A machine has the initial cost at time zero of 150000 an ann

A machine has the initial cost (at time zero) of $150,000, an annual maintenance cost of $2,500, and a salvage value of $30,000. The useful life of the machine is 10 years. At the end of Years 4 and 8, it requires a major services, which costs $20,000 and $10,000, respectively. At the end of Year 5, it will need to be overhauled at a cost of $45,000. What is the equivalent uniform annual cost of owning and operating this particular machine if interest is 5.0%?

Solution

ANSWER:

Initial cost = $150,000

Annual maintenance cost = $2,500

n =10 years

major service cost at the end of year 4 = $20,000

major service cost at the end of year 8 = $10,000

overhauling cost at the end of year 5 = $45,000

i = 5%

salvage value = $30,000

pw = initial cost + annual maintenance cost(p/a,i,n) + major service cost at the end of year 4(p/f,i,n) + major service cost at the end of year 8(p/f,i,n) + overhauling cost at the end of year 5(p/f,i,n) + salvage value(p/f,i,n)

pw = 150,000 + 2,500(p/a,5%,10) + 20,000(p/f,5%,4) + 10,000(p/f,5%,8) + 45,000(p/f,5%,5) + 30,000(p/f,5%,10)

pw = 150,000 + 2,500 * 7.722 + 20,000 * 0.8227 + 10,000 * 0.6768 + 45,000 * 0.7835 + 30,000 * 0.6139

pw = 150,000 + 19,305 + 16,454 + 6,768 + 35,257.5 + 18,417

pw = 246,201.5

now euac = pw(a/p,i,n)

euac = 246,201.5(a/p,5%,10)

euac = 246,201.5 * 0.1295

euac = $31,883.09

so the equivalent uniform annual cost is $31,883.09