Question

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?
ii) Which project does the firm prefer? Firm prefers project 1 because
iii) How about debtholders? 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?

Answer 1

i) Which project exhibits a higher NPV?

project 2

ii) Which project does the firm prefer?

project 1 since it has the potential to earn $400,000 (resulting in an NPV of $300,000) and if things go wrong, they will not lose their money. When you gamble with someone else's money, you are willing to take higher risks.

iii) How about debtholders?

project 2 since it guarantees that the loan will be paid back

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?

This depends on what type of business Firm XYZ is. If it is a corporation, LLC or a LLP, then I doubt that the loan will be made because the firm's owners are not personally liable for the debt. If the firm is a sole proprietorship or a general partnership, then depending on the financial position of the owners, the loan can be made.

Step-by-step explanation:

since the discount rate is 0:

the NPV of project 1 = [($400,000 x 0.4) + $0] - $100,000 = $160,000 - $100,000 = $60,000

the NPV of project 2 = $200,000 - $100,000 = $100,000