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IRR selection among A, B, C, D

Short answer

Part 1: All four mutually exclusive. Incremental IRRs: A→B 45.1%, B→D 50.0%, D→C 3.1% (<12%). Select D. Part 2: A,B,C mutually exclusive, D independent. Best of A,B,C is C; add D. Select C+D combination.

Use IRR method to select best project. MARR = 12%.

ABCD
Initial Investment1100150027502000
Annual Income5007001200950
Useful Life4444
Salvage Value2505008001000
MARR15%15%15%15%
Select the best combination if A, B and C are mutually exclusive.

Assumptions: MARR = 12% as stated in the question (the table repeats MARR = 15%; the decisions below are the same at 15%, see the note at the end). Cash flows over 4 years are: -Initial investment at year 0, annual income each year, and salvage value added in year 4. The IRR of an increment is compared with MARR.

Part 1: IRR of each project and incremental analysis (all four mutually exclusive)

ProjectInvestmentIncome/yrSalvageIRRResult
A1,10050025033.57%accept
B1,50070050036.87%accept
C2,750120080032.58%accept
D2,000950100040.51%accept

All IRRs are above 12%. Rank by investment: A (1,100) < B (1,500) < D (2,000) < C (2,750). Incremental cash flows are in years 0, 1-3, 4.

IncrementCash flowsIncremental IRRDecision
A → B[-400, 200, 200, 200, 450]45.1%> 12%, keep B
B → D[-500, 250, 250, 250, 750]50.0%> 12%, keep D
D → C[-750, 250, 250, 250, 50]3.1%< 12%, reject C, keep D

Best single project: D.

Part 2: A, B, C mutually exclusive; D independent

Among A, B, C only one can be taken. D can be added to whichever is chosen, and D itself is acceptable (IRR 40.5% > 12%).

Best of A, B, C by incremental IRR:

  • A → B: 45.1% > 12%, B beats A
  • B → C: 27.2% > 12%, C beats B

So C is the best of the three. Because D is independent and acceptable, it is added to the best of the exclusive group.

Answer: Part 1: select D. Part 2: select the combination C + D (total investment 4,750). Note: at MARR = 15% the same choices hold because all incremental IRRs used are above 15% (the D → C increment is only 3.1%, still rejected).

✓ Answer checked by Claude Opus 5.5 (high effort)

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