# How is Risk related to Net Present Value?

## What is Net Present Value (NPV) and Risk?

Net present value (NPV) and the risk have a strong relationship with each other. With an inappropriate risk assessment, one cannot arrive at the correct or near correct net present value.

The net present value of any asset or investment is the present value of future cash flows (generated out of that asset or investment) discounted using an appropriate discounting rate. Risk is uncertainty attached to the future cash flows.

## A Dollar Today is Worth more than a Dollar One Year Later.

One basic principle of finance establishes the base for building the concept of net present value. It is a very well-known principle and is quoted everywhere.

It is very simple to understand. For example, George earned \$1 today. He instantly goes and invests his dollar in government security today, say @ 4%. At the end of the year, he increases the future value of its dollar one year later by earning interest on that, i.e., \$1.04. Conversely, the present value of a dollar one year later is definitely less than one dollar.

## A Safe Dollar is Worth more than a Risky One.

Another fundamental principle of finance explains the relevance of the relationship between net present value with risk.

Suppose there are two options for an investor to invest his money. One, investment in real estate with a 6% rate of return, and another in government security with the same rate of return of 6%. Every rational investor will invest in government security simply because their hard-earned money is safe in government security in comparison to real estate investment.

In calculating NPV, we typically utilize present cash outflow (or initial investment), future cash inflows, and a discounting rate. Risk has relevance with 2 out of 3 components of net present value.

Commonly, we know initial investment or cash outlay with certainty. But, future cash inflow is an estimation based on certain assumptions which may or may not turn right. Therefore, the risk is associated with future cash flows.

### NPV Calculation at Stake

1. If the future cash flows turn lesser than estimated, the viability of the whole project may go for a toss, and it may turn out to be a loss-making investment.
2. Secondly, a decision regarding the discounting rate is very critical. It is because this rate applies to all the future expected cash flows to convert them into their present values. Thus, even a slight difference in decimals may change the whole calculation. A discounting rate of 9.25% may give a positive NPV, and a small change to 9.45% may make it negative.
3. The discounting rate of return is also known as an opportunity cost of capital or hurdle rate. It is the rate of return that we can earn from the next best alternative investment opportunity having a similar risk profile. Considering the same investment options discussed above, we can’t utilize the rate of return on government security for evaluating NPV for real estate investment. The reason is simple. The risk profile of the two investments is entirely different. One is highly risky, and the other is highly safe.

Just talking about problems is not something which wise people should do. We have now learned that risk associated with cash flows can pose a severe problem to the whole NPV calculation. When an analyst calculates NPV for any project, he relies majorly on this technique. It is because he knows Why NPV is the best measure for investment appraisal? If a loss-making project gets approval for implementation, the outcome could be substantial financial losses. This makes it even more critical to address the issue with NPV calculation, especially the aspect of association of risk. Using a slightly tweaked technique of risk-adjusted NPV can significantly mitigate the risk of making the wrong decision.

Risk-adjusted NPV, also known as rNPV, does not use the estimates of future cash flows as it is in the calculation. They are first adjusted with the risk factor and then used to calculate. For example, a first-year cash flow estimate is \$1 m for a project, and estimation is with 70% certainty. In rNPV, an amount of \$0.7 m ( \$1 m * 70%) will be considered in place of \$1 m. Although it amounts to the additional hassle of working, it may be worth it when dealing with big projects with heavy outcomes.

Such a technique is quite prevalent in pharmaceutical projects where the result of R&D is highly uncertain.

What are the fundamental principles that explain the relevance of the relationship between NPV and risk?

Two fundamental principles are:
1. A safe dollar is worth more than a risky one.
2. A Dollar Today is Worth more than a Dollar One Year Later

Why risk is associated with future cash flows?

Future cash flows are nothing but an earnings estimate based on some past data and trends. These estimates may turn true or may not. And hence, there is always some risk associated with future cash flows. 