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

Answer:

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

$17,610.88

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:

$\frac{Maturity}{(1 + rate)^{time} } = PV$

overhaul:

 Maturity 45,000

time  5

$\frac{45000}{(1 + 0.05)^{5} } = PV$

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

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $190,063.04

time 10

rate 0.05

$190063.04 \div \frac{1-(1+0.05)^{-10} }{0.05} = C$

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