# How to Plot an NPV Profile

by Eric Bank; Updated September 26, 2017Net present value tells you the value of a stream of future cash flows, discounted by a factor, in today's dollars. Companies often make decisions based on NPV, such as whether to purchase an asset or initiate a project. An NPV profile is a chart that displays the effect of different discount factors on NPV.

## Anatomy of the Chart

The NPV profile's x-axis is cost of capital, in percentage terms. Cost of capital begins at zero percent at the origin and increases linearly as you move to the right. The y-axis is NPV, expressed in dollars. It is also zero at the origin, and increases as you head north. The y-axis is scaled to fit the expenditure for the asset. Values below the x-axis represent negative NPVs -- money-losing investments. The point where the NPV crosses the x-axis -- where the NPV is zero -- is the project's internal rate of return, which is the percentage the investment will recoup.

## Cost of Capital

A company must raise cash, or capital, to pay for assets. The cost of that capital depends on whether the company raises the money by borrowing it, issuing stock or some combination of the two. The cost of capital is the discount factor you use to express a future cash flow in today's dollars. If the company borrows all the money for the project -- for example, by issuing bonds -- the cost of capital would be the after-tax interest it pays on the bonds plus any issuance costs. The cost of capital for stock is the rate of return stockholders expect on their investments in the company.

## The NPV Calculation

To calculate the NPV of a constant annuity -- an investment that pays equal cash flows for a set number of periods -- you figure the present value of the investment and subtract this amount from the initial cost. The present value of an annuity is the payment amount per period times [(1 - (1 / (1 + r)^n)) / r], where "r" is the discount factor and "n" is the number of periods. Subtract the result from the cost of the initial investment to get the NPV. If the result is less than zero, the company would lose money by going forward with the investment. You can also use a spreadsheet or business calculator to calculate NPV.

## NPV Complications

The NPV profile shows how the current-dollar return varies with the discount rate. The plot assumes a fixed discount rate and a fixed timing of cash flows. A weakness of the NPV profile is that it doesn't account for circumstances that are more complex, such as variable discount rates, variable payment schedules, ongoing costs throughout the project, the scrap value of the investment and the after-tax effect of depreciation. Notwithstanding these additional items, a company might chart competing projects on the same chart to help decide which ones are likely to produce the biggest profits.

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