Question

A loan buyer in a secondary market believes that x % of the loans are high quality, and the rest are low quality The buyer values high quality loans at $100,000 and low quality at $75,000. Banks selling loans value high quality loans at $82,500 and value low quality at $55,500. If the buyer cannot observe the bond's type, then the maximum price the buyer will pay is equal to the seller's value of high quality loans when x is: a) 10% b) 15% c) 30% d) None of the above

Answer 1

Answer:

The correct option is c. 30%.

Explanation:

It is given that the expected value of the buyer is the same as the value of a seller selling high-quality bonds.

So, if the buyer believes that there are x% chances of being a bond of high quality then there must be a (1-x)% chance of being another bond of bad quality. Thus, from the given information it can be stated that-

x% * 100000 + (1 - x)% * 75000 = 82500

100000 x% + 75000 - 75000 x% = 82500

25000 x% = 7500

x = 30%