See Also Present Value Uneven Cash Flows

The present value of an annuity is an amount of money today which is equivalent to a series of equal payments in the future. For example ,say you have won a lottery and lottery officials give you the choice og having a lump sum payment today or a series of payments at the end of each of the next five years. The two alternatives would be considered equivalent (in monetary sense) if by investing the lump sum today you could generate (with accumulated interest) annual withdrawls equal to five installments offered by the lottery officials. An assumption is that the final withdrawl would depletethe investment completely.

The formula to compute the present value of annuity is as follows, here we assume that the cash flow begins at the end of terms.

EXAMPLE 1

First prize in a competiton is to receive an immediate payment of $40,000 or a payment of $10000 per year for each of the next five years, the first payment being made in one years time. If the discount rate is 8%, which has the higher value?

SOLUTION

The present value of the series of annual payments can be found by using the formula mentioned above, where R=$10,000, i=0.08 and n=5

The answer is $39927.10 which is less than the lump sum of $40,000

The formula to compute the present value of annuity where the cash flow begins at the beginning of terms is as follows.

If the winner of first prize in the example above chooses to receive yearly payments beginning immediately, would she be better off. Lets see the results

The answer is yes as the present value of such prize amounts to $43120.35 which is higher than $40000.

Using MS Excel to compute Present Value of Annuities

In MS Excel you can use the financial function PV(rate,nper,pmt,fv,type) to compute the present value of an investment. The present value is the total amount that a series of future payments is worth now. For example, when you borrow money, the loan amount is the present value to the lender.

Nper   is the total number of payment periods in an annuity. For example, if you get a four-year car loan and make monthly payments, your loan has 4*12 (or 48) periods. You would enter 48 into the formula for nper.

Pmt   is the payment made each period and cannot change over the life of the annuity. Typically, pmt includes principal and interest but no other fees or taxes. For example, the monthly payments on a $10,000, four-year car loan at 12 percent are $263.33. You would enter -263.33 into the formula as the pmt. If pmt is omitted, you must include the fv argument.

Fv   is the future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0). For example, if you want to save $50,000 to pay for a special project in 18 years, then $50,000 is the future value. You could then make a conservative guess at an interest rate and determine how much you must save each month. If fv is omitted, you must include the pmt argument.

Type   is the number 0 or 1 and indicates when payments are due.