A municipality is considering an investment in a small renewable energy power pl

Question

A municipality is considering an investment in a small renewable energy power plant with the following parameters. The cost is $360,000, and the output averages 50 kW year-round. The price paid for electricity at the plant gate is $0.039/kWh. The investment is to be evaluated over a 25-year time horizon, and the expected salvage value at the end of the project is $20,000. The MARR is 6%.

Calculate the NPV of this investment. Is it financially attractive? Calculate the operating credit per kWh which the government would need to give to the investment in order to make it break even financially. Express your answer to the nearest 1/1000th of dollars

Explanation / Answer

Cost of the Renewable Energy Power Plant P = 360,000

Output average = 50 kW throughout the year

Price of electricity at plant gate = 0.039 / kWh (or Kilowatt hour)

Investment Horizon = 25 Years

Expected Salvage Value S = 20,000

MARR - Minimum Acceptable Rate of Return r = 6% or 0.06

Calculation of Electricity production in kWh

kWh = kW * hours

A year is taken to be 365 days which is equal to 8760 (365*24) hours

Therefore total kwH per annum = 50 * 8760 = 438,000 kwh

Cash Inflow on sale of electricity A = total production * price

= 438000 * 0.039 = $ 17,082 per annum for 24 years

Terminal Year Cashflow T = 17082 + 20,000 (salvage value) = $ 37,082

Net Present Value of the project can be calculated using the formula

NPV = - P + A * {[1-1/(1+r)^24]/r} + T/(1+r)^25 ( This formula can be modified if present value of Salvage value can be taken separately as shown equation A below)

NPV = - 360000 + 17082 * { [1-1/(1+.06)^24]/0.06} + 37082 / (1+0.06)^25

= - 360000 + 17082 * { [1-1/1.06^24]/0.06} + 37082/1.06^25

= - 360000 + 17082 * { [ 1 - 1/4.04893]/0.06} + 37082/4.29187

= - 360000 + 17082 * { [1- 0.2469788]/0.06} + 8640.05667

= - 360000 + 17082 * {0.7530212/0.06} + 8640.0567
  
= - 360000 + 17082 * 12.55035 + 8640.0567

= - 360000 + 214385.0787 + 8640.0567

= - 136974.8646 or - $ 136,974.865

As the Net Present Value of the project is negative, the project is not financially attractive.

Part II of the answer

The project breaks even financially when the NPV = 0. This can be determined by the cash inflows (A1) required to make the NPV equals zero or

0 = - P + A1 * { [1-1/(1+r)^25]/r} + S / (1+r)^25

Substituting the values from above, we try to find out value of A1

0 = - 360000 + A1 * { [1-1/(1.06)^25]/0.06} + 20000/1.06^25

0 = - 360000 + A1 * { [1- 1/4.29187]/0.06} + 20000/4.29187

= - 360000 + A1 * {[1- 0.232999] / 0.06} + 4659.9734

= -360000 + 12.78335 A1 + 4659.9734

= 12.78335 A1 - 355340.0266

A1 = 355340.0266 / 12.78335 = 27797.0975 or 27797.098

Price required at plant gate = Cash Inflow (A1) / Total kwh = 27797.098 / 438000

Price required at plat gate = $ 0.06346 / kWh or $ 0.064 kWh (rounded off)

Estimated price paid at plant gate = 0.039 kWh

Operating credit required = 0.064 - 0.039 = $ 0.025 kWh

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