Question

A new renewable energy generation system has a life-time of 10 years. It is assumed that the salvage value of the system at the end of the 10 years' life-time is negligible. The initial (Present time) investment of the system costs $50,000. The manufacturer agrees to maintain the system every year over the 10 years' life-time with a uniform annual maintenance fee of $1000/year. At the end of the 5th year, a key component should be replaced, which will cost $10,000. Each year, this renewable energy system will generate 5,000 kWh electricity. It is assumed that the electricity price in the first year is $1/kWh, with an annual escalation rate of 3%. The interest rate is 5%.

Please investigate that how the "interest rate" and its variation will affect the results of

(1) The present value of the total maintenance fee over 10 years' life-time.

(2) The present value of the total saved electricity cost over 10 years' life-time.

(3) The net present value of this system, by considering all the cash flows mentioned in the question statement.

(4) The deposited money per year if the replacement cost $10,000 of the key component at the end of the 5th year is accumulated by depositing a fixed amount of money per year in the first 5 years.

and discuss and comment on their sensitivity. For example, the "interest rate" varies +/- 0~0.03 based on the original 0.05 (i.e. the interest rate varies in the range between 2%~8%).

Answer 1

(1) Computation of present value of the total maintenance fee over 10 years' life-time

Present value = Maintenance fees p.a. * PVAF (5%, 10 years)

= $1000 * 7.7217

= $7,722

(2) Computation of present value of the total saved electricity cost over 10 years' life-time

(3) Computation of net present value of this system, by considering all the cash flows

Net present value = Initial investment + Present value of maintenance fee + Present value of key component replaced - Present value of saved electricity cost

= $50,000 + $7,722 + ($10,000*0.7835) - $45,050

= $20,507 (Cost)

(4) Amount of deposit = Replacement amount / PVAF (5%, 5 years)

= $10,000 / 4.3295

= $2,310

I have answered 4 sub-parts fully. I think there is some missing part after end of 4th part "and discuss and comment on their sensitivity. For example, the "interest rate" varies +/- 0~0.03 based on the original 0.05 (i.e. the interest rate varies in the range between 2%~8%)".

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