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Net Present Value
Now that you have obtained reasonable figures for the future earnings, it is time to calculate the present value of those future earnings.
Firstly, you must determine the required rate of return. Consider what would you receive if you had placed the money in a riskfree alternative like government bonds. The returns you get from that alternative investment will be your required rate of return or discount rate.
In our example, we will use a discount rate of 10%. Using the formula for computing present value, we discount each future year’s earnings and the resulting figures obtained are given in the following chart.
Net present value
If we add up all the green bars in the chart above, we would obtain the net present value of XYZ company which is $17.25. This figure gives us a reasonable estimate of the fair value of the company. If XYZ stock is trading at a lower price, it is undervalued and possibly a good time to pickup some shares. Otherwise, it is overvalued and you should consider selling some shares if you own them.
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Net Present Value (NPV)
What is Net Present Value (NPV)?
Net Present Value (NPV) is the value of all future cash flows Statement of Cash Flows The Statement of Cash Flows (also referred to as the cash flow statement) is one of the three key financial statements that report the cash generated and spent during a specific period of time (e.g., a month, quarter, or year). The statement of cash flows acts as a bridge between the income statement and balance sheet (positive and negative) over the entire life of an investment discounted to the present. NPV analysis is a form of intrinsic valuation and is used extensively across finance Corporate Finance Overview Corporate finance deals with the capital structure of a corporation, including its funding and the actions that management takes to increase the value of and accounting for determining the value of a business, investment security, capital project, new venture, cost reduction program, and anything that involves cash flow.
NPV Formula
The formula for Net Present Value is:
 Z_{1} = Cash flow in time 1
 Z_{2}= Cash flow in time 2
 r = Discount rate
 X_{0} = Cash outflow in time 0 (i.e. the purchase price / initial investment)
Why is Net Present Value (NPV) Analysis Used?
NPV analysis is used to help determine how much an investment, project, or any series of cash flows is worth. It is an allencompassing metric, as it takes into account all revenues Sales Revenue Sales revenue is the income received by a company from its sales of goods or the provision of services. In accounting, the terms “sales” and “revenue” can be, and often are, used interchangeably, to mean the same thing. Revenue does not necessarily mean cash received. , expenses, and capital costs associated with an investment in its Free Cash Flow (FCF) Free Cash Flow (FCF) Free Cash Flow (FCF) measures a company’s ability to produce what investors care most about: cash that’s available be distributed in a discretionary way .
In addition to factoring all revenues and costs, it also takes into account the timing of each cash flow that can result in a large impact on the present value of an investment. For example, it’s better to see cash inflows sooner and cash outflows later, compared to the opposite.
Why Are Cash Flows Discounted?
The cash flows in net present value analysis are discounted for two main reasons, (1) to adjust for the risk of an investment opportunity, and (2) to account for the time value of money (TVM).
The first point (to adjust for risk) is necessary because not all businesses, projects, or investment opportunities have the same level of risk. Put another way, the probability of receiving cash flow from a US Treasury bill is much higher than the probability of receiving cash flow from a young technology startup.
To account for the risk, the discount rate is higher for riskier investments and lower for a safer one. The US treasury example is considered to be the riskfree rate, and all other investments are measured by how much more risk they bear relative to that.
The second point (to account for the time value of money) is required because due to inflation, interest rates, and opportunity costs, money is more valuable the sooner it’s received. For example, receiving $1 million today is much better than $1 million received five years from now. If the money is received today, it can be invested and earn interest, so it will be worth more than $1 million in five years’ time.
Example of Net Present Value (NPV)
Let’s look at an example of how to calculate the net present value of a series of cash flows Valuation Free valuation guides to learn the most important concepts at your own pace. These articles will teach you business valuation best practices and how to value a company using comparable company analysis, discounted cash flow (DCF) modeling, and precedent transactions, as used in investment banking, equity research, . As you can see in the screenshot below, the assumption is that an investment will return $10,000 per year over a period of 10 years, and the discount rate required is 10%.
The final result is that the value of this investment is worth $61,446 today. It means a rational investor would be willing to pay up to $61,466 today to receive $10,000 every year over 10 years. By paying this price, the investor would receive an internal rate of return Internal Rate of Return (IRR) The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment. (IRR) of 10%. By paying anything less than $61,000, the investor would earn an internal rate of return that’s greater than 10%.
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NPV Functions in Excel
Excel offers two functions for calculating net present value: NPV and XNPV. The two functions use the same math formula shown above, but save an analyst the time for calculating it in long form.
The regular NPV function =NPV() assumes that all cash flows in a series occur at regular intervals (i.e. years, quarters, month) and doesn’t allow for any variability in those time period.
