Financial Accounting: In an Economic Context

COMPUTING IMPLICIT RATES OF RETURN AND INTEREST RATES

In many business situations it is helpful, or even necessary, to compute the expected or actual rate of return (or interest) generated by an investment (or note). Consider a company, for example, that plans to invest $1,000 in a project expected to generate $300 per year over a five-year period. What rate of return is expected from that project? Similarly, consider a company that finances a piece of property with a fair market value of $100,000 by signing a note that requires annual cash payments of $20,000 for six years. What interest rate is the company paying on the note? These and similar questions can be answered by computing the rate of return (or interest rate) that is implied given the facts of the situation. Such computations are based on the present value computation, which can be viewed in terms of the following equation.

Present value = Future cash flow X (Table factor; n = years, i = interest rate)

So far, we have computed present values after being given a future cash flow, the number of periods (n), and an interest rate (i). For example, the value of $1,000 to be received in five years at a 10 percent interest rate can be computed as follows.

Present value = $1,000 X (Table 4 “present value of a single sum”; n = 5, i = 10%)

= $1,000 X 0.62092

= $620.92

However, a number of cases arise, similar to those mentioned above, where we wish to compute the interest rate (i) by either knowing—or having to estimate—the present ...