Accounting: The Language of Business - Vol. 2 (Intermediate: Part 102)

To say accounting for derivatives in America is a sewer is an insult to sewage.

Charlie Munger

Accounting and the Time Value of Money (Part L)

by

Charles Lamson

Present Value of Ordinary Annuity

In a present value of an ordinary annuity problem (cash flows occur at the end of the period), we know the payments, the interest rate, and the number of compounding periods, and we are asked to compute the present value. For example, assume that you have the opportunity to receive $100 at the end of each of the next three years. Given an interest rate of 8%, how much would you be willing to pay for this investment today? Exhibit 7.11 depicts this scenario graphically. 

We can solve this problem using a series of single sum problems as shown in the table below by computing the present value for each of the $100 payments. The present value for the first, second, and third payments, respectively, is $92.59, $85.73, and $79.38. We add these three present values together to get a total present value of $257.70.

The difference between the sum of the nominal cash flows ($300) and the present value of the future cash flows ($257.70) represents the interest of $42.30 earned on the investment. By using the present value of $1 factors from Table 7A.2 (excerpted text from Part 94) we can also determine that you would be willing to pay no more than $257.70.

Although present value of ordinary annuity problems can be solved using a series of single sum problems, it is more efficient to solve using a formula, table, spreadsheet, or financial calculator, all of which will be discussed in the next few parts. In the remainder of this post, we will discuss the formula solution. 

Formula Solution. Equation 7.13 is the formula for a present value of an ordinary annuity problem: 

EXAMPLE 7.21 Present Value of an Ordinary Annuity: Formula Approach

*GORDON, RAEDY, SANNELLA, 2019, INTERMEDIATE ACCOUNTING, 2ND ED., PP. 339-340*

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