The XNPV function =XNPV() allows for specific dates to be applied to each cash flow so they can be at irregular intervals. The function can be very useful as cash flows are often unevenly spaced out, and this enhanced level of precision is required.
Internal Rate of Return (IRR) and NPV
The internal rate of return ( IRR Internal Rate of Return (IRR) The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment. ) is the discount rate at which the net present value of an investment is equal to zero. Put another way, it is the compound annual return an investor expects to earn (or actually earned) over the life of an investment.
For example, if a security offers a series of cash flows with an NPV of $50,000 and an investor pays exactly $50,000 for it, then the investor’s NPV is $0. It means they will earn whatever the discount rate is on the security. Ideally, an investor would pay less than $50,000 and therefore earn an IRR that’s greater than the discount rate.
Typically, investors and managers of business look at both NPV and IRR in conjunction with other figures when making a decision. Learn about IRR vs XIRR in Excel XIRR vs IRR Why use XIRR vs IRR. XIRR assigns specific dates to each individual cash flow making it more accurate than IRR when building a financial model in Excel. The Internal Rate of Return is the discount rate which sets the Net Present Value of all future cash flow of an investment to zero. Use XIRR over IRR .
Negative vs Positive Net Present Value
If the net present value of a project or investment, is negative it means the expected rate of return that will be earned on it is less than the discount rate (required rate of return or hurdle rate Hurdle Rate Definition A hurdle rate, which is also known as minimum acceptable rate of return (MARR), is the minimum required rate of return or target rate that investors are expecting to receive on an investment. The rate is determined by assessing the cost of capital, risks involved, current opportunities in business expansion, rates of return for similar investments, and other factors ). This doesn’t necessarily mean the project will “lose money.” It may very well generate accounting profit (net income), but, since the rate of return generated is less than the discount rate, it is considered to destroy value. If the NPV is positive, it creates value.
Applications in Financial Modeling
NPV of a Business
To value a business an analyst will build a detailed discounted cash flow DCF model DCF Model Training Free Guide A DCF model is a specific type of financial model used to value a business. DCF stands for Discounted Cash Flow, so the model is simply a forecast of a company’s unlevered free cash flow discounted back to today’s value. This free DCF model training guide will teach you the basics, step by step with examples and images in Excel. This financial model will include all revenues, expenses, capital costs, and details of the business. Once the key assumptions are in place, the analyst can build a fiveyear forecast of the three financial statements Three Financial Statements The three financial statements are the income statement, the balance sheet, and the statement of cash flows. These three core statements are intricately linked to each other and this guide will explain how they all fit together. By following the steps below you’ll be able to connect the three statements on your own. (income statement, balance sheet, and cash flow) and calculate the free cash flow of the firm (FCFF) Valuation Free valuation guides to learn the most important concepts at your own pace. These articles will teach you business valuation best practices and how to value a company using comparable company analysis, discounted cash flow (DCF) modeling, and precedent transactions, as used in investment banking, equity research, , also known as the unlevered free cash flow. Finally, a terminal value is used to value the company beyond the forecast period, and all cash flows are discounted back to the present at the firm’s weighted average cost of capital. To learn more, check out CFI’s free detailed financial modeling course.
NPV of a Project
To value a project is typically more straightforward than an entire business. A similar approach is taken, where all the details of the project are modeled into Excel, however, the forecast period will be for the life of the project and there will be no terminal value. Once the free cash flow is calculated, it can be discounted back to the present at either the firm’s WACC WACC WACC is a firm’s Weighted Average Cost of Capital and represents its blended cost of capital including equity and debt. The WACC formula is = (E/V x Re) + ((D/V x Rd) x (1T)). This guide will provide an overview of what it is, why its used, how to calculate it, and also provides a downloadable WACC calculator or the appropriate hurdle rate.
Drawbacks of Net Present Value
While net present value (NPV) is the most commonly used method for evaluating investment opportunities, it does have some drawbacks that should be carefully considered.
Key challenges to NPV analysis include:
 A long list of assumptions has to be made
 Sensitive to small changes in assumptions and drivers Valuation Modeling in Excel Valuation modeling in Excel may refer to several different types of analysis, including discounted cash flow (DCF), comparable trading multiples, precedent transactions, and ratios such as vertical and horizontal analysis.
 Easily manipulated to produce the desired output
 May not capture second and thirdorder benefits/impacts (i.e. on other parts of a business)
 Assumes a constant discount rate over time
 Accurate riskadjustment is challenging to perform (hard to get data on correlations, probabilities)
Additional Resources
Net Present Value (NPV) is the most detailed and widely used method for evaluating the attractiveness of an investment. Hopefully, this guide’s been helpful in increasing your understanding of how it works, why it’s used, and the pros/cons.
