Mortgages & Bonds: YTM of Zero Par Value

[Oxymoron]

Homework Statement

If a bank issues a mortgage to a borrower, let's say that it was for $P, for t years with an annual interest rate i% compounded monthly. Then, to the bank, can this essentially be treated like a bond with price $P, coupon rate i% and maturity t years?

It could be treated like a bond with a 0 par value right?

My only problem is that when I try to calculate the yield to maturity (YTM) of a bond with a zero par value I get an undefined answer. Is it possible to calculate the YTM of a mortgage (bond with zero par)?

 

[danago]

For a zero face-value bond, wouldn't the YTM just be r, where:

<br /> P = \frac{C}{r}\left( {1 - \frac{1}{{(1 + r)^n }}} \right)<br />

and C is the coupon payment? If the coupon is just i% of the loan value i.e. C=iP, then the yield would be given by r where:

<br /> 1 = \frac{i}{r}\left( {1 - \frac{1}{{(1 + r)^n }}} \right)<br />

Have i understood the problem correctly? I don't see why the yield would be undefined.