Abstract: External rate of return(ERR)has always been favored by Chinese engineering economists, but American engineering economists deny it because they think cash flow can't be discounted on the basis of double evaluation standard. In this paper, we use reduction to absurdity the principle that the Fisher point produced by the possible intersection of the net present value of the exclusive scheme curve is the ultimate reason for the ineffectiveness of the ERR index, relax the hypothesis of the net cash flow discount, use the numerical example to calculate two External rate of return curve, and produce a intersection similar to the Fisher point. However, the numerical value of the intersection is not equal to that of the Fisher point, and this will cause new chaos when using the ERR to choose the repelling programs. According to all these discoveries, we can deem that the index of ERR is irrational. At last, we can draw the conclusions:(1)The index of ERR has a unique solution compared with the IRR and this is the only advantage compared with the IRR. (2)The iterative trial and interpolation are generally used to calculate the index of ERR. It is not easier than to calculate the IRR.(3)The index of ERR can't be used directly to choose the repelling programs, so it is less convenient than the IRR. Furthermore, the index of ERR can produce the difference between the numerical value of the intersection similar to the Fisher point and that of the Fisher point and this can lead to the chaos of choice. So we suggest that the index of ERR should be deleted from the evaluation index system.