CFI is the official provider of the Financial Modeling & Valuation Analyst certification program FMVA® Certification Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari . To continue advancing your career, check out these relevant resources:
 Guide to Financial Modeling What is Financial Modeling Financial modeling is performed in Excel to forecast a company’s financial performance. Overview of what is financial modeling, how & why to build a model.
 Financial Modeling Best Practices Financial Modeling Best Practices This article is to provide readers information on financial modeling best practices and an easy to follow, stepbystep guide to building a financial model. Best practices include: clarify the business problem, simplify as much as possible, plan your structure, build structural integrity test the model
 Advanced Excel Formulas Advanced Excel Formulas Must Know These advanced Excel formulas are critical to know and will take your financial analysis skills to the next level. Advanced Excel functions you must know. Learn the top 10 Excel formulas every worldclass financial analyst uses on a regular basis. These skills will improve your spreadsheet work in any career
 All Valuation Articles Valuation Valuation refers to the process of determining the present worth of a company or an asset. It can be done using a number of techniques. Analysts that want
Net Present Value (NPV)
What is Net Present Value (NPV)?
Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project.
The following formula is used to calculate NPV:
If you are unfamiliar with summation notation – here is an easier way to remember the concept of NPV:
A positive net present value indicates that the projected earnings generated by a project or investment – in present dollars – exceeds the anticipated costs, also in present dollars. It is assumed that an investment with a positive NPV will be profitable, and an investment with a negative NPV will result in a net loss. This concept is the basis for the Net Present Value Rule, which dictates that only investments with positive NPV values should be considered.
Apart from the formula itself, net present value can be calculated using tables, spreadsheets, calculators, or Investopedia’s own NPV calculator.
Understanding Net Present Value
How to Calculate Net Present Value (NPV)
Money in the present is worth more than the same amount in the future due to inflation and to earnings from alternative investments that could be made during the intervening time. In other words, a dollar earned in the future won’t be worth as much as one earned in the present. The discount rate element of the NPV formula is a way to account for this.
For example, assume that an investor could choose a $100 payment today or in a year. A rational investor would not be willing to postpone payment. However, what if an investor could choose to receive $100 today or $105 in a year? If the payer was reliable, that extra 5% may be worth the wait, but only if there wasn’t anything else the investors could do with the $100 that would earn more than 5%.
An investor might be willing to wait a year to earn an extra 5%, but that may not be acceptable for all investors. In this case, the 5% is the discount rate which will vary depending on the investor. If an investor knew they could earn 8% from a relatively safe investment over the next year, they would not be willing to postpone payment for 5%. In this case, the investor’s discount rate is 8%.
A company may determine the discount rate using the expected return of other projects with a similar level of risk or the cost of borrowing money needed to finance the project. For example, a company may avoid a project that is expected to return 10% per year if it costs 12% to finance the project or an alternative project is expected to return 14% per year.
Imagine a company can invest in equipment that will cost $1,000,000 and is expected to generate $25,000 a month in revenue for five years. The company has the capital available for the equipment and could alternatively invest it in the stock market for an expected return of 8% per year. The managers feel that buying the equipment or investing in the stock market are similar risks.
Step One: NPV of the Initial Investment
Because the equipment is paid for up front, this is the first cash flow included in the calculation. There is no elapsed time that needs to be accounted for so today’s outflow of $1,000,000 doesn’t need to be discounted.
Identify the number of periods (t)
The equipment is expected to generate monthly cash flow and last for five years, which means there will be 60 cash flows and 60 periods included in the calculation.
Identify the discount rate (i)
The alternative investment is expected to pay 8% per year. However, because the equipment generates a monthly stream of cash flows, the annual discount rate needs to be turned into a periodic or monthly rate. Using the following formula, we find that the periodic rate is 0.64%.
Step Two: NPV of Future Cash Flows
Assume the monthly cash flows are earned at the end of the month, with the first payment arriving exactly one month after the equipment has been purchased. This is a future payment, so it needs to be adjusted for the time value of money. An investor can perform this calculation easily with a spreadsheet or calculator. To illustrate the concept, the first five payments are displayed in the table below.
The full calculation of the present value is equal to the present value of all 60 future cash flows, minus the $1,000,000 investment. The calculation could be more complicated if the equipment was expected to have any value left at the end of its life, but, in this example, it is assumed to be worthless.
That formula can be simplified to the following calculation:

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