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									EE535: Renewable Energy:
 Systems, Technology &
     Project Financing
       Cost of Energy Drivers
1. Capital Costs (and the cost of borrowing the

2. Fuel Costs

3. Operation and Maintenance (O&M) Costs

4. 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
     • 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:
      1.   Itemise the capital and running costs for each year of the project
      2.   Calculate the separate Present Value of all these annual costs
           using an appropriate discount rate, and sum to give the NPV
      3.   Itemise the output for each year over the project life
      4.   Calculate the NPV of all these annual outputs, expressed usually
           in kWh
      5.   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

 •        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
• 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?
Year        Cashflow                         Present Value

        0   (30000 - 5000) / (1 +0.1)^0                      -100000

        1   (30000 - 5000) / (1 +0.1)^1                       22727

        2   (30000 - 5000) / (1 +0.1)^2                       20661

        3   (30000 - 5000) / (1 +0.1)^3                       18783

        4   (30000 - 5000) / (1 +0.1)^4                       17075

        5   (30000 - 5000) / (1 +0.1)^5                       15523

        6   (30000 - 5000) / (1 +0.1)^6                       14112

            NPV                                                8882

 NPV = € 8,881.52 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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