THE EQUIPMENT DIVISION'S WEIGHTED AVERAGE COST OF CAPITAL IF THAT DIVISIONS TARGET DEBT TO EQUITY RATIO IS 1.20

Answer 1

Formula
	Equity beta (Eb)	0.70	1.00	1.02
	Debt to equity ratio (D/E)	1.00	0.80	0.70
	Tax rate (T)	40%	40%	40%
Eb/(1 - (1-T)*D/E)	Asset beta (Ab)	1.75	1.92	1.76

Average asset beta = (1.75 + 1.92 + 1.76)/3 = 1.81

Using this asset beta for the equipment division, equity beta for the division is calculated as:

ke = asset beta*[1 - (1-T)*D/E] = 1.81*[1 - (1-40%)*1.20] = 0.51

Cost of equity ke for the division (using CAPM) = risk-free rate + (equity beta*market risk premium)

= 5.2% + (0.51*5%) = 7.73%

Cost of debt kd = 7%

D/E ratio for the division = 1.20

so D/V = (D/E)/(1+D/E) = 1.20/(1+1.20) = 1.20/2.20 =  0.55

E/V = 1- D/V = 1 - 0.55 = 0.45

WACC for the division = (D/V*(1-T)*kd) + (E/V*ke)

= (0.55*(1-40%)*7%) + (0.45*7.73%) = 5.81%