Question

Five mutually exclusive cost alternatives that have infinite lives are under consideration for decreasing the fruit-bruising rates of a thin skin-fruit grading and packing operation (peaches, pears, apricots, etc.). The initial costs and cash flows of each alternative are available. If the MARR is 15% per year, the one alternative to select is:

Alternative	A	B	C	D	E
Initial cost, $	−15,000	−12,000	−9,000	−14,000	−11,000
Cash flow, $ per year	−300	−900	−1400	−700	−1000

		A
		B
		D
		E

Answer 1

Present Worth method is being used to select the best alternative.

Alternative A -

Initial cost = $ -15,000

Cash flow per year = $ -300

MARR = 15%

Useful life = Infinity

Calculate the present worth of Alternative A -

PW = Initial cost + cash flow (P/A, i, n)

PW = -15,000 - 300(P/A, 15%, )

PW = -15,000 - (300 * (1/0.15))

PW = -15,000 - 1,999.98

PW = -16,999.98

The Present Worth of Alternative A is $ -16,999.98

Alternative B -

Initial cost = $ -12,000

Cash flow per year = $ -900

MARR = 15%

Useful life = Infinity

Calculate the present worth of Alternative B -

PW = Initial cost + cash flow (P/A, i, n)

PW = -12,000 - 900(P/A, 15%, )

PW = -12,000 - (900 * (1/0.15))

PW = -12,000 - 5,999.94

PW = -17,999.94

The Present Worth of Alternative B is $ -17,999.94

Alternative C -

Initial cost = $ -9,000

Cash flow per year = $ -1,400

MARR = 15%

Useful life = Infinity

Calculate the present worth of Alternative C -

PW = Initial cost + cash flow (P/A, i, n)

PW = -9,000 - 1,400(P/A, 15%, )

PW = -9,000 - (1,400 * (1/0.15))

PW = -9,000 - 9,333.24

PW = -18,333.24

The Present Worth of Alternative C is $ -18,333.24

Alternative D -

Initial cost = $ -14,000

Cash flow per year = $ -700

MARR = 15%

Useful life = Infinity

Calculate the present worth of Alternative D -

PW = Initial cost + cash flow (P/A, i, n)

PW = -14,000 - 700(P/A, 15%, )

PW = -14,000 - (700 * (1/0.15))

PW = -14,000 - 4,666.62

PW = -18,666.62

The Present Worth of Alternative D is $ -18,666.62

Alternative E -

Initial cost = $ -11,000

Cash flow per year = $ -1,000

MARR = 15%

Useful life = Infinity

Calculate the present worth of Alternative E -

PW = Initial cost + cash flow (P/A, i, n)

PW = -11,000 - 1000(P/A, 15%, )

PW = -11,000 - (1000 * (1/0.15))

PW = -11,000 - 6,666.6

PW = -17,666.6

The Present Worth of Alternative E is $ -17,666.6

The present worth of Alternative A is numerically higher.

So, based on present worth analysis, Alternative A should be selected.