The Home Loan Corp, Inc (HLC) originates a pool containing 100 five year mortgages, with an average balance of $150,000 each. All mortgages in the pool carry a fixed interest rate of 6%. HLC now wishes to sell the pool of mortgages to the FHLMC. Assuming prepayments are constant at 10%, what is the price of the pool of mortgages if the FHLMC wishes to obtain a rate of return equal to 7%?

Fin problem – the home loan corp, inc (hlc)

In order to calculate the price of the pool of mortgages, we need to first calculate its present value. The total balance of the mortgages is $15 million ($150,000 x 100), and assuming a constant rate of prepayment at 10% per annum, this would mean that an average principal amount of $1.5 million would be repaid each year ($15 million x 0.10). Given that the FHLMC wishes to obtain a return rate equal to 7%, then the price for this mortgage pool can be calculated using the formula: PV = PMT*(((1+r)^n-1)/(r*(1+r)^n)), where PV is the present value, PMT is the annual payment (in this case $1.5 million), r is the required interest rate (7%) and n is number of years (5). This calculation results in a present value for HLC’s mortgage pool equal to $11.09 million.