Net Present Value (NPV)

Net present value theory may be the most important theory in capital budgeting and financial decision-making. Case in point:

Would you rather have $5,000 today or $7,000 today?
The answer to the above is obvious. But what if I asked you the following:

Would you rather have $5,000 today or $5,000 in two years?
The answer to the above is still obvious. Generally speaking, a dollar today is worth more than a dollar tomorrow for two reasons:

• Over time, inflation reduces the value or buying power of the dollar.
• A dollar received today can be invested to receive a return.

Now, what if I asked you the following:

Would you rather have $5,000 today or $7,000 in two years?
The answer to the above is not as obvious. The answer is – it depends. As stated above, a dollar received today can be invested to receive a return. Thus, it depends on the rate at which the dollar could be invested or the discount rate. The discount rate is the expected return of a potential project with comparable risk. The greater the risk, the higher the discount rate.

In order to compare the above two options, the future amount must be converted into a present value. That is, it must be discounted two years into the present. Only then can it be compared to the $5,000 which is already given as a present value (received today).

The Present Value formula below is used to convert a future value into a present value:

Present Value = Future Value / (1 + R)n
R = Discount Rate
N = Number of years before the future value will be received

Example:
If we use a discount rate of 20%, the present value of the $7,000 received in two years is:
Present Value = Future Value / (1 + R)^n
Present Value = $7,000 / (1 + .20)^2 = $4,861.11

In conclusion, at a 20% discount rate, having $5,000 today is worth more than having $7,000 in two years.