When comparing alternatives, use incremental rate of return (\(\Delta\)IRR) on the difference between alternatives for rate of return analysis. It is a technique ot detemine the true cost difference between alternatives.
1. Determine alternative with higher initial cost
Cash flow for the initial difference of alternatives is obtained by taking the higher initial cost alternative minus the lower initial cost of the other alternative.
2. Evaluate cash flow difference for all periods
Evaluate the difference of the net cashflow for each period. This will be used to to find present worth.
3. Solve for effective interest rate such that NPW of the incremental difference is 0
Recall that in IRR analysis, the IRR is when NPV is 0. Here we want to find the net present worth of cash flow from all periods and equate it to 0 to solve for \(\Delta\)IRR.
4. Choose the alternative based on \(\Delta\)IRR
Since we arbitrarily picked to take the alternative of higher initial costs minus the alternative iwht lower initial costs for the difference, then:
One can plot the alternative’s NPV vs. interest rate graph together. It immediately becomes apparent.
Of course, one could also use equivalent uniform annnual costs (EUAC) and equivalent uniform annual benefits (EUAB) instead of NPV.
For multiple alternatives, we are still doing the same two-alternative incremental IRR analysis. Except it’s a “battle royale” such that only the best option remains. The process is: