Question

You are trying to estimate the enterprise value of Firm X. Since this firm is private, you cannot directly estimate the firm’s cost of equity using its stock data. Fortunately, there is a similar firm, Firm Y, which is in the same industry with comparable operating risk characteristics. Assume that the CAPM holds. The risk-free rate is 2% and the market risk premium is 5%.

QUESTION 1

Firm Y has a debt-to-equity ratio of 3 and it plans to keep this ratio fixed. Firm Y’s equity beta is 6.6 and debt beta is 0.2. What is Firm Y’s unlevered equity beta?

	A.	8.6
	B.	0.3
	C.	0.1
	D.	1.8

QUESTION 2

What is Firm X’s unlevered equity beta?

	A.	1.8
	B.	8.6
	C.	0.1
	D.	0.3

QUESTION 3

Assume that Firm X’s cost of debt is 2.5%. What is Firm X’s debt beta?

	A.	1.8
	B.	0.3
	C.	0.1
	D.	8.6

Answer 1

1) Asset Beta/ Unlevered equity beta, is the actual beta of the industry. Beta is the systematic risk of the stock to the market. As a given company under the same industry faces similar systematic risk Beta of all the companies in the industry will be same. Such beta is the asset beta / unlevered equity beta. Unlevered beta tries to eliminate the fluctuation in the beta due to various capital structure. Hence unlevered beta does not change with the change in capital structure.

Unlevered Equity Beta = {Equity Levered Equity * Equity + Debt Beta * Debt (1- Tax)} / (Equity + Debt (1-Tax)

Firm Y

Debt / Equity = 3/1

Hence Total Capital = 4, equity =1, debt = 3

Unlevered Equity Beta = (6.6 * 1+ 0.2* 3) / (3+1)

= (6.6 + 0.6) / 4 = 1.8

Correct option D

2) As firm X is in the same industry as Firm Y, Asset beta/ Unlevered Equity beta will be the same for all the companies in the same industry, i.e 1.8

Correct option A

3) We use the CAPM approach to find the beta of the debt

As per CAPM, Cost = Risk Free + Market Risk Premium * Beta

2.5 = 2 + 5 * Beta

Hence beta = 0.5 / 5 = 0.1

Correct option C