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IRR choose best of four, 10-year study

Short answer

Project C is rejected (IRR 9.61% < 10% MARR). Incremental analysis: A→B IRR 16.4% > 10%, so B beats A; B→D IRR 22.6% > 10%, so D beats B. Project D is selected.

Choose the best project among these alternatives using IRR, if MARR = 10% and study period is 10 years.

ProjectABCD
First Cost Rs.900150025004000
Annual Revenue Rs.150276400925

Assumptions: each project lasts the 10-year study period with no salvage value (none is given), so the cash flow of each is a single outlay followed by 10 equal annual revenues. IRR is the rate that makes PW = 0; for the incremental analysis the project with the larger investment is accepted only if the IRR on its extra investment is at least MARR = 10%.

Step 1: IRR of each project

Solve -First cost + Revenue (P/A, i, 10) = 0, i.e. (P/A, i, 10) = First cost / Revenue.

ProjectFirst costRevenue/yr(P/A, i, 10) neededIRRvs MARR 10%
A9001506.00010.56%Accept
B1,5002765.43512.96%Accept
C2,5004006.2509.61%Reject
D4,0009254.32419.10%Accept

(Check: at 10%, (P/A, 10%, 10) = 6.1446; a needed factor below this means IRR above 10%.)

C (IRR 9.61%) is below MARR, so it is dropped. A, B, D remain, arranged by increasing investment.

Step 2: incremental analysis (investment A < B < D)

IncrementExtra investmentExtra revenue/yrIncremental IRRDecision
A → B60012616.40%> 10%, B is better than A
B → D2,50064922.57%> 10%, D is better than B

For information, B → C would give 4.12% and C → D 32.98%.

Answer: Choose project D (largest investment 4,000 whose last increment still earns 22.6% > 10%; its own IRR is 19.1%).

✓ Answer checked by Claude Opus 5.5 (high effort)

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