The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

The Net present value (NPV) of a project refers to the present value of all cash inflows minus the present value of all cash outflows, evaluated at a given discount rate. The difference between the two represents the income generated by a project. A project whose cash inflows outweigh its cash outflows is generally considered financially viable, as it generates a positive return. However, there are projects in which the present value of cash outflows exceeds the present value of cash inflows. Such a project is not financially viable. To help you understand the NPV concept, consider the following example:

Suppose the local government in a given location decides to build a bridge that will connect two cities, A and B. At the start of this project, the government will have to spend a considerable amount of money to acquire necessary construction material and also pay the constructor. Assume a risk discount rate of 10% per annum. After construction, more, but smaller amounts of money, will cater for maintenance costs. All these expenses constitute the cash outflows of the project. The project is then expected to generate a continuous stream of income in the form of toll fees paid by the users of the bridge. To simplify matters, let’s assume that the project will generate income for ten years. Fees paid will constitute the project’s cash inflows. Therefore, the government should only proceed with the project if the NPV is positive.

Net Present Value Formula

$$ NPV=\sum { C_{ t }(1+r)^{ t } } \text { for all } t\ge 0 $$

Where: Ct is the cash flow at time t

And r is the risk discount rate

Question

A project generates the following cash flows;

Beginning of years:

1 – ($100,000) (contractors’ fees)

2 – ($200,000) (contractors’ fees)

3 –  ($200,000) (contractors’ fees)

End of Year 3 : $1,000,000 (sales)

Calculate the NPV of the project using a risk discount rate of 20% per year.

A. $500,000

B. $173,148

C. $166,667

Solution

The correct answer is B.

r = 0.2

$$ \begin{align*} \text{NPV} & = – 100,000 – 200,000(1 + 0.2)^{-1} – 200,000(1 + 0.2) ^{-2} + 1000,000(1 + 0.2)^{-3} \\ & = – 100,000 – 166,667 – 138,889 + 578,704 \\ & = $173,148 \\ \end{align*} $$

Note that we do not discount cash flows occurring at the beginning of a project. Hence, the discount should be zero at t = 0.

Advantages of the NPV method

– NPV tells us whether a project will increase the value of a company, and by how much in terms of dollars.

– The method takes into account all the cash flows associated with a particular project.

– It considers the time value of money.

– Net present value method offers a convenient tool during appraisal of any given project.

Reading 7 LOS 7a:

Calculate and interpret the net present value (NPV) and the internal rate of

return (IRR) of an investment

How to calculate net present value

Guide to the Discounted Cash Flow DCF Formula

This article breaks down the discounted cash flow DCF formula into simple terms.  We will take you through the calculation step by step so you can easily calculate it on your own. The DCF formula is required in financial modeling to determine the value of a business when building a DCF model in Excel.

Watch this short video explanation of how the DCF formula works.

Video: CFI’s free Intro to Corporate Finance Course.

What is the Discounted Cash Flow DCF Formula?

The discounted cash flow (DCF) formula is equal to the sum of the cash flow in each period divided by one plus the discount rate (WACC) raised to the power of the period number.

Here is the DCF formula:

The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

Where:

CF = Cash Flow in the Period

r = the interest rate or discount rate

n = the period number

Analyzing the Components of the Formula

1. Cash Flow (CF) 
The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

Cash Flow (CF) represents the net cash payments an investor receives in a given period for owning a given security (bonds, shares, etc.)

When building a financial model of a company, the CF is typically what’s known as unlevered free cash flow.  When valuing a bond, the CF would be interest and or principal payments.

To learn more about the various types of cash flow, please read CFI’s cash flow guide.

2. Discount Rate (r) 
The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

For business valuation purposes, the discount rate is typically a firm’s Weighted Average Cost of Capital (WACC).  Investors use WACC because it represents the required rate of return that investors expect from investing in the company.

For a bond, the discount rate would be equal to the interest rate on the security.

3. Period Number (n) 
The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

Each cash flow is associated with a time period. Common time periods are years, quarters, or months.  The time periods may be equal, or they may be different.  If they’re different, they’re expressed as a percentage of a year.

What is the DCF Formula Used For?

The DCF formula is used to determine the value of a business or a security.  It represents the value an investor would be willing to pay for an investment, given a required rate of return on their investment (the discount rate).

Examples of Uses for the DCF Formula:

  • To value an entire business
  • To value a project or investment within a company
  • To value a bond
  • To value shares in a company
  • To value an income-producing property
  • To value the benefit of a cost-saving initiative at a company
  • To value anything that produces (or has an impact on) cash flow

Below is a screenshot of the DCF formula being used in a financial model to value a business.  The Enterprise Value of the business is calculated using the =NPV() function along with the discount rate of 12% and the Free Cash Flow to the Firm (FCFF) in each of the forecast periods, plus the terminal value.

The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

Image: CFI’s Business Valuation Modeling Course.

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What Does the Discounted Cash Flow Formula Tell You?

When assessing a potential investment, it’s important to take into account the time value of money or the required rate of return that you expect to receive.

The DCF formula takes into account how much return you expect to earn, and the resulting value is how much you would be willing to pay for something to receive exactly that rate of return.

If you pay less than the DCF value, your rate of return will be higher than the discount rate.

If you pay more than the DCF value, your rate of return will be lower than the discount.

Illustration of the DCF Formula

Below is an illustration of how the discounted cash flow DCF formula works.  As you will see, the present value of equal cash flow payments is being reduced over time, as the effect of discounting impacts the cash flows.

The present value of $200,000 development costs in year 0 assuming a 10% discount rate is:

Image: CFI’s free Intro to Corporate Finance Course.

Terminal Value

When valuing a business, the annual forecasted cash flows typically used are 5 years into the future, at which point a terminal value is used.  The reason is that it becomes hard to make reliable estimates of how a business will perform that far out into the future.

There are two common methods of calculating the terminal value:

  • Exit multiple (where the business is assumed to be sold)
  • Perpetual growth (where the business is assumed to grow at a reasonable, fixed growth rate forever)

Check out our guide on how to calculate the DCF terminal value to learn more.

DCF vs. NPV

The total Discounted Cash Flow (DCF) of an investment is also referred to as the Net Present Value (NPV).  If we break the term NPV we can see why this is the case:

Net = the sum of all positive and negative cash flows

Present value = discounted back to the time of the investment

DCF Formula in Excel

MS Excel has two formulas that can be used to calculate discounted cash flow, which it terms as “NPV.”

Regular NPV formula:

=NPV(discount rate, series of cash flows)

This formula assumes that all cash flows received are spread over equal time periods, whether years, quarters, months, or otherwise.  The discount rate has to correspond to the cash flow periods, so an annual discount rate of r% would apply to annual cash flows.

Time adjusted NPV formula:

=XNPV(discount rate, series of all cash flows, dates of all cash flows)

With XNPV, it’s possible to discount cash flows that are received over irregular time periods.  This is particularly useful in financial modeling when a company may be acquired partway through a year.

For example, this initial investment may be on August 15th, the next cash flow on December 31st, and every other cash flow thereafter a year apart. XNPV can allow you to easily solve for this in Excel.

To learn more, see our guide on XNPV vs. NPV in Excel.

More Helpful Resources

CFI’s mission is to help you advance your career.  With that mission in mind, we’ve compiled a wide range of helpful resources to guide you along your path to becoming a certified Financial Modeling & Valuation Analyst (FMVA)® analyst.

Relevant resources include:

  • Internal Rate of Return
  • Valuation Methods
  • DCF Modeling Tips
  • Financial Modeling Best Practices