Question

A bank offers an investment opportunity that makes payments to the investor of $800 per quarter forever. If they quote an APR of 26.0%, then what is the most you should be willing to pay for the investment today? (What numbers do I put into the financial calculator for N, I/Y, PV, PMT and FV?

Answer 1

The maximum amount an investor would pay for this perpetuity should be equal to the present value of the perpetual payments discounted at the appropriate discount rate.

APR = 26% per annum or 6.5 % (26/4) per quarter.

Perpetual Periodic Payouts = $ 800

The problem can be solved on a financial calculator as described below:

- The financial calculator cannot input the value of N as infinity which is the number of payments in perpetuity. However, the calculator can be manipulated to determine almost (approximate) the correct answer. The present value of payments very far off in the future say 500 quarters (N = 500) or 100 quarters is practically close to zero. Hence, input N = 1000

- Input I/Y = 6.5 % , PMT = $ 800, FV = $ 0, CMPT - > PV

- PV ~ $ 12307.69

NOTE: The answer can be verified by determining PV using the normal perpetuity formula of PV = Periodic Cash Flows / Interest Rate = 800 / 0.065 ~ $ 12307.69