Using NPV and Perpetuities in Cases

NPV

(credit: Finance Formulas)

The Net Present Value (NPV) of an investment is how much an investment that yields consistent cash flows in the future is worth today.

Today’s article will be about when and how you use NPV analysis in cases.

When Do You Use NPV?

There are certain cases in which you’re asked whether or not to invest in something. The way these cases usually end up going is, either you calculate a breakeven point, calculate a ROI, or conduct a NPV analysis.

The breakeven point analysis is usually for something like a new factory or a new product. You usually use it when you don’t have enough information to estimate how much profit the investment will make, so you try to figure out how much you’d have to sell to break even.

The ROI you can use for any sort of investment.

The NPV is usually used when you have a good idea of how much money you’re going to make when you buy something. For example, you’re buying a company for which you know the annual profit and you think the cash flow will be consistent for years to come.

Now, let’s imagine that you could make an acquisition of a company that makes $100 million in profit per year. The price is $800 million. Is it worth it?

Well, it’s not an easy problem. One thing to remember is that cash made in the future isn’t worth as much as cash today (the time value of money), so even if you get consistent cash from something that cash will be worth less and less compared to what you paid as time goes on.

The formula above will tell you how much an investment is worth assuming a certain price paid, annual cash flow, and discount rate (how much the cash would increase in worth if invested at a similar level of risk; industry specific).

The problem is, the calculation is too cumbersome to do during a case interview because you don’t have a calculator, so instead you use a perpetuity.

Perpetuities

PV of a Perpetuity

(credit: Finance Formulas)

A perpetuity is an investment that yields cash forever. For the most part they don’t exist in reality, but it’s easier to calculate the present value of something if we assume it goes on in perpetuity.

So what you do in a case is you calculate the annual profit of whatever you’re trying to buy, ask if you can assume its a perpetuity, ask for a discount rate, and calculate the present value of the perpetuity.

So for the acquisition we mentioned, let’s assume a discount rate of 10% and an annual profit of $100 million.

PV = $100 million / 10% = $1 billion

That means that the present value of this acquisition is $1 billion, and the price (from before) is $800 million. Since the present value > price, the investment is worth doing. (Of course, there are many other factors.)

Conclusion

NPV is a tool used to tell you how much future cash flows are worth today. Usually they’re too cumbersome to use in cases, so you make the assumption that cash flows continue in perpetuity.

As soon as you do that, you can calculate the present value of an investment by the ratio of its annual cash flow to its discount rate (which is industry and situation specific, you can ask for it). Now you can compare the present value of the investment to its price to see if its worth it.

If it does look worthwhile financially, its valuable to keep exploring whether the investment is worthwhile on the qualitative side, but it’s a good sign.

 

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