Question

Question 2.

A wind farm generating 800 GWh per year has a total capital cost of £270 million. Assume both items of data are to three significant figures. The capital is to be repaid over a period of 20 years at an interest rate of 10%. Table 1 Annual repayment per £1 000 of capital Repayment period (years) Interest rate 6% 8% 10% 12% £98.95 $112.98 €127.82 €143.39 £92.36 €106.70 £121.93 £137.94 £87.18 £101.85 £117.46 £133.88 £83.05 £98.03 £114.01 £130.81 £79.68 £94.98 €111.30 €128.46

Please show all workings out. thank you

Answer 1

1 GWH=1 Million kWH
1 Pound=100 Pence
a. Annual Capital Repayments
Total Capital cost	£270	M
Repayment period	20
Interest Rate	10%
Repayment for £1000 from table	£117.46
Annual Capital Repayment	£31.71	M
	(=117.46*270/1000)
b. Annual O&M Cost
Annual O&M Cost (% of annual capital repayment)	4%
Total Annual Cost	£1.27	M	=31.71*4%
Units generated per year (GWH)	800
Units generated per year (kWH)	800	M	=800*1000000
Unit cost Pence per Kwh	£0.16	Pence	=1.27/800 *100 Pence
c. Reduced Unit costs
(1) 20% reduction in capital cost
Total Capital cost	£216	M	=270*(1-20%)
Repayment period	20
Interest Rate	10%
Repayment for £1000 from table	£117.46
Annual Capital Repayment	£25.37	M
	(=117.46*216/1000)
Annual O&M Cost (% of annual capital repayment)	4%
Total Annual Cost	£1.01	M	=25.37*4%
Units generated per year (GWH)	800
Units generated per year (kWH)	800	M	=800*1000000
Unit cost Pence per Kwh	£0.13	Pence	=1.01/800 *100 Pence
(2) 20% increase in repayment period
Total Capital cost	£270	M
Repayment period	24		=20*(1+20%)
Interest Rate	10%
Repayment for £1000 from table	£111.30
Annual Capital Repayment	£30.05	M
	(=111.30*270/1000)
Annual O&M Cost (% of annual capital repayment)	4%
Total Annual Cost	£1.20	M	=30.05*4%
Units generated per year (GWH)	800
Units generated per year (kWH)	800	M	=800*1000000
Unit cost Pence per Kwh	£0.15	Pence	=1.20/800 *100 Pence
(3) 20% Reduction in Interest Rate
Total Capital cost	£270	M
Repayment period	20
Interest Rate	8%		=10%*(1-20%)
Repayment for £1000 from table	£101.85
Annual Capital Repayment	£27.50	M
	(=101.85*270/1000)
Annual O&M Cost (% of annual capital repayment)	4%
Total Annual Cost	£1.10	M	=27.50*4%
Units generated per year (GWH)	800
Units generated per year (kWH)	800	M	=800*1000000
Unit cost Pence per Kwh	£0.14	Pence	=1.10/800 *100 Pence