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In: Economics

An Organization buys a machine for $25,000. The annual cost ofmaintaining the machine is $500...

An Organization buys a machine for $25,000. The annual cost of maintaining the machine is $500 per year for the first 5 years (End of Year 1 thru End of Year 5) and then it increases to $750 for the next 5 years (Year 6 thru Year 10). Consider all cash flows to be end of year cash flows. For an interest rate of 8% per year compounded yearly, find the annual maintenance cost of the machine and the present worth of the total cost


Solutions

Expert Solution

Present worth is calculated as:[Annual Cost / (1 + Rate of Interest)^Year]

Present worth of cost in 1st year: [500 / 1.08^1] = 462.96

Present worth of cost in 2nd year: [500 / 1.08^2] = 428.67

Present worth of cost in 3rd year: [500 / 1.08^3] = 396.91

Present worth of cost in 4th year: [500 / 1.08^4] = 367.91

Present worth of cost in 5th year: [500 / 1.08^5] = 340.29

Present worth of cost in 6th year: [750 / 1.08^6] = 472.62

Present worth of cost in 7th year: [750 / 1.08^7] = 437.61

Present worth of cost in 8th year: [750 / 1.08^8] = 405.20

Present worth of cost in 9th year: [750 / 1.08^9] = 375.18

Present worth of cost in 10th year: [750 / 1.08^10] = 347.39

Present value of cash is sum of all present value whose sum is 4,034.38

Annual equivalent Cost: Present value of Cost / {[1 - (1 + r)^-n] / r}

where r = 0.08 and n = 10

Annu equivalent cost: 4,034.38 / {[1 - 1.08^-10] / 0.08} = 601.24

Rahul Sunny answered 2 years ago
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