Question

A CMO has been issued with 3 tranches and a residual (the residual owns no principal at origination). At origination (same set-up at previous question): - Tranche A investors own $6,000,000 of principal with a coupon rate of 3.50%. - Tranche B investors own $4,000,000 of principal with a coupon rate of 3.70%. - Tranche Z investors own $2,000,000 of principal with a coupon rate of 4.50%. The residual carries no principal and receives remaining payments. At origination, the mortgages backing the security issued are FRM with mortgage rate of 4.50% with 30 year maturities and MONTHLY payments. Assume no servicing/guarantee fee and no prepayments. Remember to adjust rates to monthly if necessary. Round your answers to cents. In month 1, what is the mortgage pool's scheduled interest?

Answer 1

Tranche A = $6,000,000

Tranche B = $4,000,000

Tranche Z = $2,000,000

Total = $12,000,000

Mortgage

Interest rate = 4.5%

Tenure = 30 years

Monthly payment =

using Excel function = pmt(rate,nper,pv) where rate = 4.5%/12 (since its monthly); nper = 30* 12 months = 360 months (since monthly) and pv = $12,000,000 = pmt(4.5%/12,360,-$12,000,000) = $60,802.24

Using formula = PV*rate*(1+rate)^nper/(((1+rate)^nper)-1)

=($12,000,000*4.5%/12*(1+(4.5%/12))^360)/(((1+(4.5%/12))^360)-1) = $60,802.24

First month payment = $60,802.24 broken as interest = $12,000,000*4.5%/12 = $45,000 and principal = $60,802.24-$45,000 = $15,802.24