# Solved Question: A firm is to choose between two mutually exclusive projects

## Description

Question:

A firm is to choose between two mutually exclusive projects. Suppose there are two possible states in the future: one is economy boom with a probability of 40% and the other is economy recession with a probability of 60%. If the payoff schedule of these two projects is the following:

A) Suppose you own this firm, and you finance this firm all with your own money, which project will you undertake? Please state the expected payoff of each project. (hint: you want to maximize the expected value of this project)

B) Suppose you still own this firm. But you finance your firm with \$100 debt. If you want to maximize the payoff to you (not to both you and the debt holder), which project will you undertake? Please state the expected payoff of each project to you.

C) What problem of debt contract is shown by the above example?

A) We need to look each project individually and each project is mutually exclusive

Probability of economic boom = 40%

Probability of economic recession = 60%

Project A Returns

Boom \$200

Recession \$100

Expected payoff for Project A = $Return_{boom}*Probability_{boom} + Return_{recession}*Probability_{recession}$

= 200*0.4 +100*0.6

= \$140

Project B   Returns

Boom \$220

Recession \$50

Expected payoff for Project B = $Return_{boom}*Probability_{boom} + Return_{recession}*Probability_{recession}$

= 220*0.4 +50*0.6

= \$118

B) So in second case when you plan to raise debt of \$100, you will choose project B as because although its expected value is less but that a probability average in real scenario either there will be boom or recession and as such when you have less stake in capital your risk tacking capability will increase and we will go with project B as in case of a boom you will get \$220 compared to \$200 in project A. Which increase your payoff. If the objective was to maximize your payoff along with debt holder then the payoff will remain same as in answer A and rationally user will go with project A

C) This can be seen as Agency issue or Agency problem which is when one party is expected to act in the best interest of other which conflicts this own best interest. Basically, here in such a contract debt holder are not protected.

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