Question 5-A-1: Plot the PW versus interest rate for the following cash flow...
Plot the PW versus interest rate for the following cash flows. Are there multiple IRRs? If so, what do they mean?
Notice there are two sign changes in net cash flows (positive, negative, positive), so at most two IRRs exist for this situation. Nordstrom’s criterion also suggests a maximum of two interest rates because there are two sign changes in cumulative cash flow
| Year, k | Net Cash Flow | i% | PW(i%) | Year, k | Cumulative Cash Flow |
| 0 | $500 | 0 | $250 | 0 | $500 |
| 1 | −1,000 | 10 | 105 | 1 | −500 |
| 2 | 0 | 20 | 32 | 2 | −500 |
| 3 | 250 | 30 | \backsim 0 | 3 | −250 |
| 4 | 250 | 40 | -11 | 4 | 0 |
| 5 | 250 | 62 | \backsim 0 | 5 | 250 |
| 80 | 24 |
Thus, the PW of the net cash flows equals zero at interest rates of about 30% and 62%, so multiple IRRs do exist. Whenever there are multiple IRRs, which is seldom, it is likely that none are correct.
In this situation, the ERR method (see Section 5.7) could be used to decide whether the project is worthwhile. Or, we usually have the option of using an equivalent worth method. In Example 5-A-1, if the external reinvestment rate (∈) is 10% per year, we see that the ERR is 12.4%.
$1,000(P/F, 10%, 1)(F/P, i′%, 5) = $500(F/P, 10%, 5) + $250(F/A, 10%, 3)(P/F, 10%, 1)(F/P, i′, 5) = 1.632
i′ = 0.124 (12.4%).
In addition, PW(10%) = $105, so both the ERR and PW methods indicate that this project is acceptable when the MARR is 10% per year.
