# Net present value

Consider the following situation: PowerCo, a medium-sized power company, generates and sells electricity throughout several states in the southeast United States. The company has been in business for over 30 years and is the largest power generator in the region. The company believes that a significant increase in the demand for electricity over the next 10-12 years will cause it to be unable to meet the expected demand with its current generation capabilities.

PowerCo's senior management believes that they must build a new generator to meet this increased demand and their Treasury department was tasked with developing the financial projections for building a new generator. Taking the expected revenues from the new facility, which were developed by the firm's economists, and the expected costs of building the new plant, which were provided by the firm's engineers, the Treasury department has developed financial projections to allow it to analyze the prospective investment in a new generating facility.

It is expected that building the new generator will take approximately two years and will remain functional for at least 10 years. While Treasury expects that the facility will continue to generate electricity for longer than 10 years, the department believes that financial projections for a period longer than 10 years are too uncertain and so has limited its estimates to 10 years of use.

The financial projections, given on an annual basis in after-tax dollars, are as follows (assume all cash flows occur at the end of the year):

The expected cash costs, in millions of dollars, of building the facility:

Year Expected Costs

1 25

2 28

The expected profits from the sale of electricity, in millions of dollars:

Year Expected after-tax profits

3 6

4 7

5 8

6 9

7 9

8 9

9 9

10 9

11 9

12 9

The firm believes that its opportunity cost of capital is 8 percent and so will use that rate to evaluate the project.

1. What is the present value (PV) of the expected costs? Show all calculations.

2. What is the present value of the expected after-tax cash profits? Show all calculations.

3. What is the expected net present value (the difference between the PVs of the inflows and outflows)? Show the calculations. What does this number represent? Be detailed in your responses.

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#### Solution Summary

The solution provides step by step method for the calculation of net present value. Formula for the calculation and Interpretations of the results are also included.