Risk Adjusted Discount Rate – Meaning, Formula, Example and More

What is Risk-Adjusted Discount Rate?

Risk-Adjusted Discount Rate (RADR) is sum total of two components. And these components are the risk-free rate and the risk premium. This rate comes in handy when an expert or investor needs to calculate/ascertain the present value of a risky investment. So, we can say that RADR is the return that an investor expects for taking a higher risk.

The risk premium is basically the risk that one relates to the cash flows for which one needs to calculate the NPV (net present value). Or, we can say it depends on an investor’s risk level and their perceived risk in the investment. If the risk is more, then the risk premium is more. And, when we use a higher risk premium, the PV of the cash flows will reduce. And obviously, this means the RADR will be higher.

It won’t be wrong to say that NPV is inversely proportional to RADR. This is because an increase in RADR reduces the NPV and vice versa.

Generally, an investment with more net present value gets preference. So, the discount rate plays a crucial role in deciding whether or not to accept a project or investment. We can also say that RADR is the required return.

Along with accounting for the risk in the investment, the RADR could also account for the currency risk and the geography risk.

Why use Risk-Adjusted Discount Rate?

Talking of why we need a risk-adjusted discount rate, a simple answer is that it accounts for all risks. Everyone is aware that the future is uncertain, which is true with investments or projects.

There are several risks in the case of a long-term investment. These risks are primarily related to future market conditions, inflation, credit risk, political risk, etc. And, if the project is in another country, then there is a currency risk as well. There could be regulatory risks as well if there are chances of the project facing potential lawsuits.

Thus, it is very important that the decision on whether or not to invest in a project takes into account thoroughly all these risks. And for that purpose, the use of RADR is an easy and simple way to account for all these risks.

Formula for Risk Adjusted Discount Rate

Simply stated RADR calculation formula is the summation of – Prevailing Risk-free rate Plus Risk premium for the kind of risk proposed/expected.

The formula for risk premium (under CAPM) is – (Market rate of return Less Risk-free rate) * beta of the project.

Example 1

An example will help us to understand the RADR concept better.

Suppose Company A is considering a project that requires an initial cash outflow of $80,000. This project will result in a cash inflow of $100,000 in three years. A similar project is offering a return of 5%. So, Company A will use the same rate to discount the cash flow.

On this basis, the PV of the cash flow is $86,384. Since PV is more than the initial investment, so Company A should accept the project.

However, this project is in another country. So Company A wants to include currency risk in the discount rate as well. Thus, Company A determines a risk-adjusted discount rate of 8% (5%, the return available on another project, or the Risk-Free Rate plus 3% on account of currency risk). On this basis, the PV of the cash inflow is $79,383.

After considering the currency risk, the PV of cash inflow is less than the initial cash outflow. This makes the project unacceptable.

Use Risk-Adjusted Discount Rate Calculator

Example 2

Let’s consider another example to understand the importance of a risk-adjusted discount rate.

Suppose Company A has an offer to invest in three projects – B, C, and D. However, Company A has funds to invest in only one project. So, it decides to use the NPV method to decide on the project that it should invest in.

Following are the details:

Project B – $56,000 (Initial Investment), Cash flows for year 1,2 and 3 ($25,000; $10,000; $15,000), Risk-free rate is 2%, while Risk premium is 5%.

Project C – $68,000 (Initial Investment), Cash flows for year 1,2 and 3 ($32,000; $12,000; $41,000), Risk-free rate is 1.2%, while Risk premium is 4%.

Project D – $85,000 (Initial Investment), Cash flows for year 1,2 and 3 ($12,000; $30,000; $53,000), Risk-free rate is 3%, while Risk premium is 7%.

Now, the risk-adjusted discount rate for each project will be:

Project B = 2% + 5% = 7%

Project C = 1.2% + 4% = 5.2%

Project D = 3% + 7% = 10%

Now, we need to calculate the PV of cash flows for each project using the above RADR. Following is the NPV of the three projects:

Project B – $53,103

Project C – $71,400

Project D – $75,522

Now, to decide on the most profitable project, we need to deduct the initial cash outflow from the PV to get the NPV.

Project B = $53,103 – $56,000 = -$2,897

Project C = $71,400 – $68, 000 = $3,400

Project D = $75,552 – $85,000 = -$9,448

Since Project C has a positive NPV, so Company A should invest in Project C.

Advantages and Disadvantages of Risk Adjusted Discount Rate

As usual with any concept or approach, the RADR approach also has certain advantages and disadvantages. Let us first talk about the advantages:

• This approach is simple and easy to understand.
• It is appealing to a risk-averse investor.
• This approach helps to reduce uncertainty and fluctuations in the expected return.
• It also helps to bring out the risk level in an investment or project.

Following are the disadvantages of RADR:

• Getting an accurate risk premium is a challenging task. So, if the risk premium is not accurate, then the final result (net present value) may also be inaccurate.
• This approach assumes that investors are risk-averse. However, this is not always true. There are investors who would accept more risk only if they believe the cash flows will be higher as well.

Final Words

The major advantage of using a risk-adjusted discount rate is that it is easy to understand. Also, this approach helps in quantifying risk. However, it is very difficult to arrive at an accurate risk premium. So, at times, such an approach may give inaccurate results.

Also, read about certainty equivalent to learn about a new technique for reducing risk.