**As you remember the Net Present Value formula requires three variables: the initial investment amount, projections of expected cash flows from investment over time and, finally, the discount rate the interest rate used to put future cash flows into their present value equivalents. But this is way to complicated and some alternatives are needed.**

### Imperfect but user friendly is better

In the real world the internal rate of return (IRR), the profitability index and equity multiples are used even if all the experts recognize that these are imperfect tools compared to the NPV model, which gives the best information for investment decision-making. Yet, simplicity sometimes is preferred even when scientifically sound arguments argue against.

As terrific a tool as net present value is for evaluating investment opportunities it does have its practical limitations and challenges when we apply it in the real world. One of the **difficulties is how to determine the proper discount rate** we should use when computing the present values for the cash flows an investment is expected to generate over time.

The other challenge in using Net Present Value as an investment tool is that it is hard to interpret what it means beyond telling us whether investment should or should not be made, but investors usually want to know more like what the rate of return will be on the investment. As a result of these practical shortcomings a very common and widely used return measure is something known as the Internal Rate of Return (IRR).

### The Internal Rate of Return

In some industries it is one of the principal metrics that is used to evaluate the attractiveness of investment opportunity. These include venture capital funds and private equity funds that invest in real estate or individual companies.

Mathematically the Internal Rate of Return is the discount rate at which the net present value is equal to zero. So to get the internal rate of return you pull the NPV formula from your finance toolkit then you set the NPV value equal to zero and solve for the missing variable i.

Another helpful way to look at this is to imagine a graph of what happens to the net present value of any investment as the discount rate goes up. As the discount rate goes up the value of all future cash flows go down, therefore the NPV goes down. This is an important intuition you should have.

### Calculating the Internal Rate of Return

There are actually three ways to calculate the internal rate of return: one is the good old trial and error, you can simply keep trying different discount rates until one gives you an NPV equal to zero.

The second approach is to graph the function calculate at the first few guesses of a trial and error approach graph these and extrapolate where the graph crosses the X axis and you have your internal rate of return.

The third way is to use a financial calculator or computer spreadsheet like Microsoft Excel. For those of you with smart phones there are free financial calculator apps available as well as those available for purchase. These can be very handy.

Essentially if the internal rate of return you compute or estimate from investment opportunity is greater than the rate of return you require on investment you proceed with the opportunity. If the internal rate of return is less than the required rate of return you rejected and continue looking.

### The Profitability Index

When you want to know which project or projects do you choose among the competing alternatives, the profitability index will certainly help. The profitability index is defined as the net present value of an opportunity divided by the amount of the initial investment.

Basically this works by weighing investment options you calculate the profitability index and you do to rank all of the various investment alternatives that are being considered. Then working from the highest ranked opportunity one of the highest profitability index the lowest you can invest in one project after another until all the available funds are expended.

### The Equity Multiple

Commonly used in private equity and venture capital investments, the equity multiple is actually fairly easy to calculate and that is partly what makes it attractive. You simply take the cumulative amount of her terms that you’ve been paid on an investment over time divided by the amount of the investment actually made.

Obviously the time value of money is ignored under this approach which differentiates the equity multiple from other valuation methods such as the internal rate of return or net present value, but it is simple and for certain types of investments that are relatively short in duration like private equity or venture funds it can be a reasonable way of comparing different funds fund sponsors

Again, from a theoretical standpoint the Net Present Value is certainly the most robust and people with training in finance would recommend it to be used. However, what one finds empirically out in the real world is that different organizations and investors use different methods, each of which has significant shortcomings. But, the fact that they are easier to communicate and understand trumps their academic in theoretical shortcomings.