1 A renewable energy electricity supply technology has the following characteristics:

Capital cost ($) | Annual operating cost ($) | Lifetime (years) | Salvage value ($) | Annual electricity supplied (MWh) |

145 000 | 17 000 | 20 | 35 000 | 190 |

1.1 If the owner can sell the electricity at 32 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 maximum three-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 two-year payback period?

1.4 What is the Present Worth (Net Present Value) of the investment over a 20 year assessment period and real discount rate of 5% when the electricity price is 32 c/kWh?

1.5 What is the real internal rate of return for the owner of this technology over a 20-year assessment period when the electricity price is 32 c/kWh? Would the owner invest if their threshold real rate of return was 20%

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).

2

2.1 Using the same figures as in question 1, calculate the lifecycle cost of the technology over an assessment period of 20 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 Assuming there is no price on carbon, what externalised costs are likely to be excluded from this LCOE? If a Clean Energy Target is introduced as recommended by the Finkel Report (2017), how would the inclusion of externalised costs be changed? (To be covered in week 3 lecture.)

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.