You are evaluating whether to use a new higher-voltage transmission line. It wil

Question

You are evaluating whether to use a new higher-voltage transmission line. It will cost $250,000 more initially, but it will reduce transmission losses. The optimistic, most likely, and pessimistic projections for annual savings are $25,000, $20,000, and $13,000. The interest rate is 8%, and the transmission line should have a life of 30 years. a) Use the range of estimates to compute the mean annual savings, and determine the net present worth based on this mean annual savings. b) For this part only, assume that the optimistic probability is 20%, the most likely is 50%, and the pessimistic is 30%. Compute the expected value for the annual savings, and the corresponding net present worth.

Explanation / Answer

a) If all the three scenarios is equally likely, then mean annual savings = (25,000 + 20,000 + 13,000) / 3 = 19,333.3

Now, present worth of these savings for 30 years at 8% can be calculated using PV function on a calculator

N = 30, PMT = 19,333.3, FV = 0, I/Y = 8% = $217,650.48

Net present worth = 217,650.48 - 250,000 = -$32,439.52

b) If the probabilities are different, then annual savings = 20% x 25,000 + 50% x 20,000 + 30% x 13,000 = $18,900

With it present worth = $212,772.11

Net present worth = -37,227.89

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