Accounting: The Language of Business - Vol. 2 (Intermediate: Part 91)

I hear Raleigh's new accounting business isn't doing well. Maybe up in New York or somewhere it's a good thing, but in Jackson, Mississippi, people just don't care to do business with a rude, condescending asshole.

Kathryn Stockett

Accounting and the Time Value of Money (Part D)

by

Charles Lamson

Single-Sum Problems

We begin our discussion by illustrating applications of compounding (moving from the PV to the FV) and discounting (moving from the FV to the PV) a single sum, usually known as an amount of $1. There are four important variables in a single sum problem:

1. Present value (PV)

2. Future value (FV)

3. Interest rate per compounding period (I/Y)

4. Time period or number of compounding periods (N)

If you know any three of these variables, you can solve for the fourth one. The interest rate per compounding period is the annual interest rate (I) divided by the number of times per year that interest compounds (Y). For example, if you are earning 8% interest compounded quarterly, then the interest rate per compounding period is 2% ( i.e., 8% / 4 quarters). The number of compounding periods (N) is the number of times per year that interest compounds multiplied by the total number of years for which a present or future value is computed. For example, if you are holding a 5-year note receivable that pays interest quarterly, then there are 20 compounding periods (i.e., 5 years * 4 quarters). 

We begin by solving for the future value and illustrating various techniques to solve each problem. There are a number of techniques available to solve time value of money problems, such as financial calculators, smart phones, and spreadsheets. We illustrate four methods in the next several parts of this analysis. Note that in all time value of money problems, different approaches may give you slightly different answers due to rounding.

1. The Formula Solution

2. The Factor Table Solution

3. The Spreadsheet Application

4. The Financial Calculator Solution

Future Value of a Single Sum

For the future value of a single sum, we know the present value of the single cash flow, the interest rate, and the number of periods—and the need to compute future value. Consider a single bank deposit with $100 left on deposit for one year at an 8% rate of interest, as depicted in Exhibit 7.4.

Formula Solution. To compute the future value of a single sum, we compute interest one period at a time and determine the new principle plus interest balance at the end of each period, as in Example 7.2. from Part 89. However, this approach is quite burdensome, particularly for problems involving many periods. A less cumbersome approach is to restate the problem using the time value of money variables defined in the previous section using the following formula:

where PV is the present value, FV is the future value, I / Y is the interest rate per compounding period, and N is the number of compounding periods. Note that the future value (FV) is directly related to the rate of interest, I / Y, and the period of time, N.

We illustrate annual compounding in Example 7.4. 

Example 7.5 illustrates a more complex problem.

*GORDON, RAEDY, SANNELLA, 2019, INTERMEDIATE ACCOUNTING, 2ND ED., PP. 319-321*

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