Foundations of Financial Management: An Analysis (part 26)

“I will tell you the secret to getting rich on Wall Street. You try to be greedy when others are fearful. And you try to be fearful when others are greedy.” 

– Warren Buffett

The Time Value of Money

by

Charles Lamson 

The time value of money applies to many day-to-day decisions. Understanding the effective rate on a business loan, the mortgage payment in a real estate transaction, or the true return on an investment depends on understanding the time value of money. As long as an investor can garner a positive return on idle dollars, distinctions must be made between money received today and money received in the future. The investor/lender essentially demands that a financial rent be paid on his or her funds as current dollars are set aside today in anticipation of higher returns in the future.

Relationship to the Capital Outlay Decision

The decision to purchase new plant and equipment or to introduce a new product in the market requires using capital allocating or capital budgeting techniques. Essentially we must determine whether future benefits are sufficiently large to justify current outlays. It is important that we develop the mathematical tools of the time value of money as the first step toward make making capital allocation decisions. Let us now examine the basic terminology of "time value of money."

Future Value---Single Amount

In determining the future value, we measure the value of an amount that is allowed to grow at a given interest rate over a period of time. Assume an investor has $1,000 and wishes to know its worth after 4 years if it grows at 10 percent per year. At the end of the first year, the investor will have $1,000 X 1.10, or $1,100. By the end of year two, the $1,100 will have grown to $1,210 ($1,000 X 1.10). The four-year pattern is indicated below.

After the fourth year, the investor has accumulated $1,464. Because compounding problems often cover a long period, a more generalized formula is necessary to describe the compounding procedure. We shall let:

The simple formula is:

Table 1   Future value of $1

The table tells us the amount that $1 would grow too if it were invested for any number of periods at a given interest rate. We multiply this factor times any other amount to determine the future value.  

Present Value of a Single Amount

The present value is the exact opposite of the future value. For example, earlier we determined that the future value of $1,000 for four periods at 10 percent was $1,464. We could reverse the process to state that $1,464 received four years into the future, with a 10 percent interest or discount rate, is worth only $1,000 today---its present value. The relationship is depicted in Figure 1. 

The formula for present value is derived from the original formula for future value.

The present value can be determined by solving for a mathematical solution to the formula above, or by using cable too, the present value of a dollar. and the latter instance, we restate the value for present value as:

Let's demonstrate that the present value of $1,464 based on our assumptions, is $1,000 today. 

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 239-242*

end