An unlevered firm U has its value at the end of the year depending on the states

Question

An unlevered firm U has its value at the end of the year depending on the states of the economy as follows:

Good = V = $1800 = 50% probability

Bad = $1200 = 50% probability

Risk Free rate = 5%

Market expected return E(Rm) = 10%

Unlevered equity beta, Bu = 1.5

Assume perfect capital markets and the CAPM holds.

a) What is the value of the firm today?

b) Suppose that there is a levered firm L that has the same cash flow as the firm U above. Firm L has a debt due in one year with the amount D = $1000. What is the expected stock return of Firm L?

c) What is the stock return volatility of Firm U and L?

d) Suppose you buy shares of Firm U, but want your investment to achieve the same expected return as that of Firm L stock. Explain in detail how to do that.

Explanation / Answer

b) Debt = $1000

     Equity = $1500 -$1000 = $500

    D/E ratio = 1000/500 = 2

Beta Levered = Beta Unlevered x (1+ (1-t)x D/E)

                        = 1.50 x (1+ (1-0)x 2)

                        = 4.50

Expected return on stock using CAPM = Rf + (ERm – Rf) x beta

                                                                           = 5% + ( 10%-5%) x 4.50

                                                                           = 27.50%

Part C

Stock return volatility is measured by Beta. For firm U, it is 1.50 and for the firm L, it would be 4.50.

Part D

I will use homemade arbitrage and sell the stocks in Firm U. I’ll further use the proceeds and invest in firm L.

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