1 A renewable energy electricity supply technology has the following characteristics: Capital cost Annual Lifetime {years} Salvage iralue_ Annual operating cost electricity [$1 supplied {main} 550ml: 33am 45w: 1.1 1.2 1.3 1.4 1.5 1.6 If the owner can sell the electricity at 30 ckah. what is the simple payback period for the technology? Would the owner invest in this technology it (s}he set a strict maximum six-year payback period? 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 ve-year payback period? What is the Present Worth (Net Present Value} of the investment over a i E assessment period and real discount rate of 5% when the electricity price is 30 ckah'? 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 3!] ckah'? Would the owner invest if their threshold real rate of return was 2%? 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 xed capital payment (K) at the beginning of year 1 and equal constant-dollar annual net benets over this period (B). Hint: the simple payback period will be KER. Use the equation for IR 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.? With reference to your answers to 1.1 to 1.6, discuss briey the limitations of the simple payback period as an evaluation criterion and why this Sustainable Energy Systems and Design l'leETE 129 can disadvantage renewable energy technologies compared to conventional fossil fuel power supply (at least EDD words). 2.1 Using the same gures as in question 1, calculate the life-cycle 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 centscWh} supplied by the technology over its lifetime at this real discount rate. 3.1 What is the Levelised Cost of Electricity (LCDE) (in centskah) for this case, with a salvage value of zero, and calculated using method 1 presented in lecture 3 (that is, nding the constant price to charge for the electricity that gives a zero NPV at a real discount rate of 5% over 25 years)? (Note: LCOE will not be covered in lectures until week 3.) 3.2 Calculate this LCGE using method 2 presented in lecture 3 (add aunualised 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 aunualised capital cost and annual operating cost in your answer. (The aunualised capital cost formula is the inverse of the Uniform Series Present Worth Factor formula presented in lecture 2.) Using the gures in the table in Q] 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. Qnthebgsispf these graphs and the lectures presented, critically discuss the relative inuence 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. 3110 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