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:
- If \(\Delta\)IRR (the effective interest rate such that NPW of differences =0) is higher than MARR, then go with the alternative with higher initial cost.
- If \(\Delta\)IRR is lower than MARR, go with the alternative with lower initial cost.
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:
- Order all alternative from highest to lowest initial cost. If applicable (include the do nothing option).
- Compute the IRR for the lowest cost option.
- If IRR < MARR, then eliminate this alternative from the pool and move on to the alternative with next lowest cost
- If IRR > MARR, then this alternative becomes the defender
- If IRR > MARR while there is a defender, this alternative becomes the challenger
- Challenger and defender faces off: incremental IRR analysis is done on challanger-defender
- If \(\Delta\)IRR > MARR: challenger becomes the new defender
- If \(\Delta\)IRR < MARR: defender remains, challenger eliminated from the pool
- Go to the next alternative and repeat step 3 until only one alternative remains.