Problem 6: Present Value of Annuities

Two people wish to buy your house. The first person offers you $200,000 today, while the second person offers you twenty-five annual payments of $15,000. Assume a 5 percent interest or discount rate. What is the present value of each offer? If you could take either offer, which person would you sell your house to?

What is the present value of each offer?

• First offer: The present value of offer one is $200,000 because the buyer can pay you all of the money today.
• Second offer: This offer is a little different because you will not receive all of the money today; therefore, you must calculate the present value of this offer.

To calculate the preset value of the first offer using a financial calculator, clear your calculator's memory, set the number of payments to one annual payment, and make sure your calculator is set to “end mode.” Then, input the following information:

• PMT = –$15,000
• N = 25
• I = 5
• PV = ?

The present value of the second offer is $211,409. If you do not have a financial calculator, use the following formula to solve for the present value:

PV_n,i = PMT * [1 – (1/(1 + i)ⁿ )]/i

PV_n,i = $15,000 * [1 – (1/(1.05)²⁵]/0.05 = $211,409

Which is the better offer? The second offer has a higher present value: if we can assume that you don't need the money right away, and that you are willing to wait for payments, and that you are confident they will pay you on schedule, you should accept the second offer. As you can see from this example, it is very important that you know how to evaluate different cash flows.

Future Value of Annuities

Just as it is possible to calculate the present value of an annuity, it is also possible to calculate the future value of an annuity.