# EE535: Renewable Energy: Systems, Technology & Economics

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EE535: Renewable Energy: Systems, Technology & Economics
Project Financing

Cost of Energy Drivers Capital Costs (and the cost of borrowing the money) Fuel Costs Operation and Maintenance (O&M) Costs Decomissioning Costs

Simple Payback Time Payback Time = Number of years taken to recover capital outlay Simple Annual Method Calculate the cost per unit energy on an annual basis Capital is first annuitized (considered to be repaid in equal amounts over the project lifetime) Average fuel and O&M costs added to annual payments Average Cost of Energy: Cost per unit of energy = (annual capital repayment + average running costs) / average annual energy output

Discounted Cash Flow For capital intensive power projects, analysis based on discounted cash flow (DCF) is typically used Related to the time preference for cash We can forego the use of a euro today in order to have a euro plus an additional sum in the future A sum of money today (e.g. €100 today has a future value of €260). OR The present value of €260 in 10 years time at a certain interest rate is only €100). Inflation must also be included Real Interest Rate = Monetary Interest Rate – Rate of Inflation Value of a sum in n years at a discount rate of r is given by: Vn = Vp(1 + r)n Present value of a sum received or paid in the future is given by: Vp = Vn / (1 +r)n

Choice of Discount Rate

Annuitized Value of Capital
The Discount Rate (or real interest rate) is the rate used to discount future cash flows to their present values is a key variable in the DCF process. Determined by the company in the light of risk, inflation, etc The annuitized value of capital costs (annual repayment in € ) (or equivalent annual cost EAC) for various discount rates and capital repayment periods is calculated by first calculating the loan repayment factor : A = (1 – 1/(1+r)n) / r EAC = NPV / A Where NPV is the Net Present Value, which is the summation of all the present values of future income and expenditures NPV = Rt / (1 + r)t Where Rt is the net cashflow at time t, r is the discount rate

Net Present Value For projects that take several years to build and may be subject to periodic refurbishment, a full net present value calculation is required Process: Itemise the capital and running costs for each year of the project life Calculate the separate Present Value of all these annual costs using an appropriate discount rate, and sum to give the NPV Itemise the output for each year over the project life Calculate the NPV of all these annual outputs, expressed usually in kWh Calculate the unit cost in pence per kWh as: Net Present Value of Costs (cent) / Net Present Value of Output (kWh)

Net Present Value NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if Rt is a positive value, the project is in the status of discounted cash inflow in the time of t. If Rt is a negative value, the project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV could be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. A decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation. NPV > 0 Adds Value to Company NPV < 0 Subtracts Value from Company NPV = 0 the investment would neither gain nor lose value for the firm

Exercise A company must decide whether to introduce erect a new wind turbine. The project will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of €100,000 Other cash outflows for years 1-6 are expected to be €5,000 per year. Cash inflows are expected to be €30,000 each for years 1-6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. Is this a good investment for the company?

Solution NPV = € 8,881.52 is positive so probably a good investment!
Year Cashflow Present Value ( ) / (1 +0.1)^0 1 ( ) / (1 +0.1)^1 22727 2 ( ) / (1 +0.1)^2 20661 3 ( ) / (1 +0.1)^3 18783 4 ( ) / (1 +0.1)^4 17075 5 ( ) / (1 +0.1)^5 15523 6 ( ) / (1 +0.1)^6 14112 NPV 8882 NPV = € 8, is positive so probably a good investment!

Internal Rate of Return
The internal rate of return on an investment or potential investment is the annualized effective compounded return rate that can be earned on the invested capital. In more familiar terms, the IRR of an investment is the interest rate at which the costs of the investment lead to the benefits of the investment. This means that all gains from the investment are inherent to the time value of money and that the investment has a zero net present value at this interest rate. Because the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment. This is in contrast with the net present value, which is an indicator of the value or magnitude of an investment. An investment is considered acceptable if its internal rate of return is greater than an established minimum acceptable rate of return.

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