Question

4. A manufacturer wants to buy a new machine. He has two alternative technologies. The cash flows of the alternatives are given below Initial Investment Cost Annual Expenses Annual Revenues Salvage Value Useful Life ProjectA 50000 TL 22000 TL 9000 TL Project B 65000 TL 24000 TL 8000 TL 20000 TL 13000 T ears Calculate the payback period of each alternative and decide the best alternative without taking into account the time value of the money. (15 points) A. B. Use conventional benefit cost ratio analysis to define which alternative should be selected. (MARR %10) (10 points) C. Use modified benefit cost ratio to define which alternative should be selected. (MARR %10) (10 points)

Answer 1

(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