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# 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. NPV is the result of calculations used to find the current value of a future stream of payments.

### Key Takeaways

• Net present value, or NPV, is used to calculate the current value of a future stream of payments from a company, project, or investment.
• To calculate NPV, you need to estimate the timing and amount of future cash flows and pick a discount rate equal to the minimum acceptable rate of return.
• The discount rate may reflect your cost of capital or the returns available on alternative investments of comparable risk.
• If the NPV of a project or investment is positive, it means its rate of return will be above the discount rate.
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## Net Present Value (NPV) Formula

If there’s one cash flow from a project that will be paid one year from now, then the calculation for the NPV is as follows:

\begin{aligned} &NPV = \frac{\text{Cash flow}}{(1 + i)^t} - \text{initial investment} \\ &\textbf{where:}\\ &i=\text{Required return or discount rate}\\ &t=\text{Number of time periods}\\ \end{aligned}

If analyzing a longer-term project with multiple cash flows, then the formula for the NPV of a project is as follows:

\begin{aligned} &NPV = \sum_{t = 0}^n \frac{R_t}{(1 + i)^t}\\ &\textbf{where:}\\ &R_t=\text{net cash inflow-outflows during a single period }t\\ &i=\text{discount rate or return that could be earned in alternative investments}\\ &t=\text{number of time periods}\\ \end{aligned}

If you are unfamiliar with summation notation, here is an easier way to remember the concept of NPV:

$NPV = \text{Today’s value of the expected cash flows} - \text{Today’s value of invested cash}$

## What Net Present Value Can Tell You

NPV accounts for the time value of money and can be used to compare the rates of return of different projects, or to compare a projected rate of return with the hurdle rate required to approve an investment. The time value of money is represented in the NPV formula by the discount rate, which might be a hurdle rate for a project based on a company's cost of capital. No matter how the discount rate is determined, a negative NPV shows the expected rate of return will fall short of it, meaning the project will not create value.

In the context of evaluating corporate securities, the net present value calculation is often called discounted cash flow (DCF) analysis. It's the method Warren Buffett uses to compare the net present value of a company's discounted future cash flows with its current price.

The discount rate is central to the formula. It accounts for the fact that, so long as interest rates are positive, a dollar today is worth more than a dollar in the future. Inflation erodes the value of money over time. Meanwhile, today's dollar can be invested in a safe asset like government bonds; investments riskier than Treasuries must offer a higher rate of return. However it's determined, the discount rate is simply the baseline rate of return that a project must exceed to be worthwhile.

For example, an investor could receive $100 today or a year from now. Most investors would not be willing to postpone receiving$100 today. However, what if an investor could choose to receive $100 today or$105 in one year? The 5% rate of return might be worthwhile if comparable investments of equal risk offered less over the same period.

### Step 2: NPV of future cash flows

• Identify the number of periods (t): The equipment is expected to generate monthly cash flow for five years, which means there will be 60 periods included in the calculation after multiplying the number of years of cash flows by the number of months in a year.
• Identify the discount rate (i): The alternative investment is expected to return 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, compound rate. Using the following formula, we find that the periodic monthly compound rate is 0.64%.

$\text{Periodic Rate} = (( 1 + 0.08)^{\frac{1}{12}}) - 1 = 0.64\%$

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.

## Why Are Future Cash Flows Discounted?

NPV uses discounted cash flows to account for the time value of money. So long as interest rates are positive, a dollar today is worth more than a dollar tomorrow because a dollar today can earn an extra day's worth of interest. Even if future returns can be projected with certainty they must be discounted for the fact time must pass before they're realized, time during which a comparable sum could earn interest.

Article Sources
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1. Harvard Business Review. "A Refresher on Net Present Value."

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