3. Consider the case of Henrietta Ketchup, a budding entrepreneur with two possible investment projects that offer the following payoffs:
| Investment | Payoff | Probability of Payoff | |
| Project 1 | 20.4 | 25.5 | 1.0 |
| Project 2 | 20.4 | 40.8 | 0.6 |
| 0 | 0.4 |
Ms. Ketchup approaches her bank and asks to borrow the present value of $10 (she will fund the rest out of internal funds).
a. Calculate the expected payoffs to the bank and to Ms. Ketchup if the bank lends the present value of $10. Which project would Ms. Ketchup undertake?
a. Project 1 – 5.1 or 15.5 ; Project 2 – 4 or 18.48 .(Ms. Ketchup); Project 1 – 10 ; Project 2 – 6.(Bank) ; Ms. Ketchup would take Project 2 because there is a probability for a higher payoff.
b. Is this the same project that the bank would want Ms. Ketchup to undertake? Explain why or why not.
a. No the bank would choose project 1 because there is less risk involved and more probability that they can get their money back.
c. What is the maximum amount the bank could lend that would induce Ms. Ketchup to take the bank’s preferred project?
a. $15.30 or $2.54
d. If the bank was to lend the $10, but was acting strategically in its own interest, what interest rate would the bank require on its loan?
a. 1.96% or 25.4%