- 2069 Bhadra · 4+8 marks
Best project for 4-year and 8-year service periods
Short answer
For 4-year service, FW method: Project A has FW Rs. 11,178 while B has FW Rs. -21,365, so choose A. For 8-year service, incremental IRR of B over A is 3.17% below 10% MARR, so A is best.
From the following information select the best project.
| Project A | Project B | |
|---|---|---|
| Initial Investment | 35,000 | 50,000 |
| Annual Revenue | 16,450 | 25,000 |
| Annual costs | 3,000 | 13,830 |
| Useful life | 4 years | 8 years |
| Salvage value at the end of useful life | 0 | 0 |
| MARR = 10% | ||
| When service period required is: | ||
| i) 4 years by FW method | ||
| ii) 8 years by IRR method with PW formulation |
Net annual revenue: A = 16,450 - 3,000 = Rs. 13,450; B = 25,000 - 13,830 = Rs. 11,170. MARR = 10%.
(i) Service period 4 years, FW method
Project A completes its 4-year life; B is used for only 4 of its 8 years. Assumption: the only market value given for B is zero at the end of its life, so the market value of B at the end of year 4 is taken as zero (nothing recovered).
FW(A) = -35,000(F/P, 10%, 4) + 13,450(F/A, 10%, 4) (F/P, 10%, 4) = 1.4641, (F/A, 10%, 4) = 4.6410 FW(A) = -51,244 + 62,421 = Rs. 11,178
FW(B) = -50,000(1.4641) + 11,170(4.6410) = -73,205 + 51,840 = Rs. -21,365
Answer (i): Select A (positive FW; B is negative if its assets have no resale value at year 4).
(ii) Service period 8 years, IRR with PW formulation
A is repeated once (second machine bought at year 4 for the same cost); B runs its full 8 years.
Year 0 1-3 4 5-8
A -35,000 13,450 -21,550 13,450 (-35,000 + 13,450 at yr 4)
B -50,000 11,170 11,170 11,170
B - A -15,000 -2,280 +32,720 -2,280
IRR of each project on its own (8-year flows):
- A: PW(i) = -35,000 + 13,450(P/A,i,8) - 35,000(P/F,i,4) = 0 → IRR = 19.73%
- B: PW(i) = -50,000 + 11,170(P/A,i,8) = 0 → IRR = 15.08% Both exceed 10%.
Incremental (B - A): PW(i) = -15,000 - 2,280(P/A,i,8) + 35,000(P/F,i,4) = 0 At i = 0%: +1,760; at 4%: -433; so IRR(B - A) ≈ 3.17%, which is less than MARR = 10%. (PW at 10% = -3,258, negative.)
Answer (ii): Select A. The extra Rs. 15,000 in B earns only 3.2% < 10%. (Also PW(A) = 12,849 > PW(B) = 9,591.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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