Net Present Value (NPV) Made Simple

Net Present Value (NPV) concept just means that money now is more valuable than money later on. Why? Simply because you can use money to make more money! You can either start a business with money, or simply put it in the bank to earn interest !

Imagine that your parents just won the lottery and offered you the choice of receiving $10,000 now or next year. Which one would you chose?

If you place the $10,000 in your bank account today and assuming you can earn 4% interest, your money could earn $10,000 x 4% = $400 in a year. In other words your $10,000 now would become $10,400 in a year’s time.

In other words, $10,000 now is more valuable than $10,000 next year. $10,000 now is actually the same as $10,400 next year (at 4% interest).

There are many different ways that people use these terms in the industry.

  • We can say that the Present Value (PV) of $10,400 next year is $10,000.
  • We can also say that the Future Value (FV) of $10,000 invested today is $10,400 in one year.

Using the same logic applied to multiple years (n) and a given interest rate (r) we can link Present Value (PV) and Future Value (FV) to each other by a formula:

PV = FV / (1+r)n

  • PV is Present Value
  • FV is Future Value
  • r is the interest rate (as a decimal, so 0.04, not 4%)
  • n is the number of years

Let’s use this formula to calculate Present Value of $900 in 3 years with 10% interest rate:

PV = FV / (1+r)n

PV = $900 / (1 + 0.10)3 = $900 / 1.103 = $676.18

In some finance books, you see a formula PV(r,n) showing a function of r and n:

PV(10%, 3) = 1 / (1 + 0.10)3

so for the above example you can write PV = PV(10%,3) X $900 = $676.18

NPV and Project Selection

The concept of NPV is often used for selecting projects that are worth doing. You subtract the initial investment on the project from the total Present Values of inflows to arrive at Net Present Value (NPV). You proceed with the project only if NPV is positive.

There are two main formulas for the calculation of NPV:

 

When cash inflows are even:

NPV = C × 1 − (1 + r)-n − Initial Investment
r

In the above formula:

C is the net cash inflow expected to be received each period
r is the required rate of return per period (or interest rate over the period)
n are the number of periods during which the project is expected to operate and generate cash inflows

 

When cash inflows are uneven:

NPV = C1 + C2 + C3 + … − Initial Investment
(1 + r)1 (1 + r)2 (1 + r)3

where:

r is the target rate of return per period (or interest rate per period);
C1 is the net cash inflow during the first period;
C2 is the net cash inflow during the second period;
C3 is the net cash inflow during the third period, and so on …

In some books Initial Investment is also presented as Cbut with a negative value when you add it in the equation:

NPV = Co  + C1 + C2 + C3 + …
(1 + r)1 (1 + r)2 (1 + r)3

Now time for a Quiz:

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