Question

A B

capital investment 50000 65000

annual expenses 9000 8000

annual revenues 22000 24000

salvage value 13000 20000

useful life 8 year 8 year

A_ Calculate the payback period of each alternative and decide the best alternative without taking into account the time value of the money

B- Use conventional benefit cost ratio analysis to define which alternative should be selected.

C-Use modified benefit cost ratio to define which alternative should be selected (MARR %10)

Answer 1

(A)

Payback period (PBP) is the time by when project's cumulative net benefit equals zero.

Annual net benefit (NB) = Annual revenue - Annual expense

Project - A						Project - B
Year	Revenue ($)	Expense ($)	NB ($)	Cumulative NB ($)		Year	Revenue ($)	Expense ($)	NB ($)	Cumulative NB ($)
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 NB, 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 NB, year 4 / NB, year 5)

= 4 + (1,000 / 16,000) = 4 + 0.0625 = 4.0625 years

Since Project A has lower PBP, Project A should be selected.

(B)

Conventional benefit-cost ratio = PW of Revenue / (Initial cost + PW of Annual cost - PW of Salvage value)

Project A: [22,000 x P/A(10%, 8)] / [50,000 + 9,000 x P/A(10%, 8) - 13,000 x P/F(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 P/A(10%, 8)] / [65,000 + 8,000 x P/A(10%, 8) - 20,000 x P/F(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, Project B should be selected.

(C)

Modified Benefit-cost ratio = (PW of Revenue - PW of Annual cost) / (Initial cost - PW of Salvage value)

Project A: [(22,000 - 9,000) x P/A(10%, 8)] / [50,000 - 13,000 x P/F(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 P/A(10%, 8)] / [65,000 - 20,000 x P/F(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, Project A should be selected.

**From P/A and P/F Factor tables