A company is considering two alternatives for manufacturing a certain part. meth

Question

A company is considering two alternatives for manufacturing a certain part. method R will have a first cost of $40,000, an annual operating cost of $25,000, and a $10,000 salvage value after its five year life. method S will have an initial cost of $100,000, an annual operating cost of $15,000, and a $12,000 salvage value after its 10 year life. At an interest rate of 12% per year, a- the present worth values of the two alternatives are closest to: (a) PW_R = $124,446, PWS = $180,889 (b) PW_R = $195,057, PW_S = $180,889 (c) PW_R = $124,446, PWS = $147,263 (d) PW_R = $195,057, PW_S = $147,263 b- For the alternatives, their annual worth values are closet to: (a) AW_R = $31,510, AW_S = $32,016 (b) AW_R = $31,510, AW_S =$50,851 (c) AW_R = $34,522, AW_S = $32,016 (d) AW_R = $34,522, AW_S = $50,851

Explanation / Answer

Method R

Initial cost = $40000

Rate (R) = 12%

Life (n) = 5 years

Salvage value = $10000

Annual O&M cost = $25000

Thus,

Present worth of Method R = initial cost + present value of O&M cost - present value of salvage value

Present worth of Method R = 40000 + 25000*(1-1/(1+R)^n)/R – 10000/(1+R)^n

Present worth of Method R = 40000 + 25000*(1-1/(1+12%)^5)/12% - 10000/(1+12%)^5

Present worth of Method R = $124445.1 or $124446

Equivalent Annual Cost (EAC) = Present worth / ((1-1/(1+R)^n)/R) = 124445.1/ ((1-1/(1+12%)^5)/12%)

Equivalent Annual Cost (EAC) = $34522.28 or $34522 approx.

Method S

Initial cost = $100000

Rate (R) = 12%

Life (n) = 10 years

Salvage value = $12000

Annual O&M cost = $15000

Thus,

Present worth of Method R = initial cost + present value of O&M cost - present value of salvage value

Present worth of Method R = 100000 + 15000*(1-1/(1+R)^n)/R – 12000/(1+R)^n

Present worth of Method R = 100000 + 15000*(1-1/(1+12%)^10)/12% - 12000/(1+12%)^10

Present worth of Method R = $180889.7 or $180889 approx.

Equivalent Annual Cost (EAC) = Present worth / ((1-1/(1+R)^n)/R) = 180889.7/((1-1/(1+12%)^10)/12%)

Equivalent Annual Cost (EAC) = 32014.61 or $32015

So,

Correct Answer for a: (a) PWR = $124446 PWs = 180889

Correct Answer for b: (c) AWR = $34522    AWS = $32016

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