Question

What discount rate would make you indifferent between receiving $3,139.00 per year forever and $5,052.00 per year for 29.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

Let interest rate be r

So, Present value of receiving $3,139.00 per year forever can be calculated using perpetuity model

Present value = Annual cash flow/interest rate = 3139/r

Present values of $5,052.00 per year for 29.00 years is calculated using PV formula of ordinary annuity

Present value = PMT*(1 - (1+r)^(-t))/r = 5052*(1 - (1+r)^(-29))/r

Since we need to find r at which PV of both the annuity is same, so equating these equations, we get

3139/r = 5052*(1 - (1+r)^(-29))/r

=> 3139/5052 = 1 - (1+r)^-29

=> (1+r)^-29 = 1 - 0.6213

=> (1+r)^-29 = 0.3787

=> 1 + r = (0.3787)^(-1/29) = 1.034054

=> r = 0.034054 or 3.41%

So, discount rate = 3.41%