Question

What discount rate would make you indifferent between receiving $3,991.00 per year forever and $5,916.00 per year for 24.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

For $3991 received forever, PV can be calculated using Perpetuity formula

Let interest rate be r

So, PV = PMT/r = 3991/r

For $5916 received per year for 24 years, PV is calculated using PV formula of annuity

So, PV = PMT*(1 - (1+r)^(-t))/r = 5916*(1 - (1+r)^-24)/r

To make both the stream indifference, PV of the both should be same.

=> 3991/r = 5916*(1 - (1+r)^-24)/r

=> 3991/5916 = 1 - (1+r)^-24

=> (1+r)^24 = 3.07

=> r = 3.07^(1/24) - 1 = 4.79%

So, an interest rate of 4.79% make both the streams indifferent.