Question

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 worth of owning and operating this particular machine if interest is 5%?

Answer 1

The equivalent uniform annual worth of the machine is calculated by converting the initial cost, maintenance, major service, overhaul costs, and salvage value to their present values and then transforming these present values into a uniform annual series over the 10-year life at a 5% interest rate.

Step-by-step explanation:

To calculate the equivalent uniform annual worth (EUAW) of owning and operating the machine given the initial cost, maintenance, service, overhaul costs, salvage value, and an interest rate, we need to convert all costs and the salvage value to their equivalent annual amounts taking into account the time value of money using the concept of present worth and annual worth. The step-by-step calculation involves finding the present worth of all costs and converting them into an equivalent annual series over the useful life of the machine using the given interest rate of 5%.

The initial cost, maintenance costs, costs of major services and overhaul, and eventual salvage value must all be considered at their respective times and converted to present values using the formula PV = FV /
`(1+i)^n`, where PV is present value, FV is future value, i is the interest rate per period, and n is the number of periods. Then the EUAW can be found using the formula EUAW = PV(A/P, i, n), where (A/P, i, n) is the capital recovery factor.

Breakdown of costs:

• Initial cost (time 0): -$150,000
• Annual maintenance cost: -$2,500 (for 10 years)
• Major service at the end of Year 4: -$20,000
• Major service at the end of Year 8: -$10,000
• Overhaul at the end of Year 5: -$45,000
• Salvage value at the end of Year 10: $30,000

All values in the future need to be brought to present value before calculating EUAW. Then all present worth values are converted into a uniform annual series across the 10 years of the machine's life. The EUAW is found by summing all these annual equivalents.

Answer 2

the equivalent uniform annual worth of owning and operting the machien at 5% diiscount rate:

$17,610.88

Step-by-step explanation:

we will bring each exceptional value to present date and then calcualte the PTM of that

First step:

present value of eahc lump sum:

`(Maturity)/((1 + rate)^(time) ) = PV`

overhaul:

Maturity 45,000

time 5

`(45000)/((1 + 0.05)^(5) ) = PV`

PV 35,258

Services:

20,000 year 4 = 16,454.05

10,000 year 8 = 6,768.39

salvage value

30,000 10 years = 18,417.40

total present worth:

150,000 + 6,768.39 + 16454.05 + 35258 - 18,417.40 = 190,063.04

now we calcualtethe PTM of this present value

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $190,063.04

time 10

rate 0.05

`190063.04 / (1-(1+0.05)^(-10) )/(0.05) = C\\`

C $ 15,110.881

we add the 2,500 maintenance cost

$17,610.88

This will be the equivalent uniform annual worth of owning and operting the machien at 5% diiscount rate