# NPV - net present value:

The NPV is a standard method for the financial appraisal of long-term projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met.

By definition, NPV = Present value of net cash flows. For its expression, see the formula section below.

NPV is the classic method taught at most MBA business schools. Its a technique that allows managers to compare future cash flows in terms of todays dollars. Its allows managers to put a dollar value on expected future cash flows, and to compare one project vs another. When comparing projects on NPV analysis, the one with the higher NPV always wins.

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# Calculating Present Value

NPV = - Cost + PV

where PV of a stream of cash flows - Cost of initial investment. Its called "net" because you subtract the initial outflow of money to find the net result.

Question: how much money do you have to put in a bank today to have $1000 in one year, at 10% interest? This is the same thing as asking...what is the present value (today) of $1000 in one year

PV * (1+r)^n = FV

PV = 1000 / (1+.10)^1

PV = 1000 / (1.10)

PV = 909.09

where r = discount rate, interest

## Using Tables

One common method for solving present value problems is to use financial tables (as found in most common text books,or online). The present value tables give you the "present value factor", which can be used simply to find the present value.

All the tables have really done is calculated the exponent for you. For example, a 10 percent interest, for 5 years, will have (1+r)^n = (1.10)^5 = 1.61051 (which you can get by typing in 1.10 x 1.10 five times in your calculator), or you can just look it up in a table, and find 1.61051. So, $1 will be worth $1.61 in 5 years if you earn 10% per year. The 1.61051 is called the Future value factor.

## Effect of Uncertainty

If an investment produces certain, guaranteed payments in the future,then its easy to discount those cash flows to the present value using an interest rate that is similar to what you would get by simply placing your money in a bank account for one year. But, if the project has risk, then its not guaranteed that you will get that cash flow in the future, any you should be compensated for taking that additional risk. Therefore, you should discount the future cash flows (back to the present) at a slightly higher interest rate discount rate.

To determine what the appropriate discount rate is, there is as much of an art as there is a science. One common method is to use WACC, or the "weighted average cost of capital" of the firm as the appropriate discount rate.

## Effect of interest rates

interest is one of the key concepts to understand in order to do the NPV calculations

In general - the higher the interest rate, the lower the NPV, so

For bonds - the higher the interest rate (market rates), the lower the value of the bond

# Using NPV to make investment decisions

NPV is an important tool for capital budgeting, when there is a decision that needs to be made, and there needs to be a process for accepting or rejecting projects.

- Projects should be accepted if NPV is >0, and rejected if NPV <0
- Accepting positive NPV projects adds shareholder value, and raised the value of the firm by that amount

key issue = selecting the appropriate discount rate to account for risk

# Problems with NPV

The problem with this method is that it seems very precise. The output is a very exact number, and managers can be fooled into thinking that precise is the same thing as accurate. It is not. The NPV analysis can be very inaccurate, depending upon which assumptions you base your calculations. If you change one assumption (future growth, market size, competition, etc), it can dramatically change your NPV output.

So, if you are ever presented with an NPV analysis, please take a moment to critically challenge the underlying assumptions.

Another problem with NPV, is that it depends upon which discount rate the analyst has chosen. But, this discount rate can be very difficult to estimate properly. The trouble is that different projects might be more attractive than others depending upon which discount rate is chosen for the analysis. Be very careful when presented with an NPV analysis that compares two projects, and digg deep into how the discount rate was calculated. One project might be better at lower interest rates, but another is better at higher rates.

## Not accounting for options:

The core of the NPV analysis assumes that you are sitting at time T=0, and that you have one decision to make.... You first calculate the expected cash flows, and then you discount them to the present value to compare NPV of the various choices. If the project has a positive NPV, you accept the project, if its negative you reject it.

The problem with this analysis is that it doesn't properly value Options. You often have the choice to invest more at a later date. You might have the option to invest just a little now...to get the project rolling, and then if its going well...then you invest a little bit more at a later date. This is the essence of the Venture Capital Method of Valuation. This is often referred to as a "decision tree" analysis which handles risk in a more sophisticated manner. With this method, you value the firm today assuming that future decisions will be optimal (even before knowing what those decisions are going to be).

Starting a project is like purchasing a call option. If further information is revealed that makes the investment seem attractive, then you have bought the right to that investment in the future. In general, it is in investors best interest to not exercise the call option immediately, but rather to wait until the end of the time period to see what new information is presented.

The problem with standard NPV analysis is that it does not consider the very real world flexibility that most managers (and Venture Capitalists) face. An NPV analysis might show that a project should not be undertaken, but thinking in terms of options, you might be willing to invest a little for the option of being there in the future. This explains alot of seed funding of a few million dollars of Silicon Valley companies (that no-one but Venture Capitalist's can figure out why they are being funded). Sometimes, its just a matter of believing in the vision of the entrepreneur, or the idea, or seeing potential for untapped market share, and a little VC money makes sense (if not in an NPV world). By allowing the investing firm to change its investment policy later according to new information, a seemingly unwarranted investment can be justified.

Managers that just use NPV are ignoring real-world flexibility in their analysis.

# Online Calculators

calculator: http://formularium.org/en/10.html?go=44.281

# Good NPV attributes

1. It uses cash flows, and not accounting earnings. this is important when making investment decisions....do not use "slippery" accounting terms because they can be manipulated by accountants, and might not give an accurate picture of reality.

2. It uses the time value of money. All cash flows are discounted to the present, so that the time value of money is taken into consideration. Other capital budgeting techniques might not take this into consideration.

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