Accounting: The Language of Business - Vol. 1 (Part 156)

We don't invest in financial literacy in a meaningful way. We should be teaching elementary school children how to balance a checkbook, how to do basic accounting, why it's important to pay your bills on time. First, education. Begin the learning process as early as possible, in elementary school. Second, encourage and support entrepreneurism. Third, policy. I know it's a priority of the US Treasury to augment financial inclusion and increase financial literacy.

Kabir Sehgal

 Capital Investment Analysis (Part B)

by

Charles Lamson

Present Value Methods

An investment in fixed assets may be viewed as acquiring a series of net cash flows over a period of time. The period of time over which these net cash flows will be received may be an important factor in determining the value of an investment. Present value methods use both the amount and the timing of net cash flows in evaluating an investment. Before illustrating how these methods are used in capital investment analysis, we will review basic present value concepts.

Present Value Concepts

Present value concepts can be divided into the present value of an amount and the present value of an annuity. We describe and illustrate these two concepts next. 

Present Value of an Amount If you were given the choice, would you prefer to receive $1 now or $1 three years from now? You should prefer to receive $1 now, because you could invest the dollar and earn interest for three years. As a result, the amount you would have after three years would be greater than $1. To illustrate, assume that on January 1, 2023, you invest $1 in an account that earns 12% interest compounded annually. After one year, the $1 will grow to $1.12 ($1 * 1.12), because interest of $0.12 is added to the investment. The $1.12 earns 12% interest for the second year. Interest earning interest is called compounding. By the end of the second year, the investment has grown to $1.254 ($1.12 * 1.12). Thus, if money is worth 12%, you would be equally satisfied with $1 on January 1, 2023, or $1.404 three years later.

On January 1, 2023, what is the present value of  $1.404 to be received on January 1, 2009? This is a present value question. The answer can be determined with the add of a dove a present value of $1 table. For example, the partial table in exhibit 1 indicates that the present value of $1 to be received three years hence, with earnings compounded at the rate of 12% a year, is 0.712. Multiplying 0.712 by 1.404 yields $1, which is the present value that started the compounding process.

Present Value of an Annuity An annuity is a series of equal net cash flows at fixed time intervals. Annuities are very common in business. For example, monthly rental, salary, and bond interest cash flows are all examples of annuities. The present value of an annuity is the sum of the present values of each cash flow. In other words, the present value of an annuity is the amount of cash that is needed today to yield a series of equal net cash flows at fixed time intervals in the future.

EXHIBIT 1 Partial Present Value of $1 Table

To illustrate, the present value of a $100 annuity for five periods at 12% could be determined by using the present value factors in Exhibit 1. Each $100 net cash flow could be multiplied by the present value of $1 at 12% factor for the appropriate period and summed up to determine a present value of $360.50, as shown in the following timeline:

Using a present value of an annuity table is a simpler approach. Exhibit 2 is a partial table of present value of annuity factors. These factors are merely the sum of the present value of $1 factors in Exhibit 1 for the number of annuity periods. Thus, 3.605 in the annuity table (Exhibit 2) is the sum of the five individual present value of $1 factors at 12%. Multiplying $100 by 3.605 yields the same amount ($360.50) that was determined in the preceding illustration by five successive multiplications. 

EXHIBIT 2 Partial Present Value of an Annuity Table

*WARREN, REEVE, & FESS, 2005, ACCOUNTING, 21ST ED., PP. 1038-1040*

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