Question

Consider a $400 million pass-through MBS that has just been created (so the 'seasoning' of the pass-through is equal to 0). The underlying pool of mortgages each has a maturity of 20 years and an annual mortgage coupon rate of 6%. The pass-through rate of the mortgage pool is 5% and the total number of prepayments if the rate of prepayments increases to 200 PSA is 268.15.

Suppose we construct principal-only (PO) and interest-only (IO) mortgage-backed securities (MBS) using the mortgage pass-through of the above question. Assume a prepayment multiplier of 100 PSA. What is the present value of the PO MBS if we use an annual risk-free rate of 4.5% to value the cash-flows?

Answer 1

As per the Given Information we need to calcukate the Present value of the PO MBS with the assumtion of the 4.5% Risk-Free Return.

Given,

Future Value = $400 Million

Maturity (n No. of Years) = 20 Years.

Risk Free rate = 4.5%

Present Value = ?

The Calculation can be done by the Following formula.

Present Value = Future Value / (1+r)^n

Here,

Future Value = $400 Million

R (Risk free rate) = 4.5

N (number of Years) = 20

Hence,

Present value = $400/(1+4.5%)^20

.: Present Value = $165.86.