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Problem 2 Four mutually exclusive alternatives, each with a useful life of 20 years, have been presented to the city council.Answer is in bold. Need to know how to work the problem. Thanks!

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Answer #1

Option 1

Initial cost = $4,000

Annual cost = $4,000

Annual benefits = $6,480

Time period = 20 years

MARR = 6%

Calculate the PW of cost -

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

PW = 4000 + 4000(P/A, i, n)

PW = 4000 + 4000(P/A, 6%, 20)

PW = 4000 + [4000 * 11.4699]

PW = 4000 + 45,879.60

PW = 49879.60

The PW of cost is $49,879.60

Calculate the PW of benefits -

PW = Annual benefits(P/A, i, n)

PW = 6480(P/A, 6%, 20)

PW = 6480 * 11.4699

PW = 74324.95

The PW of benefits is $74,324.95

Calculate the B/C ratio -

B/C ratio = PW of benefits/PW of cost

B/C ratio = $74,324.95/$49,879.60

B/C ratio = 1.49

The B/C ratio of Option 1 is 1.49

Option 2

Initial cost = $8,200

Annual cost = $9,000

Annual benefits = $11,250

Time period = 20 years

MARR = 6%

Calculate the PW of cost -

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

PW = 8200 + 9000(P/A, i, n)

PW = 8200 + 9000(P/A, 6%, 20)

PW = 8200 + [9000 * 11.4699]

PW = 8200 + 103229.10

PW = 111429.10

The PW of cost is $111,429.10

Calculate the PW of benefits -

PW = Annual benefits(P/A, i, n)

PW = 11250(P/A, 6%, 20)

PW = 11250 * 11.4699

PW = 129036.37

The PW of benefits is $129,036.37

Calculate the B/C ratio -

B/C ratio = PW of benefits/PW of cost

B/C ratio = $129,036.37/$111,429.10

B/C ratio = 1.16

The B/C ratio of Option 2 is 1.16

Option 3

Initial cost = $5,500

Annual cost = $6,000

Annual benefits = $5,700

Time period = 20 years

MARR = 6%

Calculate the PW of cost -

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

PW = 5500 + 6000(P/A, i, n)

PW = 5500 + 6000(P/A, 6%, 20)

PW = 5500 + [6000 * 11.4699]

PW = 5500 + 68819.40

PW = 74319.40

The PW of cost is $74,319.40

Calculate the PW of benefits -

PW = Annual benefits(P/A, i, n)

PW = 5700(P/A, 6%, 20)

PW = 5700 * 11.4699

PW = 65378.43

The PW of benefits is $65,378.43

Calculate the B/C ratio -

B/C ratio = PW of benefits/PW of cost

B/C ratio = $65,378.43/$74,319.40

B/C ratio = 0.88

The B/C ratio of Option 3 is 0.88

Option 4

Initial cost = $3,700

Annual cost = $2,000

Annual benefits = $4,400

Time period = 20 years

MARR = 6%

Calculate the PW of cost -

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

PW = 3700 + 2000(P/A, i, n)

PW = 3700 + 2000(P/A, 6%, 20)

PW = 3700 + [2000 * 11.4699]

PW = 3700 + 22,939.80

PW = 26639.80

The PW of cost is $26,639.80

Calculate the PW of benefits -

PW = Annual benefits(P/A, i, n)

PW = 4400(P/A, 6%, 20)

PW = 4400 * 11.4699

PW = 50467.56

The PW of benefits is $50,467.56

Calculate the B/C ratio -

B/C ratio = PW of benefits/PW of cost

B/C ratio = $50,467.56/$26,639.80

B/C ratio = 1.89

The B/C ratio of Option 4 is 1.89

The B/C ratio of option 4 is highest.

So,

Option 4 should be selected.

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