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Economic Analysis

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- 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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- 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

AKM/Distribution

- 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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- 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 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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- 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

AKM/Distribution

- 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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- equivalent annual capital cost of an investment of $1 million over ten years, at a rate of interest of 12% is

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

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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

AKM/Distribution

- 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 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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- 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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- 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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