# NPV Explanation and Calculation

I would like to have the solution to the following sample problems in EXCEL format so that I can see the formulas used. Thanks

1. A firm that purchases electricity from the local utility for $300,000 per year is considering installing a steam generator at a cost of $340,000. The cost of operating this generator would be $160,000 per year, and the generator will last for five years. If the firm buys the generator, it does not need to purchase any electricity from the local utility. The cost of capital is 11%.

For the local utility option, consider five years of electricity purchases. For the 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 alternative?

Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.

2. A firm that purchases electricity from the local utility is considering installing a steam generator. A large generator costs $300,000 whereas a small generator costs $240,000. The cost of operating the generator would be $100,000 per year for the large and $135,000 for the small. Either generator will last for five years. The cost of capital is 9%.

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.

3. A prospective MBA student earns $60,000 per year in her current job and expects that amount to increase by 11% per year. She is considering leaving her job to attend business school for two years at a cost of $45,000 per year. She has been told that her starting salary after business school is likely to be $75,000 and that amount will increase by 18% per year. Consider a time horizon of 10 years, use a discount rate of 12%, and ignore all considerations not explicitly mentioned here.

Assume all cash flows occur at the start of each year (i.e., immediate, one year from now, two years from now,..., nine years from now). Also assume that the choice can be implemented immediately so that for the MBA alternative the current year is the first year of business school.

What is the net present value of the more attractive alternative?

Please round your answer to the nearest dollar.

#### Solution Preview

1. A firm that purchases electricity from the local utility for $300,000 per year is considering installing a steam generator at a cost of $340,000. The cost of operating this generator would be $160,000 per year, and the generator will last for five years. If the firm buys the generator, it does not need to purchase any electricity from the local utility. The cost of capital is 11%.

For the local utility option, consider five years of electricity purchases. For the 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 alternative?

Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.

NPV

1. Generator

Purchase electricity 300000

5 years of purchase 1500000

Investment of generator 340000

PV -340000

operating cost 160000

capital interest 0.11

5 years interest

Year 1 37400/1.11 33693.69

Year 2 37400/(1.11)2 30406.5

Year 3 37400/(1.11)3 27359.18

Year ...

#### Solution Summary

The net present value is the net value of the initial investment and the money that went in after the investment. Proper formatting attached in Word; calculations in Excel.