Economic Analysis of RE

Economic analysis of RE

Before investing in a rural electrification system, it is necessary to determine the economic and financial feasibility of the system. In addition to having some positive socio-economic impacts, the system must also yield a fair amount of profit to the investing company or utility.

The time-value of money is one of the fundamental concepts of finance. The purchasing power of money decreases with time. The basic time value of money concepts are as follows:

1. Future value

The future value of a sum of money is given as:

FV = PV * (1 + i)^N where PV stands for present value of the sum, i stands for interest rate and N stands for time period

2. Present value

The present value of a sum of money is given as:

PV = FV / (1 + i)^N where FV stands for future value of the sum, i stands for interest rate and N stands for time period

3. Future value of annuity

Annuities are series of payments made at regular intervals over a period of time. The most common payment intervals are 1 month, 3 months, 6 months and 1 year.

When the payments are made at the end of each period, it is known as ordinary annuity and when the payments are made at the beginning of each period, it is known as annuity due.

The future value of ordinary annuity is calculated as:

$${\rm{FVA}}\,{\rm{ = }}\,{\rm{PMT}}\,{\rm{*}}\,{{{{(1 + i)}^N} - 1} \over i}$$

where PMT is the value of periodic payment

The future value of annuity due is calculated as:

$${\rm{FV}}{{\rm{A}}_{{\rm{due}}}}\,{\rm{ = }}\,{\rm{FV}}{{\rm{A}}_{{\rm{ordinary}}}}\,*\,\,(1 + i)$$

4. Present value of annuity

The present value of ordinary annuity is obtained as:

$${\rm{PVA}}\,{\rm{ = }}\,{\rm{PMT}}\,{\rm{*}}\,{{1 - {1 \over {{{(1 + i)}^N}}}} \over i}$$

The present value of annuity due is obtained as:

$${\rm{PV}}{{\rm{A}}_{{\rm{due}}}}\,{\rm{ = }}\,{\rm{PV}}{{\rm{A}}_{{\rm{ordinary}}}}\,*\,\,(1 + i)$$

Capital budgeting

Capital budgeting is defined as the firm's decision to invest in a particular project. A company must make a reasonable decision keeping in view the profitability of the project. The most common methods of profit appraisal are

1. Payback period

In this method, the payback period of a project is determined which is nothing but the time duration required to cover up the initial cost or investment. For a project yielding equal cashflows, the payback period is simply calculated by dividing the investment by annual cashflow. For example, if the investment made is Rs. 1,00,000 and the annual cashflow is Rs. 20,000, the payback period is 5 years.

For calculating payback periods with unequal cashflow, the following formula can be used.

PB period = N_F-1 + I_F/CF_F

where, N_F-1 = Year before full recovery of investment

I_F = Amount to be recovered at the year of full recovery

CF_F = Cashflow at the year of recovery

The simple payback period ignores the time value of money and also ignores the benefit after the payback period. Thus the profitability of the project is not measured. For example, a project may have a payback period of 3 years but may have less profit after 3 years. On the other hand, a project having a payback period of 5 years may have very high profit after 5 years. A company is likely to choose the first project owing to its shorted payback period.

The discounted payback period is more suitable as it gives the time duration or the number of years it takes to break even on the initial expenditure or investment.

2. Net present value

In this method, the investment is subtracted from the sum of all the discounted cashflows to determine the profitability of the project. If the NPV is greater than 0, the project is profitable and should be accepted. If the NPV is equal to 0, the project yields neither profit nor loss. If the NPV is less than 0, the project incurs loss and should be rejected.

The NPV is calculated as follows:

$${\rm{NPV}}\,{\rm{ = }}\,{{{\rm{CF1}}} \over {{{(1 + i)}^1}}}\, + \,{{{\rm{CF2}}} \over {{{(1 + i)}^2}}}\, + ......\, + \,{{{\rm{CFn}}} \over {{{(1 + i)}^n}}}\, - \,{\rm{Investment}}$$

If one project is to be selected from many, the project having highest NPV should be selected.

3. IRR value

The Internal Rate of Return is another method to determine the profitability of a project. IRR is defined as the discount rate which makes the present value of cash inflows equal to the present value of cash outflows of the project. The IRR of any project can be determined by solving the equation given below.

$$0\,{\rm{ = }}\,{{{\rm{CF1}}} \over {{{(1 + k)}^1}}}\, + \,{{{\rm{CF2}}} \over {{{(1 + k)}^2}}}\, + ......\, + \,{{{\rm{CFn}}} \over {{{(1 + k)}^n}}}\, - \,{\rm{Investment}}$$

In the equation above, k is the IRR value. If IRR is greater than the cost of capital, the project should be accepted. If it is less than the cost of capital, the project should be rejected.

Numerical example:

Capital cost

• Distribution line cost per km = Rs. 600,000
• Cost per transformer s/s = Rs. 1,000,000

Cost of capital = 10%

Project life = 15 years

Average annual energy consumption/consumer = 300 - 700 kWh

Net Cash Flow/kWh/year

• up to 300 units = Rs. 1.0
• up to 350 units = Rs. 1.5
• up to 400 units = Rs. 2.0
• up to 450 units = Rs. 2.5
• up to 500 units = Rs. 3.0
• up to 550 units = Rs. 3.5
• up to 600 units = Rs. 4.0
• up to 650 units = Rs. 4.5
• up to 700 units = Rs. 5.0

Details about the RE system

1. RE Network detail

Line length = 6 km

No. of transformer = 1

Total consumers = 400

2. Capital cost

Cost of line = 6 * 600,000 =3,600,000

Cost of s/s = 1 * 1,000,000 = 1,000,000

Total cost = 4,600,000

3. Operating parameters

Annual Energy sale per consumer year = 650 kWh/yr

Annual Energy sale = 400 * 650 = 260,000 kWh

Annual Net Cash flow/kWh = Rs. 4.5/kWh

Annual Net Cash flow = 4.5 * 260,000 = Rs. 1,170,000

PB = N_F-1 + I_F / CF_F

= 5 + 164.8 / 660.4 = 5.25 yrs.

Cumulative cash flow becomes positive from 6^th year. If a payback period of fewer than 6 years is acceptable, the project can be accepted.

Note: The students are assumed to be familiar with the various methods of financial appraisal of projects as they have already studied them in their course of Engineering Economics. They will also study these methods in their course of Project Engineering. The numerical example was taken from the slide notes provided by my lecturer Mr. Gopal Joshi Subedi.