*The Business Professor*, updated April 20, 2019, last accessed August 11, 2020, https://thebusinessprofessor.com/lesson/risk-adjusted-discount-rate-definition/.

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**Risk-Adjusted Discount Rate Definition**

A risk-adjusted discount rate is the rate obtained by combining an expected risk premium with the risk-free rate during the calculation of the present value of a risky investment. A *risky investment *is an investment such as real estate or a business venture that entails higher levels of risk. Although it is the usual convention to use the market rate as the discount rate in most applications, under certain circumstances, the application of a risk-adjusted discount rate becomes crucial.

**A Little more on What is Risk-Adjusted Return**

The risk-adjusted discount rate signifies the requisite return on investment, while correlating risk with return. This essentially means that an investment that is exposed to higher levels of risk also tends to bring in potentially higher returns, especially since the magnitude of potential losses is also greater. A risk-adjusted discount rate reflects such a correlation since discount rates are adjusted based on the magnitude of the risk involved.

**Factors that Necessitate a Risk-Adjusted Discount Rate**

Discount rates are mostly adjusted for unpredictability pertaining to the timing, value or time span of cash flows. In case of long-term projects, additional aspects such as future market conditions, inflation and profitability also need to be factored in. Companies adjust discount rates in keeping with risks associated with their projected liquidity, while also taking into account the risks associated with possible defaults by other parties. If the project is based in a foreign country, companies will also need to factor in other aspects such as currency risks and geographical risks. In case of investments that involve potential future lawsuits, regulatory issues or damage to the company’s image, it is essential to adjust discount rates accordingly. Other factors that influence adjustments are projected competition and challenges to the competitive edge achieved by the companies.

**Correlation of Discount Rate with Present Value**

Adjusting the discount rate to account for risks also increases the discount rate itself, leading to a lower present value. This phenomenon can be best explained with the help of the following example.

Two different projects, P1 and P2 both have cash flows of $1 million in a year. However, P1 involves higher risk levels than P2. Naturally, P1 will be adjusted to have a higher discount rate than P2. This will result in a lower present value calculation of P1 given its potential for raking in higher profit levels. A lower present value for P1 directly translates to a lower upfront investment required to make the exact same money as P2.

**Determining Risk-adjusted Discount Rate with a Capital Asset Pricing Model**

A capital asset pricing model is an instrument used to determine the risk-adjusted discount rate for a particular investment. This model adjusts the risk-free interest rate by combining it with an expected risk premium that is based on the beta of the project.

**Risk-adjusted discount rate = Risk-free interest rate + Expected risk premium**

The risk premium is obtained by subtracting the risk-free rate of return from the market rate of return and then multiplying the result by the beta of the project.

**Risk premium = (Market rate of return – Risk free rate of return) x Beta**

The beta of the project is calculated as,

**Beta = (Covariance) / (Variance)**

where, *Covariance *is a measure of the asset’s return relative to the return on the market, and V*ariance *is a measure of the market’s movement relative to its mean.

**Advantages and Disadvantages of Using Adjusted Rates**

Employing a risk-adjusted discount rate has its own set of advantages. First, such an adjustment is easy to understand and apply. Secondly, risk-adjusted rates prepare investors to face any uncertainties. Thirdly, risk-adjusted discount rates appeal to an investor’s institution, especially any investor that is averse to taking risks.

However, a risk-adjusted discount rate is not without its limitations. To begin with, the process of obtaining an adjusted rate is not a straightforward process, especially since capital asset pricing model have limited practical applications. Secondly, such an adjustment is based on the fundamental assumption that all investors are averse to taking risks, which is not true.

### References for Risk Adjusted Discount Rate

- https://www.investopedia.com/articles/budgeting-savings/083116/guide-riskadjusted-discount-rate.asp
- https://www.myaccountingcourse.com/accounting-dictionary/risk-adjusted-discount-rate
- https://www.readyratios.com/reference/analysis/risk_adjusted_discount_rate.html
- https://www.nasdaq.com/investing/glossary/r/risk-adjusted-discount-rate
- https://financial-dictionary.thefreedictionary.com/Risk-adjusted+discount+rate

**Academic Research for Risk Adjusted Discount Rate**

**Risk**‐adjusted **discount rates**‐extensions from the average‐**risk **case, **Harris, R. S., & Pringle, J. J. (1985). ***Journal of Financial Research***, ***8***(3), 237-244. **This article illustrates the procedure of obtaining a risk-adjusted discount rate based on the standard presentation of the weighted average capital cost. The authors scrutinize the implicit assumptions about corporate debt valuation and proceed to demonstrate the didactic utilities of their proposed procedure. An implicit assumption about risk-adjusted discount rates is that risk increases as time increases, as developed by the authors.

