Question

A perpetuity immediate pays 1000 each month for 7 years, and then 500 each month thereafter. If the nominal annual interest rate is 3% convertible monthly, and the present value of the perpetuity. Be sure to include the appropriate equation or expression of value that you use.

Answer 1

PV of Perpetuity = Perpetual Cash Flows / Interest Rate

Monthly Interest Rate = 3%/12 = .25%

PV of Perpertuity at end of Year 7 = 500 / .25%

PV of Perpertuity at end of Year 7 = 200,000

Present value at time 0 = FV / (1+int%)^n

Present value at time 0 = 200,000 / (1.03)^7

Present value at time 0 of perpetual payments of 500 every month = 162,618.30

Present Value of monthly payments of 1000 each month for 7 years.

Monthly Payments (PMT) = 1,000

Interest (i/Y) = .25%

Number of Periods in months (N) = 7 * 12 = 84

Future Value = 0

Period : END

Using PV Function in excel and inputting the above mentioned values

Present Value = 75,681.32

OR Using Financial Calculator and inputting the above mentioned values. Then Press "CPT" and then "PV"

Present Value = 75,681.32

Total Present Value of Perpetual Payments = 162,618.30 + 75,681.32

Total Present Value of Perpetual Payments = 238,299.62