(A)
Payback period (PBP) is the time by when project's cumulative net annual benefit equals zero, where
Net Annual benefit (NAB) = Annual revenue - Annual cost
Project - A | Project - B | |||||||||
Year | Revenue | Expense | NAB | Cumulative NAB | Year | Revenue | Expense | NAB | Cumulative NAB | |
0 | 50,000 | -50,000 | -50,000 | 0 | 65,000 | -65,000 | -65,000 | |||
1 | 22,000 | 9,000 | 13,000 | -37,000 | 1 | 24,000 | 8,000 | 16,000 | -49,000 | |
2 | 22,000 | 9,000 | 13,000 | -24,000 | 2 | 24,000 | 8,000 | 16,000 | -33,000 | |
3 | 22,000 | 9,000 | 13,000 | -11,000 | 3 | 24,000 | 8,000 | 16,000 | -17,000 | |
4 | 22,000 | 9,000 | 13,000 | 2,000 | 4 | 24,000 | 8,000 | 16,000 | -1,000 | |
5 | 24,000 | 8,000 | 16,000 | 15,000 |
PBP of project A lies between years 3 & 4.
PBP, Project A = 3 + (Absolute value of cumulative NAB, year 3 / NB, year 4)
= 3 + (11,000 / 13,000) = 3 + 0.85 = 3.85 years
PBP of project B lies between years 4 & 5.
PBP, Project B = 4 + (Absolute value of cumulative NAB, year 4 / NB, year 5)
= 4 + (1,000 / 16,000) = 4 + 0.06 = 4.06 years
Since Project A has lower PBP than Project B (3.85 < 4.06), Project A should be selected.
(B)
Conventional benefit-cost ratio = PV of Annual Revenue / (Initial cost + PV of Annual cost - PV of Salvage value)
Project A: [22,000 x PVIFA(10%, 8)] / [50,000 + 9,000 x PVIFA(10%, 8) - 13,000 x PVIF(10%, 8)]
= (22,000 x 5.3349**) / [50,000+ (9,000 x 5.3349**) - (13,000 x 0.4665**)]
= 117,368 / (50,000 + 48,014 - 6,065)
= 117,368 / 91,949
= 1.28
Project B: [24,000 x PVIFA(10%, 8)] / [65,000 + 8,000 x PVIFA(10%, 8) - 20,000 x PVIF(10%, 8)]
= (24,000 x 5.3349**) / [65,000+ (8,000 x 5.3349**) - (20,000 x 0.4665**)]
= 128,038 / (65,000 + 42,679 - 9,330)
= 128,038 / 98,349
= 1.30
Since Project B has higher Conventional BCR thatn project A (1.30 > 1.28), Project B should be selected.
(C)
Modified Benefit-cost ratio = (PV of Revenue - PV of Annual cost) / (Initial cost - PV of Salvage value)
Project A: [(22,000 - 9,000) x PVIFA(10%, 8)] / [50,000 - 13,000 x PVIF(10%, 8)]
= (13,000 x 5.3349**) / [50,000 - (13,000 x 0.4665**)]
= 69,354 / (50,000 - 6,065)
= 69,354 / 43,935
= 1.58
Project B: [(24,000 - 8,000) x PVIFA(10%, 8)] / [65,000 - 20,000 x PVIF(10%, 8)]
= (16,000 x 5.3349**) / [65,000 - (20,000 x 0.4665**)]
= 85,358 / (65,000 - 9,330)
= 85,358 / 55,670
= 1.53
Since Project A has higher modified BCR than project B (1.58 > 1.53), Project A should be selected.
**From PVIFA and PVIF Factor tables
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