You are considering making a loan for $100,000 at an interest rate of 5%. The loan can either
(a) be prepaid immediately, in which case you receive back your $100,000 at zero profit
or
(b) be repaid in one period at interest rate 5% (a repayment of $105,000 in one year).
You do not know the right rate to discount cashflows, but will learn that appropriate discount rate at the moment after loan closing. There is a 50% chance your discount rate will be .03 and a 50% chance your discount rate will be .07. (thus repayment a year from now would be worth $105,000/1.03 with 50% probability and $105,000/1.07 with the remaining 50% probability).
Suppose that there is a 25% chance that the borrower will repay the loan immediately regardless of what you learn about discounting.
Of the remaining 75% of borrowers, none will prepay immediately should your discount rate be 7%. But if your discount rate is 3%, 25% of remaining borrowers will be "woodheads" and only repay next year. The remaining 75% will prepay immediately.
In other words, 25% of borrowers prepay randomly, and 25%*75% are woodheads, and 75%*75% are rational prepayers.
What is the expected value (Net of the initial $100,000, so expected profitability) to you of this loan before uncerainty is revealed?In the question above, the value of the loan to you would rise if the proportion of woodheads also rose. True or false？