The question below was given in class and I have doubts about the use of the word "fair value". THe provided solution is to have Bank B make an overall return on the mortgage of 12%, but I don't agree with this and I feel the question is incomplete and the "fair value" can be computed only with a risk-free rate. The question is provided below
￼You are looking to finance your first home purchase. The price of your dream home is $250,000.You have $25,000 cash but need to finance the rest. Bank A has offered to loan you the rest of the value at 12% per annum compounded monthly for 5 years. On the other hand, bank B has offered you a deal for 40% of the initial loan, amortized at 6% per annum compounded monthly over 2.5 years, after which, they would set your monthly payments to amount X for the remaining 2.5 years to pay off the rest of the loan. What would be a ‘fair’ amount that bank B should charge for X? As a consultant to bank B, would you recommend an amount great or less than X – why?
It would be awesome if someone could show their calculations, but mostly I want to know which interpretation of "fair value" they agree with. If mine (hopefully), how I would go about best arguing it in a logical manner.