You are considering an acquisition in one of two mutually exclusive investments,

Question

You are considering an acquisition in one of two mutually exclusive investments, either purchasing a company that manufactures locks and safes (SafeCo) or a company that manufactures fancy undergarments (Ris-Kay). Each costs $100 and is to be financed with debt; each has a 50-50 chance of good outcome or a bad outcome. For SafeCo, the good outcome is a payoff of 150 and the bad outcome is a payoff of 100. For Ris-Kay, the good outcome is a payoff of 160 and the bad outcome is payoff of 80. For simplicity, assume risk neutrality (risk doesn't bear expected return) and no discounting (all discount rates are zero). How much expected net present value does each investment add to the firm overall? Compute the equilibrium face value of the debt assuming the bondholders break even in expectation. First, compute this value assuming that SafeCo is selected, then re-compute it assuming that Ris-Kay is selected. What is the promised yield to maturity on the debt in each case in part (b)? Assume that the face value of the debt is actually 110. Which project do the shareholders prefer and why?

Explanation / Answer

a) The expected net present value for SafeCo=-100+.50*(150)+.50*(100)=$25

The expected net present value for Ris-Kay=-100+.50*(160)+.50*(80)=$20

b)The equilibrium face value=$.50*(150)+.50*(100)=$125 if SafeCo is selected.

The equilibrium face value=$.50*(160)+.50*(80)=$120 if Ris-Kay is selected.

c)promised yield to maturity=0% for SafeCo is selected.(at breakeven profit =0)

promised yield to maturity=0% for Ris-Kay is selected.

d)If face value is 110,$ yield on SafeCo=125-110=$15

$ yield on  Ris-Kay=120-110=$10

Thus SafeCo should be selected with a higher $ yield.

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