A. The maintenance on a machine is expected to be $155 at the end of the...

A. The maintenance on a machine is expected to be $155 at the end of the first year, then increasing by $35 each year for the next 7years, what sum of money would need to be set aside now and pay the maintenance for the 8-year period ? Assume 10% interesrt.

B. what is the uniform annual equivalent maintenance cost for the above machine ? compute equivalent for A for the maintenance cost.

pls draw the cash flow and show the explantion for the workings.

Solutions

Expert Solution

Ans. Cost of machine in year,

Year 1, CF1 = $155

Year 2, CF2 = $190

Year 3, CF3 = $225

Year 4, CF4 = $260

Year 5, CF5 = $295

Year 6, CF6 = $330

Year 7, CF7 = $365

Year 8, CF8 = $400

a) Present value of these cashflows at 10% interest rate,

PV = CF1/(1+0.10) + CF2/(1+0.10)^2 + CF3/(1+0.10)^3 + CF4/(1+0.10)^4 + CF5/(1+0.10)^5 + CF6/(1+0.10)^6 + CF7/(1+0.10)^7 + CF8/(1+0.10)^8

=> PV = $1387.92

Thus, $1387.92 must be set aside now to pay for the maintainance cost for 8 years.

b) For annual equivalent cost (A) we will use formula for present value of the annual equivalent cash flow having present value (= 1387.92), interest rate 10% and 8 years.

=> Present value = 1387.92 = A*[(1-1/(1+0.10)^8)/0.10]
=> A = $260.157

Thus, annual equivalent cost is $260.157

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Thank You

Rahul Sunny answered 1 year ago

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