Foundations of Financial Management: An Analysis (part 29)

“Rule No.1: Never lose money. Rule No.2: Never forget rule No.1.” 

– Warren Buffett

The Time Value of Money (Part D)

by

Charles Lamson

Determining the Yield on an Investment

In our discussion thus far, we have considered the following time value of money problems.

In each case we knew three out of the four variables and solved for the fourth. We will follow the same procedure again, but now the unknown variable will be i, the interest rate, or yield on the investment.

Yield---Present Value of a Single Amount

An investment producing $1,464 after 4 years has a present value of $1,000. What is the interest rate, or yield, on the investment?

We take the basic formula for the present value of a single amount and rearrange the terms.

We next express this value (0.003) as a fraction of the preceding value (0.024) and multiply by the difference between the two interest rates (6 percent minus 5 percent). The value is added to the lower interest rate (5 percent) to get a more exact answer of 5.125 percent rather than the estimated 5 percent.

Yield---Present Value of an Annuity

We may also find the yield related to any other problem. Let's look at the present value of an annuity. Take the basic formula for the present value of an annuity, and rearrange the terms.

The appropriate table is Table 4 from last post (the present value of an annuity of $1). Assuming a $10,000 investment will produce $1,490 a year for the next 10 years, what is the yield on the investment?

Is the student will flip back two tables for and read across the columns 4 in equals 10 periods, he or she will see that the yield is 8%.

The same type of approximated or interpolated yield that applied to a single amount can also be applied to an annuity when necessary. 

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 254-256*

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