Sample Exam Problems

Transmission Line with Uncertainty

A private firm is considering building a new 115 kilovolt (kV) transmission line that would connect a proposed wind farm to the electric grid. Building the line would cost $140,000 per mile and the line would need to be 30 miles long. The firm expects to be able to charge $4 per megawatt-hour (MWh) transmitted.

The wind farm itself would be built in two stages.  The first stage would be years 1-10 during which it would have 50 megawatts (MW) of installed capacity.  The second stage would be years 11-30 and during that period it would have 100 MW of capacity. A 115 kV transmission line can carry up to about 150 megawatts (MW) of power, so it would be able to handle the wind farm’s peak output.

In all years, the wind farm is expected to operate with an average capacity factor of 20%.  That is, its power output will be its capacity times the number of hours in a year times 20%. For example, when the capacity is 50 MW, it will produce 50 MW * 365 * 24 * 0.2 = 87,600 megawatt-hours (20% of its maximum potential output of 438,000 MWh per year).

For simplicity, you may assume that if the project goes ahead, the line could be built immediately (year 0). After that (beginning in year 1), it would require minor annual maintenance equal to 1% of the line’s construction cost. The useful life of the line would be 30 years (years 1-30) after which it would have to be shut down (at no cost and with no salvage value). In carrying out present value calculations, the firm uses an interest rate of 5%.

  1. Please construct an appropriate spreadsheet and use it to calculate the net present value of building the line. Would it be profitable for the firm to go ahead with the project?  (Please turn in a printed copy of the spreadsheet.)
  2. Now suppose both the price and the capacity factor of the wind farm are uncertain.  The possible values of each, and their probabilities, are listed below.  You may assume that two variables are independently distributed.  

    Capacity Factor 0.15 0.20 0.25
    Probability 40% 50% 10%
    Price $3 $4 $5
    Probability 40% 50% 10%
    What is the expected net present value of the line?  In carrying out this calculation, it is perfectly OK to compute the NPV of each case by reusing your spreadsheet from part 1 with different values of the price and capacity factor. Also, you may assume that the true capacity factor and price become known immediately after the decision is made and don't change after that (i.e., the capacity factor and the price don't vary from one year to the next).

Please note that the assignment is just to evaluate the transmission line itself, not the wind farm. The construction schedule of the wind farm is only provided because it is needed to determine the amount of power the line will carry. 

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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 05/01/2018