Question
Here are Multi-Universals Project Payoffs on a $100m. investment: Cash Flow if State of the Economy is Good Bad Probability of Good Expected Value Project
Here are Multi-Universals Project Payoffs on a $100m. investment:
| Cash Flow if State of the Economy is |
|
| |
| Good | Bad | Probability of Good | Expected Value |
Project A | $130 million | $50 million | 0.8 | $114 million |
Project B | $150 million | $50 million | 0.2 | $70 million |
Assume that investors are risk neutral and that the risk-free required rate of return is zero. Suppose bondholders assume that the firm will choose Project A. Then the stated interest rate will be 12.5% because at this stated rate, the expected return to bondholders will be exactly 0%, which is the equilibrium risk-free required rate of return. This can be seen from the table below:
Project A | Payoff to project | Payoff to bondholders | Payoff to equityholders |
Good State (p=0.8) | 130 | 112.5 | 17.5 |
Bad State (p=0.2) | 50 | 50 | 0 |
Expected Payoff | 114 | 100 | 14 |
However, if bondholders make this assumption and require a stated rate of interest of only 12%, stockholders have an incentive to choose project B. This can be seen by comparing the above payoff matrix with the following payoff matrix detailing payoffs from project B:
Project B | Payoff to project | Payoff to bondholders | Payoff to equityholders |
Good State (p=0.2) | 150 | 112.5 | 37.5 |
Bad State (p=0.8) | 50 | 50 | 0 |
Expected Payoff | 70 | 62.5 | 7.5 |
Complete the payoff matrix from the Credit Rationing Problem with a 0% risk-free required rate of return for the case where the bondholders assume project B will be chosen. In particular, answer the question as to which project equity holders will choose under this assumption.
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