Question

Incentive Structure (25 pt)

On 1/1/2019, Firm XYZ signs a debt contract. According to the debt contract, Firm XYZ raises $100,000 from an investor and promises to pay the investor $100,000 on 1/1/2020 (i.e., the interest rate is zero). On 1/2/2019, Firm XYZ finds that there are two investment opportunities, and each project costs the firm $100,000:

Project 1: $400,000 with probability 0.4 and $0 with probability 0.6

Project 2: $200,000 with probability 1.

i) Which project exhibits a higher NPV? (4 pt)

ii) Which project does the firm prefer? (7 pt) Firm prefers project 1 because

iii) How about debtholders? (7 pt) Debtholders would prefer project 2 because

iv) Suppose that, on 1/1/2019, the investor knows that the firm will choose a project between project 1 and 2. Would the investor choose to sign the debt contract? (7 pt)

Answer 1

i) NPV in probability weighted terms is higher for project 2 as calculate below:-

Project 1 = $400,000 * 0.4 + $ 0 * 0.6 = $160,000

Project 2 = $200,000 * 1 = $200,000

However, in an absolute terms, Project 1 offer higher NPV of $400,000 compared to the Project 2 which has an NPV of $200,000.

ii) Firm would prefer Project 1 because even though the probability of getting $400,000 is 40%, the firm would still gain a considerable $300,000 gain if this situation plays out favourably. And since they are using the money of debholders, the firm would take risk and go for project 1.

iii) Debtholders would prefer Project 2 because they stand nothing to gain even by taking the additional risk involved in Project 1 (60% chance of loss of $100,000) because they would only get their money back after 1 year to the tune of $100,000. Hence, they would prefer the safe alternative which is Project 2 which would return $200,000 with a 100% probability which ensures that repayment of bonds would be made when due.

iv) If the investor already knows about the upcoming choice that firm would have to make, then it is most likely that the investor would not give money to the firm as he would fear for the loss of his capital as one option has 60% chance of full loss of capital. Hence, the investor would probably just choose to hang on to his money or look for better alternatives. It is to be noted that the debt does not earn any interest, which will also be factored in this decision.

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