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a machine that have the

equivalent A manufacturing equipment has the following costs. The MARR is 10% compounded sen annualy. It is an acceptable alternative? Compu ethe annual worth First cost: $70,000 Semiannual operating cost: 8,000 Semiannual income: 18,000 Semiannual income gradient: 100 Salvage value: 10,000 Life in years: 4 years a. EAW-$54 b. EAW $741 G. EAW $541 d.EAW $44
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Answer #1

ANSWER:

first cost = $70,000

I = 10% per year or 5% per semi annual year

N = 4 years or 8 semi annual years

1st semiannual income = $18,000

2nd semiannual income = 1st semiannual income + semiannual income gradient = $18,000 + $100 = $18,100

3rd semiannual income = 2nd semiannual income + semiannual income gradient = $18,100 + $100 = $18,200

4th semiannual income = 3rd semiannual income + semiannual income gradient = $18,200 + $100 = $18,300

5th semiannual income = 4th semiannual income + semiannual income gradient = $18,300 + $100 = $18,400

6th semiannual income = 5th semiannual income + semiannual income gradient = $18,400 + $100 = $18,500

7th semiannual income = 6th semiannual income + semiannual income gradient = $18,500 + $100 = $18,600

8th semiannual income = 7th semiannual income + semiannual income gradient = $18,600 + $100 = $18,700

semi annual operating cost = $8,000

benefits in 1st semi annual year = 1st semi annual income - semi annual operating cost = $18,000 - $8,000 = $10,000

benefits in 2nd semi annual year = 2nd semi annual income - semi annual operating cost = $18,100 - $8,000 = $10,100

benefits in 3rd semi annual year = 3rd semi annual income - semi annual operating cost = $18,200 - $8,000 = $10,200

benefits in 4th semi annual year = 4th semi annual income - semi annual operating cost = $18,300 - $8,000 = $10,300

benefits in 5th semi annual year = 5th semi annual income - semi annual operating cost = $18,400 - $8,000 = $10,400

benefits in 6th semi annual year = 6th semi annual income - semi annual operating cost = $18,500 - $8,000 = $10,500

benefits in 7th semi annual year = 7th semi annual income - semi annual operating cost = $18,600 - $8,000 = $10,600

benefits in 8th semi annual year = 8th semi annual income - semi annual operating cost = $18,700 - $8,000 = $10,700

salvage value = $10,000

pw = initial investment + benefits in 1st semi annual year(p/f,i,n) + benefits in 2nd semi annual year(p/f,i,n) + benefits in 3rd semi annual year(p/f,i,n) + benefits in 4th semi annual year(p/f,i,n) + benefits in 5th semi annual year(p/f,i,n) + benefits in 6th semi annual year(p/f,i,n) + benefits in 7th semi annual year(p/f,i,n) + benefits in 8th semi annual year(p/f,i,n) + salvage value(p/f,i,n)

pw = -70,000 + 10,000(p/f,5%,1) + 10,100(p/f,5%,2) + 10,200(p/f,5%,3) + 10,300(p/f,5%,4) + 10,400(p/f,5%,5) + 10,500(p/f,5%,6) + 10,600(p/f,5%,7) + 10,700(p/f,5%,8) + 10,000(p/f,5%,8)

pw = -70,000 + 10,000 * 0.9524 + 10,100 * 0.907 + 10,200 * 0.8638 + 10,300 * 0.8227 + 10,400 * 0.7835 + 10,500 * 0.7462 + 10,600 * 0.7107 + 10,700 * 0.6768 + 10,000 * 0.6768

pw =-70,000 + 9,091 + 9,160.7 + 8,810.76 + 8,473.81 + 8,148.4 + 7,835.1 + 7,533.42 + 7,241.76 + 6,768

pw = $3,495.95

aw = pw(a/p,i,n)

aw = $3,495.95(a/p,15%,8)

aw = 3,495.95 * 0.1547

aw = $540.35 or $541 (approx)

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