Question

A firm has the choice of investing in one of two projects. Both projects last one year. Project 1 requires an investment of $11,000 and yields $11,000 with a probability of 0.5 and $13,000 with a probability of 0.5. Project 2 also requires an investment of $11,000 and yields $5,000 with a probability of 0.5 and $20,000 with a probability of 0.5. The firm is capable of raising $10,000 of the investment required through a bond issue carrying an annual interest rate of 10 percent.

a. Assuming that the investors are concerned only about expected returns, which project would stockholders prefer? Why?
b. Which project would bondholders prefer? Why?

Answer 1

Stockholders would prefer Project 1 because it has a higher expected return, while bondholders would prefer Project 1 because it is less risky.

Step-by-step explanation:

In this scenario, the firm is considering two investment projects, Project 1 and Project 2. a. Assuming that the investors are concerned only about expected returns, they would prefer the project with the higher expected return. To determine the expected return, we multiply each possible outcome by its probability and sum the results. For Project 1, the expected return is ((11000 * 0.5) + (13000 * 0.5)) - 11000 = $6000. For Project 2, the expected return is ((5000 * 0.5) + (20000 * 0.5)) - 11000 = $5000. Therefore, stockholders would prefer Project 1 because it has a higher expected return.

b. Bondholders, on the other hand, are concerned about receiving their principal and interest payments. They would prefer the project with the lower risk, assuming all else equal. Project 1 has a higher probability of achieving the expected return compared to Project 2, making it less risky for bondholders. Therefore, bondholders would prefer Project 1.

Answer 2

a. Assuming that the investors are concerned only about expected returns, stockholders would prefer Project 2. It yields more returns with the high risk variability attached to the better yield of $20,000.

b. Bondholders would prefer Project 1. It yields good returns with moderate risk variability. Bondholders are generally risk-averse. They avoid risk wherever possible.

Step-by-step explanation:

a) Data and Calculations:

Project 1 Project 2

Investment $11,000 $11,000

Expected Returns $12,000 $12,500

Bond issue = $10,000 with interest rate of 10%

Expected Returns for Project 1:

Yield Probability Expected Value

$11,000 0.5 $5,500

$13,000 0.5 $6,500

Total expected returns = $12,000

Expected Returns for Project 2:

Yield Probability Expected Value

$5,000 0.5 $2,500

$20,000 0.5 $10,000

Total expected returns $12,500