When analyzing investments or projects for profitability, cash flows are discounted to present value to ensure the true value of the undertaking is captured. Typically, the discount rate used in these applications is the market rate. However, based on circumstances related to the project or investment, it may be necessary to utilize a risk-adjusted discount rate.

## Theory Behind Risk and Return

The concept of the risk-adjusted discount rate reflects the relationship between risk and return. In theory, an investor willing to be exposed to more risk will be rewarded with potentially higher returns, since greater losses are also possible. This is shown in the risk-adjusted discount rate as the adjustment changes the discount rate based on the risk faced. The expected return on an investment is increased because there is increased risk in the project.

## Reasons to Use Risk-Adjusted Discount Rate

The most common adjustment relates to uncertainty to the timing, dollar amount or duration of cash flows. For long-term projects, there is also uncertainty relating to future market conditions, profitability of the investment and inflation levels. The discount rate is adjusted for risk based on the projected liquidity of the company, as well as the risk of default from other parties. For projects overseas, currency risk and geographical risk are items to consider. A company may adjust the discount rate to reflect Investments with the potential to damage a company’s reputation, lead to a lawsuit or result in regulatory issues. Finally, the risk-adjusted discount rate is altered based on projected competition and the difficulty of retaining a competitive advantage.

## Example of Discounting with Adjusted Rate

A project requiring a capital outflow of \$80,000 will return a cash inflow of \$100,000 in three years. A company can elect to fund a different project that will earn 5%, so this rate is used as the discount rate. The present value factor in this situation is ((1 + 5%)³), or 1.1577. Therefore, the present value of the future cash flow is (\$100,000/1.1577), or \$86,383.76. Because the present value of the future cash is greater than the current cash outflow, the project will result in a net cash inflow, and the project should be accepted.

However, the outcome may change as a result of adjusting the discount rate to reflect risks. Suppose this project is in a foreign country where the value of the currency is unstable and there is a higher risk of expropriation. For this reason, the discount rate is adjusted to 8%, meaning that the company believes a project with a similar risk profile will yield an 8% return. The present value interest factor is now ((1 + 8%)³), or 1.2597. Therefore, the new present value of the cash inflow is (\$100,000/1.2597), or \$79,383.22. When the discount rate was adjusted to reflect the extra risk of the project, it revealed that the project should not be taken because the value of the cash inflows does not exceed the cash outflow.

## Relationship Between Discount Rate and Present Value

When the discount rate is adjusted to reflect risk, the rate increases. Higher discount rates result in lower present values. This is because the higher discount rate indicates that money will grow more rapidly over time due to the highest rate of earning. Suppose two different projects will result in a \$10,000 cash inflow in one year, but one project is riskier than the other. The riskier project has a higher discount rate that increases the denominator in the present-value calculation, resulting in a lower present value calculation, as the riskier project should result in a higher profit margin. The lower present value for the riskier project means that less money is needed upfront to make the same amount as the less risky endeavor.

## Capital Asset Pricing Model

A common tool used to calculate a risk-adjusted discount rate is the capital asset pricing model. Under this model, the risk-free interest rate is adjusted by a risk premium based upon the beta of the project. The risk premium is calculated as the difference between the market rate of return and the risk-free rate of return, multiplied by the beta. For example, a project with a beta of 1.5 is being planned during a period when the risk-free rate is 3% and the market rate of return is 7%. Although the market rate of return is 7%, the project is riskier than the market because its beta is greater than one. In this situation, the risk premium is ((7% - 3%)x1.5), or 6%.

## Calculating Beta

To use the capital asset pricing model, the beta of the project or investment must be calculated. The beta is calculated by dividing the covariance between the return of the asset and the return on the market by the variance in the returns on the market. This formula calculates the relationship between the returns of the investment and the returns of the market. Investments with a similar relationship to the market will report a beta of one, while investments riskier than the market will yield a value greater than one.