Think & Done

Formula to calculate profitability index from a series of cash flows illustrated with example profitability index calculation. On this web page we discuss profitability index method used in financial management to find profitability of an investment project.

Profitability Index Calculator

Here you will find an online Profitability Index calculator that calculates profitability index given that you provide a series of cash flows and the discount rate

What is Profitability Index

Benefits to costs ratio (B/C ratio) also referred to as profitability index is a ratio of discounted benefits over discounted costs. It is a measure of profitability of an investment that we can compare with that of other investments that are under evaluation. Alternative investments may vary in size of cash flows or life span and these may provide more or less net benefits. Yet by using profitability index method, we can see for ourselves which one of these investments is more profitable as compared to the rest.

What is the formula for Profitability Index?

The Profitability index formula shows the numerator that is the discounted sum of benefits and the denominator that is the discounted sum of costs associated with a particular project. This particular equation may also be used to infer the internal rate of return which occurs when profitability index is equal to 1. We will leave that discussion to another tutorial, here we will emphasize the use of profitability index method

Profitability Index Example

Let me illustrate profitability index calculation with an example investment. Assume that we have to incur an initial cost of $100,000 followed by interim cash flows of $25,000 $30,000 $35,000 $-20,000 $25,000 and $30000. And our cost of capital (discount rate) is 10%. Should we accept or reject this investment proposal using the profitability index method.

Profitability Index Calculation

To find the profitability index, we will find the sum of discounted benefits and the sum of discounted costs and finally find it's ratio as shown in the following calculations.

Discounted Costs at 10%

DCF0 =	-100000 / (1+0.1)0 =	-100000
DCF4 =	-20000 / (1+0.1)4 =	-13660.27
PV Costs=		113660.27

Discounted Benefits at 10%

DCF1 =	25000 / (1+0.1)1 =	22727.27
DCF2 =	30000 / (1+0.1)2 =	24793.39
DCF3 =	35000 / (1+0.1)3 =	26296.02
DCF5 =	25000 / (1+0.1)5 =	15523.03
DCF6 =	30000 / (1+0.1)6 =	16934.22
PV Benefits=		106273.93

Profitability Index = Discounted Benefits / Discounted Costs
Profitability Index = 106273.93 / 113660.27
Profitability Index = 0.94

Profitability Index Calculation Online

This online tool will perform Profitability index calculation and will display step by step workout similar to one you have seen in this discussion.

Acceptance Criteria for Profitability Index

A proposal or investment project that has a Profitability Index of greater than 1 is considered a profitable investment. Here we find a Profitability Index of 0.94 which suggests that the project will not make us any profits and to the contrary we will lose out on our investment at the cost of capital of 10%. A Profitability Index of exactly 1 suggets that we will only break even on our investment without making any gains.

Effect of discount rate on Profitability Index

As we will shortly see that a lower cost of capital can drive up the Profitability Index. Let us say that our cost of capital for this project had been 6% instead of 10%, what effect this drop in discount rate have on Profitability Index. Let us do the calculations again with a discount rate of 6%

Discounted Costs at 6%

DCF0 =	-100000 / (1+0.06)0 =	-100000
DCF4 =	-20000 / (1+0.06)4 =	-15841.87
PV Costs=		115841.87

Discounted Benefits at 6%

DCF1 =	25000 / (1+0.06)1 =	23584.91
DCF2 =	30000 / (1+0.06)2 =	26699.89
DCF3 =	35000 / (1+0.06)3 =	29386.67
DCF5 =	25000 / (1+0.06)5 =	18681.45
DCF6 =	30000 / (1+0.06)6 =	21148.82
PV Benefits=		119501.74

Profitability Index = Discounted Benefits / Discounted Costs
Profitability Index = 119501.74 / 115841.87
Profitability Index = 1.03

Conclusion

Now we note that at our cost of capital of 6%, the profitability index is 1.03 thus making it a viable investment although it will provide very small gains. When compared to our earlier analysis, we will be more inclined to accept an investment proposal with a profitability index higher than 1 instead of an investment proposal where profitability index was less than 1.

Related DCF analysis methods

Following is a list of related readings that cover other 5 commonly used DCF analysis methods

1. Internal Rate of Return
2. Modified Internal Rate of Return
3. Net Present Value
4. Payback period
5. Discounted payback period