Question

8. Use the following table to answer questions I, ii, iii and iv

	A	B	C
Initial cost	$15,000	$9,000	$12,000
Annual benefit	$8,000	$2,000	$1,800
Salvage value	$5,000	$9,000	0
Life in years	2 years	3 Years	Infinity
MARR	10%

i. The NPW of alt. A is __________________. A) $13,420

B) $17,380 C) $11,000 D) $6,00

ii. The NPW of alt. B is __________________. A) $13,420

B) $17,380 C) $11,000 D) $6,000

iii. The NPW of alt. C is __________________. A) $13,420

B) $17,380 C) $11,000 D) $6,000

iv. The best alternative among the three alternatives using the PW analysis is ____________. A) Alt. A

B) Alt. B
C) Alt. C
D) Either alt. B or alt. C

Answer 1

In the given question, the alternatives do not have equal life. Therefore, for evaluation we need to convert the unequal life into equal life. The alternative A and B has a definite unequal life. Hence, first of all we need to use to the common multiple method and convert the unequal life. The life of A is 2 years and B has 3 years. So the common multiple is 6 years.

The alternative A has to be repeated 3 times and B has to repeat 2 times.

But if we see the alternative C, it has infinity life. For that we have to convert the life all alternatives into infinity. Therefore, the common life should be taken as infinity.

At first we need to calculate the PW of alternative A and B. Then convert the NPV into annual worth and calculate the capitalized cost.

We have to finally compare the capitalized cost of all the three alternatives and select the alternative of which the capitalized cost is highest.

i. NPW of alternative A

Step – 1

Calculate NPW using common multiple assumption.

NPW = -15,000 – 15,000 (P/F, 10%, 2) – 15,000 (P/F, 10%, 4) + 8,000 (P/A, 10%, 6) + 5,000 (P/F, 10%, 2) + 5,000 (P/F, 10%, 4) + 5,000 (P/F, 10%, 6)

NPW = -15,000 – 15,000 (0.8264) – 15,000 (0.6830) + 8,000 (4.3553) + 5,000 (0.8264) + 5,000 (0.6830) + 5,000 (0.5645) = 7,571

Step – 2

Calculate Annual Worth

AW = NPW (A/P, 10%, 6)

AW = 7,570 (0.2296) = 1,738

Step – 3

Calculate CC

CC = A/I

CC = 1,738 / 0.10 = 17,380

Answer – b) $17,380

ii. NPW of alternative B

Step – 1

Calculate NPW using repetition assumption.

NPW = -9000 – 9000 (P/F, 10%, 3) + 2,000 (P/A, 10%, 6) + 9,000 (P/F, 10%, 3) + 9,000 (P/F, 10%, 6)

NPW = -9000 – 9000 (0.7513) + 2,000 (4.3553) + 9,000 (0.7513) + 9,000 (0.5645) = 4,791

Step – 2

Calculate Annual Worth

AW = NPW (A/P, 10%, 6)

AW = 4,791 (0.2296) = 1,100

Step – 3

Calculate CC

CC = A/i

CC = 1,100 / 0.10 = 11,000

Answer – c) $11,000

iii. NPW of alternative C

The life is infinity. So directly we can calculate CC

CC = I + A/i

CC = -12,000 + 1,800/0.10

CC = 6000

Answer – d) $6,000

iv. The best alternative among the three alternatives using PW analysis is

Answer – A) Alternative A (It has more PW than the other two)