Question

Suppose that you have invested in a perpetuity that pays $500 per year. Now, you forecast that the interest rate for the first 50 years to be 5%, but the interest rate will rise to 10% after the year 50. What’s the present value of this perpetuity with this information?

Give me the specific explanation plz

Answer 1

Present value of perpetuity = Present value of first 50 years payments + present value of perpetuity after 50 years.

Present value of first 50 years payments is calculated using PV function in Excel :

rate = 5%

nper = 50

pmt = -500

PV is calculated to be $9,127.96.

Present value of first 50 years payments is $9,127.96.

A1 fac =PV(5%,50,-500) D -B C i $9,127.96

The value of the perpetuity after 50 years = annual payment / interest rate after 50 years.

The value of the perpetuity after 50 years = $500 / 10% = $5,000.

Present value of perpetuity after 50 years = value of the perpetuity after 50 years / (1 + interest rate during first 50 years)⁵⁰

Present value of perpetuity after 50 years = $5,000 / (1 + 5%)⁵⁰ = $436.02.

Present value of perpetuity = Present value of first 50 years payments + present value of payments after 50 years.

Present value of perpetuity = $9,127.96 + $436.02

Present value of perpetuity = 9,563.98