Question

A firm that purchases electricity from the local utility is considering installing a steam generator. A large generator costs $320,000 whereas a small generator costs $230,000. The cost of operating the generator would be $200,000 per year for the large and $230,000 for the small. Either generator will last for five years. The cost of capital is 15%. For each generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now,..., four years from now). What is the net present value of the more attractive generator? Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.

Answer 1

Option 1: Large generator

Year 0 (immediate cost) = 320,000 +200,000 = 520,000

Cost in the next 4 years = 200,000

Net present value = 520,000 + 200,000/1.09 + 200,000/1.09^2 + 200,000/1.09^3 + 200,000/1.09^4 =1,167,943.98

Net present value = -$1,167,943.98 (because this is a cost)

Option 2: Small generator

Year 0 (immediate cost) = 230,000 +230,000 = 460,000

Cost in the next 4 years = 230,000

Net Present value = 460,000 + 230,000/1.09 + 230,000/1.09^2 + 230,000/1.09^3 + 230,000/1.09^4 = 1,205,135.57

Net present value = -$1,205,135.57(because this is a cost)

As we can see the NPV of costs for the large generator (Option 1) is lower than the costs of small generator. Hence the large generator would be a more attractive option.