Net present value and the profitability index are helpful tools that allow investors and companies make decisions about where to allocate their money for the best return.

Net present value tells us what a stream of cash flows is worth based on a discount rate, or the rate of return needed to justify an investment.

The profitability index helps make it possible to directly compare the NPV of one project to the NPV of another to find the project that offers the best rate of return.

Calculating net present value of a lemonade stand
Suppose you have the opportunity to start a lemonade stand for $100. You believe this lemonade stand will produce $20 in cash each year for the next 10 years, or $200 in total. However, being a smart investor, you only want to start the lemonade stand if it creates value for you -- if the return exceeds your required rate of return.

Let's suppose you want to earn 8% per year on your investment. Should you open the lemonade stand?

To find the answer, we'll have to calculate the net present value of the lemonade stand. We determined that the cash flow profile looks like this:

Year 0: -$100
Year 1: $20
Year 2: $20
Year 3: $20
Year 4: $20
Year 5: $20
Year 6: $20
Year 7: $20
Year 8: $20
Year 9: $20
Year 10: $20

Just as described, we need to invest $100 today to receive $20 per year in profits from the lemonade stand for the next 10 years.

Now we have to calculate the net present value of the project by discounting these cash flows back to the present. The $100 initial investment doesn't need to be discounted because it happens right now. It's already in present dollars. However, each subsequent cash flow needs to be discounted to find the value of the cash flow in present dollars.

The math for discounting each cash flow is as follows.

Year 0: -$100/(1.08^0)= -$100
Year 1: $20/(1.08^1)= $18.52
Year 2: $20/(1.08^2)= $17.15
Year 3: $20/(1.08^3)= $15.87
Year 4: $20/(1.08^4)= $14.70
Year 5: $20/(1.08^5)= $13.61
Year 6: $20/(1.08^6)= $12.60
Year 7: $20/(1.08^7)= $11.67
Year 8: $20/(1.08^8)= $10.81
Year 9: $20/(1.08^9)= $10.00
Year 10: $20/(1.08^10)= $9.26

Discounting tells us what an amount of cash is worth today, given our required rate of return. For example, the 10th cash flow of $20 has a present value of $9.26 today. Thus, if we had an opportunity to buy $20 in cash 10 years from now, we could pay no more than $9.26 for that cash flow to get an 8% annual return on our $9.26 investment.

Once you have calculated a present value for each cash flow, the next step is to add up all of the present values. After adding up all 11 cash flows from the initial -$100 outlay to the 10th year's present value of $9.26, we arrive at a net present value of the project of $34.20.

The NPV is positive, so we should open the lemonade stand. We will generate a return that is higher than 8% per year because the NPV is positive. If the NPV were negative, we would know that the project generates a return of less than 8% per year. If the NPV were $0, then the project is expected to produce a return equal to our discount rate, or 8% per year.

Calculating a profitability index
The next step is to use the information from the net present value calculation to determine a profitability index for the investment.

The profitability index is calculated with the following formula:

Profitability index = present value of future cash flows / initial investment

We calculated that the net present value of all of the lemonade stand's cash flows was $34.20. However, to calculate the profitability index, we need the present value of the future cash flows only.

To get the present value of all the future cash flows, we can add up the present values of the cash flows that occur from Year 1 to Year 10 and get $134.20. Alternatively, we can simply add the $100 original investment back to the NPV we calculated earlier ($34.20) to get $134.20. Either way, you get the same value.

This figure, $134.20, goes into the numerator. We originally invested $100 into the project, so that goes into the denominator.

Thus, the profitability index is $134.20 / $100, or 1.342.

What the profitability index tells us
When the profitability index is greater than 1, the project creates value -- it generates a return greater than our required return. When the profitability index is less than 1, the project destroys value -- it generates a return less than our required return. If it is equal to 1, then the profitability index tells us the project generates a return equal to the discount rate.

One of the central weaknesses here is that the size of the project has a big impact on the project's NPV. A $1,000 lemonade stand that produces $175 in cash flows for 10 years would have a larger NPV ($174.26) than our $100 lemonade stand that produces $20 in cash flows for 10 years.

However, despite a smaller NPV, the $100 lemonade stand produces a much better return for each dollar invested. If you do the math, you'll find the $100 lemonade stand produces a profitability index of 1.342, versus 1.174 for the $1,000 lemonade stand.

Because the size of a project's NPV is related to the size of the original investment, NPV is not useful for determining which project has a higher return in percentage terms. The profitability index fixes that basic problem by allowing you to compare the profitability indexes of two or more projects to one another to find the project that creates the most value for each dollar invested.

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