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Feb 2016 CA2/CP2 - calculation of present value

S

Sankar Krishna

Keen member
The model is regarding calculation of mortgage payments under fixed and varying forward interest rates scenarios.
The forward rates are fixed for a period of 5 years and are recalculated every 5 yrs under the fixed rate scenario
The forward rates vary each year under varying rates scenario

My Doubt:
The Present value annuity for remaining term should be calculated using the interest rates for each of those years, whereas in the solution provided they have calculated assuming that the interest rate for that year holds across the remaining term.

PV = a(12):<5> + v^5*a(12):<5> + ... + v^20*a(12):<5> with different rates for each of the 5 yr term under Fixed rate scenario
PV = a(12):<1> + v*a(12):<1> + ... + v^24*a(12):<1> with different rates for each of the year under Varying rate scenario

The solution provided calculates PV as (1 - v^n) / i(12) which is correct only when interest rate is same across all remaining years.

Kindly clarify
Thanks in advance!
 
I'm not sure that I understand your question, so hopefully this answer makes some sort of sense!

The annuity at any point (for both variable and fixed) is calculated assuming that the interest rate is the same across all remaining years. When the interest rate changes, the annuity is recalculated. For the 5-year version, this happens 4 times (years 6, 11, 16, 21) and for the variable, it happens every year.

For your solution - how would you calculate the annuity payment amount (it's missing in your formula)? Would you try keep the annuity payment level throughout and do a goalseek for the amount that pays off the mortgage at the right time?

Remember that you're doing this calculation in a position of having an estimate of what those future interest rates will be. Normally, you wouldn't - so the assumption that interest rates stay the same until the end of the mortgage period is reasonable to make, and is the appropriate one to make each time the calculation needs to be re-done.
 
I assumed a dummy amount as annuity payment and used GOALSEEK to make level payments throughout to pay off the mortgage.
My doubt still remains:
It is still not clear to me why we would assume rates to be constant for the remaining term when varying forward rates are given for each of the 25 years.
 
It's because you're trying to find the difference between two approaches. Both need to be approached with how you'd act in real life. You may know the interest rates ahead of time, but you use them to model what you'd actually do over the 25 year period. So after five years, you recalculate the payment amount based on the interest rate at the time (which you just happen to know in advance in the exercise).
 
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