When analyzing the profitability of an investment or project, discount the cash flow to the present value to ensure that the true value of the enterprise is obtained. Usually, the discount rate used in these applications is the market interest rate.

However, depending on the circumstances related to the project or investment, it may be necessary to use a risk-adjusted discount rate.

Key points

- The discount rate takes into account the time value of money in order to commensurate the dollar earned in the future with its purchasing power today.
- In addition to the time frame, the level of risk involved in the investment or project that may cause future cash flow fluctuations should also be considered.
- There are several ways to incorporate risk into the discount rate; however, in any case, the greater the perceived risk, the greater the discount rate adjustment.

## The theory behind risk and reward

The concept of risk-adjusted discount rate reflects the relationship between risk and return. In theory, investors who are willing to take more risks will get potentially higher returns, because greater losses may also occur. This is shown in the risk-adjusted discount rate, because the adjustment changes the discount rate based on the risk faced. As project risks increase, the expected return on investment increases.

Discounting includes the recognition of the time value of money (TVM), or the concept that the money you have now is more valuable than the same amount in the future because of its potential profitability. This core principle of finance is that as long as you have money, you can earn interest. *any *The sooner you receive the money, the more valuable it is.

## Reasons for using risk-adjusted discount rates

The most common adjustments are related to the uncertainty of the timing, amount, or duration of the cash flow. For long-term projects, there are also uncertainties about future market conditions, investment profitability and inflation levels. The discount rate is adjusted according to the company’s expected liquidity and the risk of other parties’ default.

For overseas projects, currency risk and geographic risk are items that need to be considered. The company may adjust the discount rate to reflect investments that may damage the company’s reputation, cause litigation, or cause regulatory issues. Finally, the risk-adjusted discount rate will change based on the expected competition and the difficulty of maintaining a competitive advantage.

## Example of adjusted discount

A project that requires capital outflow of US$80,000 will return a cash inflow of US$100,000 within three years. A company can choose to fund a different project, which will receive a 5% return, so this ratio is used as the discount rate. The present value coefficient in this case is ((1 + 5%)³), which is 1.1577. Therefore, the present value of future cash flow is ($100,000/1.1577), which is $86,383.76.

Since the present value of future cash is greater than the current cash outflow, the project will generate net cash inflows and the project should be accepted.

However, the result may be changed by adjusting the discount rate to reflect the risk. Assuming that the project is abroad, the currency value is unstable, and the risk of being expropriated is relatively high. For this reason, the discount rate is adjusted to 8%, which means that the company believes that projects with similar risk profiles will generate 8% returns. The present value interest coefficient is now ((1 + 8%)³), which is 1.2597. Therefore, the new present value of the cash inflow is ($100,000/1.2597), which is $79,383.22.

When the discount rate is adjusted to reflect the additional risks of the project, it indicates that the project should not be taken because the value of the cash inflow does not exceed the cash outflow.

## The relationship between discount rate and present value

When the discount rate is adjusted to reflect risk, the discount rate will increase. A higher discount rate leads to a lower present value. This is because the higher discount rate indicates that the currency will grow faster over time due to the highest income rate. Suppose that two different projects will generate a cash inflow of US$10,000 in one year, but one project is more risky than the other.

Riskier projects have a higher discount rate, which increases the denominator in the present value calculation, resulting in a lower present value calculation, because riskier projects should result in a higher profit margin. The lower the present value of a riskier project means that less upfront capital is required to obtain the same amount as a lower risk project.

## Use the capital asset pricing model

A common tool used to calculate the risk-adjusted discount rate is the Capital Asset Pricing Model (CAPM). Under this model, the risk-free interest rate is adjusted by the risk premium based on the project’s beta. The risk premium is calculated by multiplying the difference between the market rate of return and the risk-free rate of return by the beta coefficient.

For example, in the period when the risk-free interest rate is 3% and the market rate of return is 7%, a project with a beta of 1.5 is being planned. Although the market rate of return is 7%, the project is more risky than the market because its beta is greater than 1. In this case, the risk premium is ((7%-3%)x1.5), or 6%.

## Use the beta version

To use the capital asset pricing model, the Beta of the project or investment must be calculated. Beta is calculated by dividing the covariance between asset returns and market returns by the variance of market returns. This formula calculates the relationship between investment returns and market returns. Investments with a similar relationship to the market will report a beta value of 1, while investments with higher risk than the market will produce a value greater than 1.

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