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Two processes can be used for producing a polymer that reduces friction loss in engines. Process K will have a first cost of $160,000, an operating cost of $7000 per month, and a salvage value of $40,000 after its 2-year life. Process L will have a first cost of $210,000, an operating cost of $5000 per month, and a $26,000 salvage value after its 4-year life. Which process should be selected on the basis of an annual worth analysis at an interest rate of 12% per year, compounded monthly?

Respuesta :

Answer:

process L selected.

Explanation:

Effective annual interest rate (r)

= (1 + 12% ÷ 12)^12 -1

= 12.68%

K Process

Initial cost = $160000

Monthly operating cost = $7000

Salvage value after 2 year = $40000

Time = 2 years or 24 months

Annual interest rate = 12% annual compounding monthly

Monthly interest rate R = 12% ÷ 12

= 1%

Present worth = $160,000 + $7,000 × (1 - 1 ÷ (1 + R)^24) ÷ R – $40,000÷ (1 + R)^24

= $160,000 + $7,000 × (1 - 1 ÷ 1.01^24) ÷ 0.01 – $40,000 ÷ 1.01^24

= $277,201.06

Let, annual worth = AW

Present worth = AW × (1 - 1÷ (1+r)^2) ÷ r

= AW × (1-1 ÷ 1.1268^2)/.1268

= AW*1.675

AW = $277,201.06 ÷ 1.675

AW (for process K) = $165,493.17

For Process L

Initial cost = $210,000

Monthly operating cost = $5,000

Salvage value after 4 year = $26,000

Time = 4 years or 48 months

Annual interest rate = 12% annual compounding monthly

Monthly interest rate R = 12% ÷ 12

= 1%

Present worth = 210000 + 5000 × (1 - 1 ÷ (1 + R)^48) ÷ R – $26,000 ÷ (1 + R)^48

= $210,000 + $5,000 × (1 - 1÷ 1.01^48) ÷ 0.01 – $26,000 ÷ 1.01^48

= $383,743.03

If annual worth = AW

Present worth = $383,743.03 = AW × (1 - 1 ÷ 1.1268^4) ÷ 0.1268

= AW × 2.9943

AW = 383743.03 ÷ 2.9943

AW (for process L) = $128157.84

Therefore, Process K is higher than the annual cost of process L or AW. So, process L selected.

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