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)
380 000	29 500	25	42 000	380

1. If the owner can sell the electricity at 30 c/kWh,
2. 1. calculate the lifecycle cost of the technology over an assessment period of 25 years at a real discount rate of 5%                                
   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.
3. 1. What is the Levelised Cost of Electricity (LCOE) (in cents/kWh) for this case, with a salvage value of zero, and calculated using method 1 (that is, finding the constant price to charge for the electricity that gives a zero NPV at a real discount rate of 5% over 25 years)?
   2. Calculate this LCOE (add annualised capital cost to the annual operating cost, and divide by annual electricity supplied), and show that this gives the same value as method 1. Give values for the annualised capital cost and annual operating cost in your answer. (The annualised capital cost formula is the inverse of the Uniform Series Present Worth Factor formula.)

4. Using the figures in the table above 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.

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.

I would appreciate if you can solve any part of this question.

Answer 1

		LIFECYCLE COST
	Pmt	Annual Operating Cost	$29,500
	Rate	Discount Rate	5%
	Nper	Number of years	25
	Fv	Salvage value (Future value)	$42,000
	PV	Present Value of Net Annual Costs	$403,369	(Using PV function of excelwith Rate=5%, Nper=25, Pmt=-29500,Fv=42000)
	I	Initial Capital Cost	$380,000
	LC=PV+I	Life Cycle Cost	$783,369
	E	Annual Electricity supply(MWh)	380
	LE=E*25	Lifetime supply of electricity(MWh)	9500
	CMWh=LC/LE	Cost Per MWh	$82.46
	CKWh=CMWh/1000	Cost Per KWh	$0.08
		Cost in Cents/KWh	8	(0.08*100)
		LEVELISED COST OF ELECTRICITY-METHOD I
		Assume Salvage value=0
	Pv	Cost of capital	$380,000
	Rate	Discount Rate	5%
	Nper	Number of years	25
	PMT	Annual Cash Inflow Needed for zero NPV	$26,961.93	(Using PMT function of excelwith Rate=5%, Nper=25, Pv=-380000)
	AOC	Annual Operating Cost	$29,500
	LAC=PMT+AOC	Levelised annual cost	$56,461.93
		Annual Electricity supply(MWh)	380
	E	Annual Electricity supply in KWh	380000
	LCOE=LAC/E	Levelised Cost of electricity/Kwh	$0.15
		Levelised Cost of electricity(Cent/Kwh)	15
		LEVELISED COST OF ELECTRICITY-METHOD II
	Pv	Capital Cost	$380,000
	Rate	Discount Rate	5%
	Nper	Number of years	25
	PMT	Annualized Capital Cost	$26,961.93	(Using PMT function of excelwith Rate=5%, Nper=25, Pv=-380000)
	AOC	Annual Operating Cost	$29,500
	LAC=PMT+AOC	Levelised annual cost	$56,462
	E	Annual Electricity supply in KWh	380000
	LCOE=LAC/E	Levelised Cost of electricity/Kwh	$0.15
		Levelised Cost of electricity(Cent/Kwh)	15