Value mortgages with partial interests

CFA General
#1

[This question is NOT related to the CFA exam]

Anybody knows how to value a mortgage when interest payments and principal repayments are different in frequency? For example capital repayment is monthly and interest payment is quarterly, I’m given the outstanding amount and need to figure out the payment amount each month / quarter.

Current value: 317,267

Maturity: 38 months from now

Coupon: 10%. paid quarterly

Principal: equal payment monthly

How do I calculate principal/interest payment each month? Also, what interest rate do I use to discount the CFs? Is it LIBOR? And if so what maturity?

Thanks!

#2

That’s interesting. So the total amount you pay every month is NOT constant, is it?

i.e. do you pay

option 1: $1000 (all principal) in month 1, $1000 (all P) in M2, $500 P + $500 interest in M3 OR

option 2: $1000 all P in M1 and M2, $1000 P + $500 I = $1500 in M3?

If option 2, then compute the monthly principal repayment: current value / #months = $317,267/38 = $8,349.13.

Coupon: 2.5% (10%/4) of V = the outstanding principal at the beginning of the quarter (or whatever rule they follow).

Assuming this loan was originally for a whole number of years, right now you have 2 months left in the quarter. V (beginning of quarter) = $317,267 + $8,349.13 = $325,616.13 and you will owe 2.5% of it = $8,140.40 in interest alone, at the end of the next two months.

For any month Mx, assuming today is M0, x = 1 to 38;

if x+2 is not dividible by 3 then you owr just the principal = $8,349.13.

If it is, then you owe $8,349.13 + I where

I = ($317,267 - x * $8,349.13) * 0.025.

I am sure you can make an Excel formula out of this.

#3

Thanks 1Recho! It’s option 2.

However I’m not sure if it’s interest based on the principal at the beginning of the quarter or of that month. Which one is common practice, do you know?

Also, what is the appropriate discount rate to discount the payments? Is it LIBOR of the same maturity, if the mortgage is assumed to be riskless?

However, I wonder if the mortgage is truly riskless and LIBOR was 3% let’s say. Then why would the bank choose a high coupon of 10%? I’d imagine they would choose a coupon such that the mortgage is at par, no?

Thanks!

#4
  1. If there was $1000 Principal outstanding at the beginning of M1, $900 P outstanding at the beginning of M2 and $800 P outstanding at the beginning of M3; the Interest payment at the end of M3 would be: [(1000*Stated Annual Rate/12)*((1+(Stated Annual Rate/12))^2)] + [(900*Stated Annual Rate/12)*((1+(Stated Annual Rate/12))^1)] + (800*Stated Annual Rate/12) 2. If its backed by Ginnie Mae use the Treasury YTM with the same maturity. If its backed by Freddie Mac or Fannie Mae I would use the YTM of Fannie Mae/Freddie Mac’s corporate bonds with similar maturity. If its backed by someone else I would use the YTM of the Guarantor’s bonds or LIBOR plus a risk premium. 3. Maybe the mortgage was created a long time ago when rates were higher? If its a commercial mortgage its probably not guaranteed. Where in the world did you get such a complex Mortgage?
#5

Edit: My Interest calculations assume that interest is compounded monthly (which is probably the case due to your monthly principal payments). And again: Where in the world did you get such a complex Mortgage?