Stock Investing 101 – Net Present Value

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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 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:

Formula to Calculate Net Present Value (NPV) in Excel

Net present value (NPV) is a core component of corporate budgeting. It is a comprehensive way to calculate whether a proposed project will be financially viable or not. The calculation of NPV encompasses many financial topics in one formula: cash flows, the time value of money, the discount rate over the duration of the project (usually WACC), terminal value and salvage value.

How to Use Net Present Value?

To understand NPV in the simplest forms, think about how a project or investment works in terms of money inflow and outflow. Say, you are contemplating setting up a factory which needs an initial investment of $100,000 during the first year. Since this is an investment, it is a cash outflow which can be taken as a net negative value. It is also called an initial outlay. You expect that after the factory is successfully established in the first year with the initial investment, it will start generating the output (products or services) second year onwards. It will result in net cash inflows in the form of revenues from the sale of the factory output. Say, the factory generates $100,000 during the second year, which increases by $50,000 each year till the next five years. The actual and expected cashflows of the project are as follows:

XXXX-A represents actual cashflows, while XXXX-P represents projected cashflows over the mentioned years. A negative value indicates cost or investment, while positive value represents inflow, revenue or receipt.

How do you decide whether this project is profitable or not? The problem in such calculations is that you are making investments during the first year, and realizing the cashflows over a course of many future years. To assess such ventures that span multiple years, NPV comes to the rescue for financial decision making, provided the investments, estimates, and projections are accurate to a high degree.

NPV methodology facilitates bringing all the cashflows (present as well as future) to a fixed point in time, at present, hence the name “present value.” It essentially works by taking how much the expected future cashflows are worth at present and subtracts the initial investment from it to arrive at “net present value.” If this value is positive, the project is profitable and viable. If this value is negative, the project is loss-making and should be avoided.

In simplest terms,

NPV = (Today’s value of the expected future cash flows) – (Today’s value of invested cash)

Calculating future value from present value involves the following formula,

As a simple example, $100 invested today (present value) at a rate of 5 percent (r) for 1 year (t) will increase to:

Since we are looking to get present value based on the projected future value, the above formula can be rearranged as,

To get $105 (future value) after one year (t), how much should be invested today in a bank account which is offering a 5% interest rate? Using the above formula,

Put another way, $100 is the present value of $105 that are expected to be received in future (one year later) considering 5 percent returns.

NPV uses this core method to bring all such future cashflows to a single point in the present.

The expanded formula for NPV is

where FV0, r0, and t0 indicate the expected future value, applicable rates and time-periods for year 0 (initial investment), respectively, and FVn, rn, and tn indicate the expected future value, applicable rates, and time-periods for year n. Summation of all such factors leads to the net present value.

One must note that these inflows are subject to taxes and other considerations. Therefore, the net inflow is taken on the post-tax basis – that, is, only the net after-tax amounts are considered for cash inflows and are taken as a positive value.

One pitfall in this approach is that while financially sound from a theory point of view, an NPV calculation is only as good as the data driving it. It is therefore recommended to use the projections and assumptions with the maximum possible accuracy, for items of investment amount, acquisition and disposition costs, all tax implications, the actual scope and timing of cash flows.

Steps to Calculate NPV in Excel

There are two methods to calculate the NPV in the Excel sheet.

First is to use the basic formula, calculate the present value of each component for each year individually, and then sum all of them up together.

Second is to use the in-built Excel function which can be accessed using the “NPV” formula.

Using Present Value for NPV Calculation in Excel

Using the figures quoted in the above example, we assume that the project will need an initial outlay of $250,000 in year zero. Second year (year one) onwards, the project starts generating inflows of $100,000, and they increase by $50,000 each year till the year five when the project gets over. The WACC, or weighted average cost of capital, is used by the companies as the discount rate when budgeting for a new project and is assumed to be 10 percent all throughout the project tenure.

The present value formula is applied to each of the cashflows from year zero to year five. For example, the cashflow of -$250,000 in the first year leads to same present value during the year zero, while the inflow of $100,000 during the second year (year 1) leads to present value of $90,909. It indicates that 1-year future inflow of $100,000 is worth $90,909 at year zero, and so on.

Calculating present value for each of the years and then summing those up gives the NPV value of $472,169, as shown in the above screenshot of the Excel with the described formulas.

Using Excel NPV Function for NPV Calculation in Excel

In the second method, the in-built Excel formula “NPV” is used. It takes two arguments, the discounting rate (represented by WACC), and the series of cashflows from year 1 to the last year. Care should be taken not to include the year zero cashflow in the formula, also indicated by initial outlay.

The result of the NPV formula for the above example comes to $722,169. To compute the final NPV, one needs to decrease the initial outlay from the value obtained from the NPV formula. It leads to NPV = ($722,169 – $250,000) = $472,169.

This computed value matches with the one obtained from the first method using PV value.

Calculating NPV in Excel – Video

The following video explains the same steps based on the above example.

Pros and Cons of the Two Methods

While Excel is a great tool to make a rapid calculation with high precision, its usage is prone to errors and as a simple mistake can lead to incorrect results. Depending upon the expertise and convenience, analysts, investors, and economists use either of the methods as each offers pros and cons.

The first method is preferred by many as financial modeling best practices require calculations to be transparent and easily auditable. The trouble with piling all of the calculations into a formula is that you can’t easily see what numbers go where, or what numbers are user inputs or hardcoded. The other big problem is that the built-in Excel formula does not net out the initial cash outlay, and even expert Excel users often forget to adjust the initial outlay value in the NPV value. On the other hand, the first method needs multiple steps in the calculation which may also be prone to user induced errors.

Irrespective of which method one uses, the result obtained is only as good as the values plugged in the formulas. One must try to be as precise as possible when determining the values to be used for cashflow projections while calculating NPV. Additionally, the NPV formula assumes that all cash flows are received in one lump sum at the year-end which is obviously unrealistic. To fix this issue and get better results for NPV, one can discount the cash flows at the middle of the year as applicable, rather than the end. This better approximates the more realistic accumulation of after-tax cash flows over the course of the year.

While assessing the viability of a single project, an NPV of greater than $0 indicates a project that has the potential to generate net profits. While comparing multiple projects based on NPV, the one with the highest NPV should be the obvious choice as that indicates the most profitable project.

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