Question

A bank uses its mortgage loans of $600 million as collateral to issue two different trenches of securities (CMOs) in mortgage markets, Trench A and Trench B. The information is given below. Assume the coupon payment is made annually.

Loan value: $600 million

Interest rate: 6.5%

Maturity: 10 years

CMOs:                          Par value                       Interest rate

Trench A                       $350 million                   4.5%

Trench B                       $250 million                   6.25%

1. Please estimate the profits from the CMO.
2. The bank would like to make a profit of $20 million from the CMO by adjusting the interest rate for Trench B. Please estimate what should be the new interest rate.

Answer 1

a. First we must calculate the profit made from the mortgage loans, assuming the ordinary, that the mortgage payments are made monthly with a component of principal and interest.

First we will use the EMI formula for calculating the monthly EMI for the total mortgage

EMI = [P x R x (1+R)^N]/[(1+R)^N-1] = $ 6,812,878

total payment = 6812878*12*10 = $817,545,360

earnings from mortgage loan = 817545360 - 600000000 = $217,545,360

coupon paid to Trench A(paid annually) = 350 *.045 *10 = $157.5 milion

coupon paid to Trench B(paid annually) = 250 * .0625 *10 = $156.25 million

total coupon paid = $313.75 million

Therefore, profit made from CMO = $217545360- $313.75 million = $(-96,204,640)

b. in order to make a profit of $20 million the total coupon paid to CMO holders must be = $217545360 - $20 M = $197545360

this has to be adjusted to the interest rate of trench B.

therefore total coupon paid on trench B must be $197,545,360 - 157.5 M(the coupon for trench A) = $40045360

substituting the value in the following equation

40045360= 250000000 *10 *R/100

we get

R= 1.60%

Therefore the new interest rate must be 1.6% for trench B.