Question

A small aerospace company is evaluating two alternatives: the purchase of an automatic-feed machine and a manual-feed machine for a product’s finishing process. The auto-feed machine has an initial cost of $23,000, an estimated salvage value of $4,400 and a predicted life of 10 years. One person will operate the machine at a cost of $12 an hour. The expected output is 8 tons per hour. Annual maintenance and operating cost is expected to be $3,500.
The manual-feed machine has a first cost of $8,000, no expected salvage value, a 5-year life and an output of 6 tons per hour. However, three workers will be required at $8 an hour each. The machine will have an annual maintenance and operation cost of $1,500. All invested capital is expected to generate a market return of 10% per year before taxes.
How many tons per year must be finished in order to justify the higher purchase cost of the auto-feed machine? If a requirement to finish 2,000 tons per year is anticipated, which machine should be purchased?

Answer 1

Given data

initial cost 23000 8000

useful life 10year 5year

AMC 3500 1500

salvage value 4400 0

operating labor cost 12 24

production/hr 8 6

interest rate 10%

so for machine 1

AE1(10%)= 23000*(A/p,i,n)+3500 -4400*(A/F,i,n)

= 23000*0.1627+3500-4400*0.0627= 6948.2 or 6948 approx

For Mechine2

AE2(10%)= 8000*0.2638+1500-0

= 3610

so the first machine is costlier then the 2nd one. so we will prefer 2nd machine over 1st one

the cost gap between two is 6948-3610=3330

The gap between production level is 8-6=2

so 3330/2=1665

so to tray that level of out put per year for both

Mechine 1= 1665/8=208.125

cost= 208.125*12= 2497.5 so final cost = 6948+2497.5= 9445.5or 9446

Mechine 2= 1665/6=277.5

cost= 277.5*24=6660, so final cost= 3610+6660=10270

so to be purchased the machine 1 have to produce minimum 1665 ton per year.

Now if the target is 2000 ton per year for both then for machine one the cost will be

2000/8tonper hr=250 hrs

per hrs 12 cost = 250*12=3000 cost for labour charge

so total cost for producing 2000 ton/year= 6948+3000=9948

for Mechine 2 the production hours will be

2000/6= 333.33hrs

labour cost= 333.33*24 =7999.92, 8000 approximately

so the total cost of production for 2000 ton= 3610+8000=11610

so when we produce 2000 ton per year definitely we will choose machine 1 upon machine 2.