Question

1 A renewable energy electricity supply technology has the following characteristics: Capital cost ($) Annual operating cost ($) Lifetime (years) Salvage value ($) Annual electricity supplied (MWh) 300 000 27 200 25 40 000 400 1.1 If the owner can sell the electricity at 25 c/kWh, what is the simple payback period for the technology? 1.2 Would the owner invest in this technology if (s)he set a strict maximum four-year payback period? 1.3 What would the selling price for the electricity have to rise to for the owner to invest in the technology if (s)he set a maximum three-year payback period? 1.4 What is the Present Worth (Net Present Value) of the investment over a 25 year assessment period and real discount rate of 5% when the electricity price is 25 c/kWh? 1.5 What is the real internal rate of return for the owner of this technology over a 25-year assessment period when the electricity price is 30 c/kWh? Would the owner invest if their threshold real rate of return was 30%? 1.6 Derive an analytical relationship between simple payback period and internal rate of return (IRR) over a 15-year assessment period for a project with a single fixed capital payment (K) at the beginning of year 1 and equal constant-dollar annual net benefits over this period (B). Hint: the simple payback period will be K/B. Use the equation for IRR given in the week 2 lecture. Then solve this equation iteratively using Excel for payback periods between 1 and 15, and plot the corresponding graph of IRR vs Payback Period 1.7 With reference to your answers to 1.1 to 1.6, discuss briefly the limitations of the simple payback period as an evaluation criterion and why this can disadvantage renewable energy technologies compared to conventional fossil fuel power supply (at least 200 words). ….Continued on next page 2 2.1 Using the same figures as in question 1, calculate the lifecycle cost of the technology over an assessment period of 25 years at a real discount rate of 5% 2.2 Calculate the average unit cost of the power in present value terms (in cents/kWh) supplied by the technology over its lifetime at this real discount rate. 2.3 What is the corresponding Levelised Cost of Electricity (LCOE) (in cents/kWh)? Why is this value higher than that obtained in question 2.2? (Note: LCOE will not be covered in lectures until week 3.) 2.4 How would the competitiveness of this electricity from a renewable energy source be changed if there was (a) a price on carbon, and (b) a Clean Energy Target? 3 Using the figures in the table in Q1 as a baseline, work out an expression for Present Worth with real discount rate, assessment period, salvage value, and electricity price as independent variables. Then changing just one variable at a time (other things being kept equal) plot graphs of Present Worth versus each of these variables. Use a range of assessment periods up to the lifetime of the technology. Explore the effects of both positive and negative salvage values. On the basis of these graphs and the lectures presented, critically discuss the relative influence of these variables on Present Worth, and hence the more general implications for the economic assessment of renewable energy technologies. You may wish to relate variations in electricity price to carbon pricing. 300 words minimum. Note: to simplify the calculation of present worth, for assessment periods less than the lifetime, neglect the residual value of the technology, and assume salvage values are only incurred at the end of the lifetime of the technology.

Answer 1

		Initial cash flow:
		Capital cost	$300,000
		Annual Cash flow:
		Annual operating cost	$27,200
		Number of years(Lifetime)	25
		Annual electricity supply (MWh)	400
		Terminal Cash flow:
		Salvage value	$40,000
	1.1	CALCULATION OF SIMPLE PAYBACK PERIOD
		Selling price per KWh	$0.25
	A	Annual Cash inflow=0.25*400000	$100,000
	B	Annual Cash out flow(Operating cost)	$27,200
	C=A-B	Net annual Cash inflow	$72,800
	D=300000/C	Simple Payback period(Initial cash flow/72800)	4.120879121	Years
		Simple Payback period	4.1	Years
	1.2
		Under Strict maximum payback period of 4 years;
		Owner will not invest in this technology	Rejected
	1.3	Maximum 3 year payback period:
		Annual net cash inflow required=300000/3	$100,000
		Annual revenue required=100000+27200	$127,200
		Selling price required=127200/400000	$               0.32	per KWh
		Selling price required=32 cents/KWh
	1.4	CALCULATION OF NET PRESENT VALUE
		Net Present value= Sum of (Present Value(PV) of cash flows)
		Present Value (PV) of Cash flow=(Cash flow)/((1+i)^N)
		i=discount rate=5%=0.05
		N=Year of the cash flow
		Yearwise cash flow and PV of cash flows are given below:
		N	A	B=A/(1.05^N)
		Year	Cash flow	PV of Cash flow)
		0	($300,000)	-300000
		1	$72,800	69333.33333
		2	$72,800	66031.74603
		3	$72,800	62887.37717
		4	$72,800	59892.74016
		5	$72,800	57040.70492
		6	$72,800	54324.48088
		7	$72,800	51737.60083
		8	$72,800	49273.90556
		9	$72,800	46927.5291
		10	$72,800	44692.88486
		11	$72,800	42564.65225
		12	$72,800	40537.76404
		13	$72,800	38607.39433
		14	$72,800	36768.94698
		15	$72,800	35018.04474
		16	$72,800	33350.5188
		17	$72,800	31762.39886
		18	$72,800	30249.90367
		19	$72,800	28809.43207
		20	$72,800	27437.55435
		21	$72,800	26131.00415
		22	$72,800	24886.67062
		23	$72,800	23701.59106
		24	$72,800	22572.94387
	(72800+40000	25	$112,800	33310.15265
			Total	737851.2753
		Net Present value= Sum of (Present Value(PV) of cash flows)=		$             737,851
	1.5	CALCULATION OF INTERNAL RATE OF RETURN WITH PRICE=30cent/KWh
		Annual Sales Revenue with 30 cents per KWh	$        120,000
		Annual Cash inflow(120000-27200)=	$          92,800
		Year	Cash flow
		0	($300,000)
		1	$92,800
		2	$92,800
		3	$92,800
		4	$92,800
		5	$92,800
		6	$92,800
		7	$92,800
		8	$92,800
		9	$92,800
		10	$92,800
		11	$92,800
		12	$92,800
		13	$92,800
		14	$92,800
		15	$92,800
		16	$92,800
		17	$92,800
		18	$92,800
		19	$92,800
		20	$92,800
		21	$92,800
		22	$92,800
		23	$92,800
		24	$92,800
	(92800+40000)	25	$132,800
		Internal Rate of Return (IRR)	30.90%	Using IRR function of excel over the cash flow)
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