In the fields of architecture, engineering and construction, a clear concept of the appraisal methods of capital investment alternatives is very important. The NPV ranking of mutually exclusive alternatives is a correct approach if the MARR (minimum attractive rate of return) is based. The IRR ranking is an incorrect approach. If the IRR methodis ever used to rank alternatives, the Incremental IRR Analysis must be used, and its result will be the same as the NPV ranking. In using the Incremental IRR Analysis, one may face the problem of multiple IRRs, but this is not reallya hindrance to the Incremental IRR Analysis. The multiple IRR problem alleged in some articles is probably due to a misunderstanding of the multiple IRR theory. The author attempts to explain it in this article. The conclusion states that all other methods such as Modified IRR, Marginal Growth Rate, Incremental IRR Analysis, etc., are supplementary to the NPV method. The NPV is an economic indicator and always correct in evaluating the economic value of an investment and in ranking mutually exclusive alternatives based on the MARR. The IRR is a financial indicator and incorrect to be used for ranking mutually exclusive alternatives, but is to be used for finding the best financial strategy to achieve optimal gain for a single investment alternative.