如果cash flow 的方向变化两次，不是IRR不能用吗？

问题如下：

2. The NPV and IRR, respectively, of the Gasup Company investment are closest to:

选项：

$509,600 and 21.4%.

$509,600 and 31.3%.

$946,700 and 31.3%.

解释：

A is correct.

The cash flows (in $ million) for the 5-year gas project are as follows:

Given the required rate of return of 18 percent, the NPV can be calculated with Equation 2 or with a financial calculator:

$begin{array}{l}NPV=-6.0+\frac{-0.5}{1.18}+\frac{4.0}{1.18^2}+\frac{4.0}{1.18^3}+\frac{4.0}{1.18^4}+\frac{-1.0}{1.18^5}\\NPV=\$509,579$

Similarly, the IRR can be calculated from Equation 3:

$-6.0+\frac{-0.5}{1+r}+\frac{4.0}{{(1+r)}^2}+\frac{4.0}{{(1+r)}^3}+\frac{4.0}{{(1+r)}^4}+\frac{-1.0}{{(1+r)}^5}=0$

Solving for r with a financial calculator or spreadsheet software will yield 21.4 percent for the internal rate of return. Note that in spite of the fact that we are dealing with a nonconventional cash flow pattern, the IRR has a unique solution. The NPV profile declines as the required rate of return increases, and the NPV value crosses the x-axis (required rate of return) only one time, at 21.4 percent.