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Economic Analysis. An important factor of the distribution investor is the value of asset invested and its recovery over time The required investment do not occur at once but needed as the work progress. Similarly the return also occur as the time passes

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Economic analysis
Economic Analysis

  • An important factor of the distribution investor is the value of asset invested and its recovery over time

    • The required investment do not occur at once but needed as the work progress.

    • Similarly the return also occur as the time passes

    • A Rupee today is more valuable than a Rupee tomorrow

    • The net investment in any year is the difference in investment and return (positive or negative)

  • So for the proper economic analysis;

    • First required to prepare schedule plan mentioning how the overall project will progress as a function of time (Time schedule)

    • Then for that amount of work how much investment will require when.

    • Yearly return after this investment

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Present value
Present Value

  • Central to the financial and economic evaluation process.

  • Present valuing will be carried out through discounting next period’s financial outlay (F1) to its present value through multiplying it by a discount factor.

  • Discount factor or present worth factor is a function of the discount rate () which is the reward that investors demand for accepting a delayed payment.

  • A Rupee today is more valuable than a Rupee tomorrow

  • An Utility expects to gain a premium on his investment with due approval of the regulator due to the following three factors:

    - inflation

    - risk taking

    - expectation of a real return.

  • expects to regain his money, plus a return which tallies with the market and his estimation of these three factors.

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  • Present value (PV) = discount factor × F1

    where Discount factor = 1 ÷ (1+)

  • With a discount rate (expected rate of return) of ten percent annually, the discount factor for the first years financial outlay will be 1 / (1+0.1) = 0.909

  • Materializing Rs22,000 after one year will be equal to 0.909 × Rs22000 = Rs 20,000 today.

  • Outlay at year 2 will have to be multiplied by 1/(1+)2

  • Discount factor in year n is equal to 1 / (1+)n

  • Present value = Fn × discount factorn = Fn × [1/(1+)n]

  • $100 occurring after five years, with a discount rate of 10 % will have a present value equal to $100 × [1/(1+0.1)5] = $62.092 today.

  • $100 occurring after 30 years will be equal to $100 × [1 / (1+0.1)30] = $5.731 today

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Cash flows
Cash Flows

  • Cash flow is the difference between money received and money paid.

  • Each year’s future cash flow can be discounted to its present value by dividing it by the discount factor for that year.

  • extended stream of cash flows M0, M1, M2… Mn occurring at years 0, 1, 2…, n has a present value of:

  • In the special case of M1 = M2 =  = Mn = M

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Example
Example

  • Consider a distribution network project involving an investment of $50,000 at the beginning of each year over four years, starting today, with a discount factor of eight percent, its present value is

= 50 × 103 (1+0.926+0.857+0.794) = $ 178850

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Future and past valuing
Future and Past Valuing

  • Future valuing (FV) of a present value (PV) means that the base year has been moved into the future by n years

  • PV is occurring now at – n years from the new base year.

  • The universal discount (compound) factor is maintained, with negative n value,

    FV = PV × [1 / (1+)-n] = PV (1+)n

  • For past valuing, the base year has been moved into the past by n years.

  • The past value will equal PV × [1/ (1+) n].

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Annuity factor
Annuity factor

  • Present valuing of a stream of equal cash flows, M

  • If we substitute ‘a’ for M / (1+) and ‘x’ for 1 / (1+)

    PV = a (1 + x + x2 + … + xn-1) Equ.(1)

  • Multiplying both sides by ‘x’

    xPV = a (x + x2 + … + xn) Equ.(2)

  • Subtracting the equation (2) from (1)

    PV (1 – x) = a (1 – xn) Equ.(3)

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  • Substituting for ‘a’ and ‘x’ and then multiplying both sides by (1+) and rearranging gives:

  • The expression in brackets in the above equation is the annuity factor, which is the present value of an annuity of $1 paid at the end of each of n periods, at a discount rate 

  • the annuity factor is the summation of all the annual values of the discount factors over the period

Annuity factor =

PV = M × Annuity factor

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Capital recovery factor crf or equivalent annual cost
Capital recovery factor (CRF) or equivalent annual cost

  • An annuity factor is a means of converting a stream of equal annual values into a present value, at a given discount rate (interest)

  • A capital recovery factor (CRF) performs the reverse calculation

  • CRF is the amount of money to be paid at the end of each year to recover (a mortise) the investment at a rate of discount, , over n years

  • The equivalent annual cost, M will be the reciprocal of equation of PV mentioned earlier

= PV × CRF

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= $ 1000000 × 0. 17698 = $ 176 980 annually

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Cost estimation
Cost Estimation million over ten years, at a rate of interest of 12% is

For calculation of the project cost first the unit costs of each of the components have to be assessed. For example for a new distribution system planning;

  • Unit Cost of Sub-transmission line.

  • Unit cost of 33/11 kV Substation (if any)

  • Unit cost of 11 kV Distribution

  • Unit Cost of Low Voltage Transmission

  • Unit cost of Distribution Transformer.

  • Unit cost for the Consumer Services.

  • Additional cost (e.g. unit cost of River-Crossing (if any))

  • Service connection cost

  • In addition to that the cost of 1 unit of Energy at Area substation should also be known.

  • There are different methods to calculate this very popular is LRMC

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Long run marginal cost lrmc
Long Run Marginal Cost(LRMC) million over ten years, at a rate of interest of 12% is

  • In case of scenario based LRMC approach, likely level and location of demand and generation are forecasted area wise for a long period(20–40 years) with intervals(2-4 years).

  • The estimated forecasted demand and generations are than included in the base system(present) and than the requirements for new investments are determined.

  • The above procedure is repeated for 20-40 years

  • Next a future cost is developed for over long period(20-40 years)

  • These costs are than discounted back to the present value, annuitised and divided by the demand and generations of respective zones.

  • Final zonal prices at different voltages can be obtained.

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Cost estimation contd
Cost Estimation (contd) million over ten years, at a rate of interest of 12% is

  • Cost estimation for new extension plan can be performed by estimating the quantities under different alternative schemes

  • For other purpose; for example loss reduction the basic principle is same only in the cost estimations slightly differ specific to the requirement.

  • Cost Disbursement schedule common in all planning procedure

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Over all planning procedure
Over all planning procedure million over ten years, at a rate of interest of 12% is

  • Explore the viable options

  • Check the technical requirements (e.g. Voltage constraints, conductor current carrying capacity, reliability equipments etc.)

  • Short out the options that satisfies technical requirements

  • Prepare the cost disbursement schedule

  • Perform economic analysis and choose the option which is best from economical point of view.

    Economic indicator

  • For comparison of the various options PV, or annual cost indicator may be used.

  • The economic feasibility of the project requires IRR or B/C ratio.

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IRR million over ten years, at a rate of interest of 12% is

  • Given a time series of cash flows involved in a project, the internal rate of return follows from the net present value as a function of the rate of return.

  • A rate of return for which this function is zero is an internal rate of return.

  • Example

    Calculate the internal rate of return for

    an investment of as shown in table

    Solution:

    We use an iterative solver to determine

    the value of r that solves the above equation:

    The result from the numerical iteration is .

    28.09 %

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