Question

Tobi owns a perpetuity that will pay $2,000 a year, starting one year from now. He offers to sell you all of the remaining payments after the next 25 payments have been paid. What price should you offer him for payments 26 onward if you desire a rate of return of 10 percent? What does your offer price illustrate about the value of perpetuities?

Answer 1

perpetuity in year 26 = 2000 (same as in first year)

discount rate (i) = 10%

Value of perpetuity in year 25 = Perpetuity payment in year 26/required return or discount rate

=2000/10%

=20000

Value of perpetuity in 25 years is future value

number of gaps in year from today (n) =25

Present value = FV/(1+i)^n

=20000/(1+10%)^25

=1845.919964

Offer price for payment from 26 onwards will be $1845.92.

This offer price illustrates that value of payment received in future perpetuity is less than what we receive today.

If we buy perpetuity today then value paid is $20000 but if we buy from 26 payment onwards value of perpetuity will be lower as payment is received in future, not today