Question

Suppose an investor with a 7-year investment horizon is considering the purchase of a 4.50% APR, monthly payment, mortgage with 22 years (264 months) remaining until maturity. The mortgage currently has an outstanding balance of $245,000 and is selling to offer a YTM of 4.8% on the secondary market. The investor expects to be able to reinvest the first 36 monthly cashflows at 4.8% (over their entire reinvestment interval), but expects to be able to reinvest the last 48 monthly payments at only 4.5%. At the end of her investment horizon, she expects to be able to sell the mortgage at a YTM of 4.5%. What is the total/expected (effective) return offered by this security?

Answer 1

Let us first calculate the payment per month the investor will get. With the given information the APR mortgage is selling at 4.8% annualized rate. Converting it to monthly rate we get = 0.4%. Now use the formula given below for calculating present value of an annuity. Here the formula gives the present value of all future payment received discounted at YTM of 0.4 per month. Pluggin in the values, where

P= payment per month

r= rate per month

n=number of months

P x [ ( 1- (1+0.004) ^-264 ) / 0.004 ]

this equation equals the present value of the mortgage i.e. $245,000. So equalling the above equation to $245,000 and solving for P we get

P = $1,504.40085

Now,

Summing all the reinvested values we get $149,360.8

and we will sell the securities after 84 months at