Question

Cadillac wishes to finance the construction of a new automobile that will replace its current Escalade model. Its parent company, General Motors, has a debt-to-equity ratio of 2.7 and a stock-market beta of 1.3. The market risk premium is 10% and the risk-free rate is 3%. Suppose that Cadillac funds its project only with equity. What is its cost of capital, if it uses General Motors as a benchmark? Assume, for convenience, that General Motos’ debt is risk-free. Please show work, thank you!

Answer 1

Debt to equity ratio			2.7
It means Debt = 2.7, Equity = 1 , total = 3.7
So, weight of Debt =			2.7/3.7
Weight of equity =			1/3.7
Beta of Assets of General motors = (Beta of equity * Weight of Equity) + (Beta of debt * Weight of debt)
	( 1.3 * 1/3.7) + (0 * 2.7/3.7)
	0.351351
Beta of Asset of General Motors is 0.351351. Cadillac uses General motors as Benchmark
So, Beta of Asset of Cadillac is also 0.351351
Cadillac has only equity. So Beta of assets of cadillac shall also be 0.351351.
Cost of capital formula = Risk free rate of return + Beta of assets * Market risk premium
	3 + (0.351351 * 10)
	6.513514	or 6.51%

So, cost of capital of cadillac is 6.51%.