Proper way to do this PV/FV problem on the calculator? Really stuck

CFA Level I
#1

You currently owe $1,000,000 on an outstanding loan. You can afford to pay $50,000 per year back. As you are paying, the remaining balance of the loan that has not been paid will continue to grow at 3% compounded annually.

A. How long will it take to pay the entire loan back and for the balance to be 0?

B. An investor offers to immediately completely pay off your $1,000,000 and in exchange will accept an annual payment for $40,000 from you in perpetuity. What is the IRR for you of accepting this offer instead of paying the loan back on your own, and what is the IRR of the investment for the investor?

#2

A. when all the parameters are fixed (as in this question)

FV = 0 PV = - 1,000,000 PMT = 50,000 I/Y = 3 CPT N --> N = 30.9989 years

And make sure P/Y is set to 1, since compounding is annual. Don’t worry about practicing too much in Quant… you will get a lot of practice with the TMV functions in the Fixed Income section

B. perpetuity needs a formula, not the calculator’s TMV functions

for a perpetuity with interst rates positive PV = a/r

1,000,000 = 40,000 / r

r = 40,000 / 1,000,000 = 4%

#3

oops

#4

Thirty-one years:

  • PV = 1,000,000
  • FV = 0
  • PMT = -50,000
  • i = 3%
  • Solve for n = 31

The IRR for the investor is 4% (= $40,000 / $1,000,000). Your IRR is -1% (= -4% – (-3%)).

#5

Thanks guys. That part B was really messing me up. I was getting A, but I thought B was a lot more complicated for some reason

#6

My pleasure.