Net Present Value

Net Present Value (NPV) is a calculation of the value of future cash flows in present-day currency.

A dollar in your hand today is considered to be worth more (or possibly less) than a dollar in a year's time, because of:

• Inflation - The value of a "dollar" (or whatever unit of currency) generally decreases over time.

• Opportunity Cost - If you receive the dollar now, you can spend it on something valuable or invest it and earn interest. If you don't receive it for a year, you can't do whatever you would have done with it.

• Risk - The person or company that says they're going to pay you a dollar in a year's time might go bankrupt and not pay up. The project that you're expecting to generate millions in revenue might fail. The economy might tank. Etc. Etc. Etc.

By calculating future income in today's dollars, one can get a better idea of the real value of a project, and make meaningful comparisons between different strategies.

Never invest in a project with negative NPV, unless there are strategic or other compelling reasons to do so. However, remember to also consider the CostOfDoingNothing.

NPV is one of those reasons that managers are always pushing to get software projects completed as soon as possible. Getting paid today is better than getting paid tomorrow.

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The formula for calculating NPV is

 NPV = future_dollars * (1 + discount_rate) ^ (- number_of_periods)

For example, with a discount rate of 10%, one dollar to be received a year from now is worth

 1.00 * (1 + 0.10)^(-1) = 0.90909

in today's dollars. A dollar to be received three years from now is worth

 1.00 * (1 + 0.10)^(-3) = 0.75131

Discount rates are based upon inflation, interest rates, and uncertainty. A risky project has a higher discount rate than a less risky project. The discount rate is sometimes called the hurdle rate, because a project with a high discount rate needs a larger payoff to be worthwhile.

What must keep in mind is that all of the factors used to determine this value, ie discount_rate (interest_rate, inflation), number_of_periods, are estimates, as is the calculated value.

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Another way to look at NPV is to ask "How much money in a bank today would it take to generate the specified cash flow?". Sometimes this is useful, sometimes it is not.

For example, to generate $1.00 in one year, if the current bank interest rate is 10%:

 x + .10 x = 1
 1.1 x = 1
 x = 1/1.1
 x = .909090(...)

Same answer :)

This approach is especially useful for evaluating continuing, constant cash flows. For example, what is the net present value of $20,000 per year (starting now, for eternity)? At 10% interest, you would need $200,000 in the bank to generate said stream. Hence NPV = $200,000.

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For more info, see http://en.wikipedia.org/wiki/Net_present_value

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CategoryEconomics, CategoryMath, EigenValue, MatrixFactoring, FuzzyMath?, FutureDiscounting