Economics Flashcards
What is the present value of the following cash flows:
(i) £2m occurring in 8years time at 5% discount rate;
(ii) £500 in 25 years time at 15% discount rate;
(iii) £1 billion occurring in 50 years time at 12% discount rate
Simple use of the present value equation. For case (i): PV = 2,000,000/(1+0.05)8 = £1,353,679. Similarly (ii) £15 and (iii) £3,460,181; these are quite low values which reflect long time delays and fairly high discount rates.
What is the present value total of £500,000 annual cash flows occurring for the next 20 years at 8% discount rate? If the cash flows started in year 2 and ran for 19 years, how could this be calculated easily?
Can be calculated using table, geometric sum or using annuity equation. Annuity used here: PV=500,000
[(1/0.08)-1/(0.08×(1+0.08)20)] = £4,909,074. If the first of
the cash flows is omitted this requires this to be subtracted from the annuity PV, i.e. £4,909,074 – 500,000/(1+0.08) = £4,446,111.
Using a discount rate of 10%, determine the NPV and levelised cost of energy for the following cases (use a tabular approach and compare with annuity method):
(i) Onshore wind farm: 50 MW capacity, 30% capacity factor, 20 year lifetime, capital costs £900/kW, operating costs £2.5m/year, decommissioning costs £5 m, energy sales price £80/MWh.
(ii) Hydropower plant: 500 MW capacity, 25% capacity factor, 50 year lifetime, capital costs £1800/kW, operating costs £27m/year, energy sales price £130/MWh.
In both cases the tabular approach would be done in the same way as those in the notes – the slight difference in (i) would be the extra decommissioning cost. Here
the annuity approach is taken. The process is to work out the capital costs then work out present value (PV) of all costs, using an annuity for the 20 years operating
costs. The next step is to work out annual energy which allows annual revenue to be calculated. The PV of 20 years of each is then needed. The NPV and LCOE can
then be calculated. The calculation for (i) wind farm is shown in full and a summary for the hydro plant (ii).
(i) Wind farm:
Capital costs, C = 50MW×£900/kW×1000 kW/MW = £45×106. PV(costs) = 45×106 + 2.5×106 [(1/0.1)-1/(0.1×(1+0.1)20)] + 5×106 / (1+0.1)20 =
45,000,000 + 21,283,909 + 743,218 = £67,027,127.
Annual production, E = Capacity × capacity factor × hours = 50 MW × 30% × 8760 = 131,400 MWh. Annual revenue R = E × P = 131,400 MWh × £80/MWh = £10,512,000.
PV(revenue, 20 years) = £10,512,000[(1/0.1)-1/(0.1×(1+0.1)20)] = £89,494,582 NPV = PV(revenue) – PV(costs) = 89,494,582 – 67,027,127 = £22,467,454 PV(energy, 20 years) = 131,400[(1/0.1)-1/(0.1×(1+0.1)20)] = 1,118,682 MWh
LCOE = PV(costs) / PV(energy) = £67,027,127 / 1,118,682 MWh = £59.9/MWh
(ii) Hydro:
Capital costs = £900m; PV(costs) = £1,167.7m; Annual energy = 1,095GWh; annual revenue = £142.35m; PV(revenue) = £1,411.4m; NPV = £243,7m; LCOE = £107.6/MWh.
The capital cost of a technology is currently £5m/MW with a deployed capacity of 2 GW. If the learning rate is 5%, what would you expect the capital cost to be when deployed capacity has increased to 4, 10 and 20 GW? If the learning rate is doubled what would you expect the cost to be at 20 GW?
A matter of using relevant values in the learning rate equation, e.g., reduction in cost moving from 2 to 4 GW deployed, CF = £5m(4/2)ln(1-0.05)/ln 2 = £4.750m. At 10 GW, CF = £4.439m and 20 GW, CF = £4.217m. Doubling the learning rate to 10% gives CF = £3.523m at 20 GW.
What are the main categories of cost used in investment appraisal of generation?
Capital cost, operating costs (including fuel), decommissioning.
What determines the revenue of a generator?
Volume of sales and the price applying to each unit sale. Expanding on this would include consideration of whether generator is selling direct into the market or via a power purchase agreement.
What is the discount rate intended to reflect?
Inflation, compensation for deferring expenditure (i.e. opportunity cost), minimum return levels, risk applicable to the investment
What is the CAPM and why is it relevant to the economics of renewable energy sources?
CAPM describes the relationship between risk and expected investor returns. Higher risk implies higher required returns. Some renewables are high risk so appraisal should be conducted with higher discount rates.
The same discount rate is often applied to different technologies for levelised cost estimations: what are the limitations to this approach?
The same discount rate implies the same risk profile applies to all technologies. This is self evidently untrue and a particular problem where fuel-cost technologies
are compared against largely capital cost ones.
What is external cost and why is it relevant to renewables policy?
External costs are costs that are not borne directly by the investor. Typically these are social, environmental or ‘knock-on’ economic costs elsewhere in the economy.
Renewables tend to have low external costs despite current relatively high direct economic costs.
Describe briefly how ROCs, FITs and CfDs work
These are very brief and greater detail would be expected. ROCs are an obligation on suppliers with price arising from extent to which obligation volumes met and will vary over time. FITs are direct subsidies paid out of taxation and the value is fixed in advance. Both now discriminate by technology. CfDs provide a stable payment to low carbon generation by hedging market prices.
