The accounting rate of return is not a ranking method of capital budgeting analysis.
"Time-adjusted rate of return" is another term that is used to refer to the internal rate of return. The internal rate of return is a project screening method, not a ranking method. If the internal rate of return of a project is equal to or higher than the required rate of return, then the project is acceptable. However, there are problems associated with trying to use the internal rate of return as a ranking method, so it is not used in that way.
The profitability index is a benefit/cost ratio. It represents the ratio of the benefits (net cash inflows) to the costs (net initial investment). The profitability index enables us to compare, or rank, the benefit/cost ratios of different sized investments, since the profitability index expresses profitability on a percentage basis rather than a total dollar amount basis. It is very useful when we must compare multiple investments that are of different investment amounts, the projects are not mutually exclusive, and we need to rank them. When there are multiple investment opportunities, we will take the project that has the highest profitability index. When the projects are independent alternatives of the same length, this method will give us the same accept/reject decisions that NPV provides. However, when the projects are of different time periods or amounts of initial investments, the profitability index may give different rankings than NPV.
Net present value is primarily a screening method (although it may be used as a ranking method in certain circumstances). The general rule is that any project that has a positive NPV should be accepted, while a project with a negative NPV should be rejected. However, for various reasons such as limited funds to invest or nonfinancial factors, not all projects with positive NPVs will be acceptable. It is probably better to state that any project that has a positive NPV is a candidate for further consideration - it has passed the first screen. A project with a negative NPV should not be considered further. This will maximize shareholder wealth. When there are limited funds to invest, NPV is useful because it enables ranking of the various projects according to the amount that they are expected to return. However, it is not primarily a ranking method rather than a screening method.
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