**Risk**-adjusted **discount rates **and capital budgeting under uncertainty, **Fama, E. F. (1977). ***Journal of Financial Economics***, ***5***(1), 3-24. **This article scrutinizes the valuation of multiperiod cash flows with the Sharpe-Lintner-Black model of capital market equilibrium as its basis. The author infers that a future net cash flow’s current market value is obtained by discounting the current expected value of the cash flow at non-stochastic risk-adjusted discount rates for all periods until the realization of the cash flow.

Market **risk adjustment **in project valuation, **Constantinides, G. M. (1978). ***The Journal of Finance***, ***33***(2), 603-616. **This paper introduces a rule that assumes the market price of risk to be ‘zero’ while evaluating a project in a continuous framework of time. The author applies the rules in a two-step procedure: The model parameters are first replaced with their effective values. Assuming the market price of risk to be ‘zero’, all expected cash flows at the riskless return rate are discounted.

How should the distant future be discounted when **discount rates **are uncertain?, **Gollier, C., & Weitzman, M. L. (2010). ***Economics Letters***, ***107***(3), 350-353. **According to the “Weitzman–Gollier puzzle”, two apparently symmetrical and equally cogent methods of engaging with uncertain future discount rates derive outcomes that are essentially diametrically opposed to each other. This paper notes that such a paradox can be resolved by agents by optimizing their consumption plans. Long-term discount rates gradually decrease to assume their lowest possible values.

On the negative **risk **premium for **risk **adjusted **discount rates**, **Berry, R. H., & Dyson, R. G. (1980). ***Journal of Business Finance & Accounting***, ***7***(3), 427-436. **This paper corroborates the findings of Professor Booth’s application of the Time State Preference framework to the negative risk premium problem and confirms their consistency with their own earlier findings. Consequently, the authors reject Professor Booth’s disapproval of their prior research, while offering additional comments about the phenomenon of negative risk premiums.

Incorporating country **risk **in the valuation of offshore projects, **Lessard, D. R. (1996). ***Journal of applied corporate finance***, ***9***(3), 52-63. **The general consensus regarding investments in offshore projects, especially in developing economies, is that such investments inherently carry higher levels of risk. As a result, companies involved in such projects tend to offer additional premiums in the discount rates. Oftentimes, offshore projects carry over-discounted cash flows, resulting in unnecessary burdens on such projects. This paper drafts a four‐step procedure for evaluating overseas risks so as to prevent arbitrary adjustments to the discount rate.

The **discount rate **in emerging markets: A guide, **Sabal, J. (2004). ***Journal of Applied Corporate Finance***, ***16***(2**‐**3), 155-166. **This article rejects the conventional approach of including a country risk premium into the discount rate; the author argues that there exists no uniformity in country risk, hence standardization is inappropriate. He also asserts that there is no discernible correlation between the discount rate and the spread on the government bonds of the country in question.

Making customers pay: measuring and managing customer **risk **and returns, **Ryals, L. (2003). ***Journal of strategic marketing***, ***11***(3), 165-175. **According to Customer Relationship Management (CRM), long-term customer relationships tend to be more lucrative than short-term relationships. However, subsequent research has demonstrated that this is not always the case. As such, it becomes extremely difficult for managers to determine which relationships will maximize shareholder value. This paper calculates returns and customer risks by employing the portfolio management model of risk and return.

**Risk **analysis and capital budgeting techniques of US multinational enterprises, **Shao, L. P., & Shao, A. T. (1996). ***Managerial Finance***, ***22***(1), 41-57. **This article scrutinizes the capital budgeting approach that is employed by overseas subsidiaries of U.S.‐based multinational companies. The authors summarize the theoretical as well as practical concerns pertaining to the analysis of international capital budgeting. They then elaborate topics such as collection of data, questionnaire drafting, and factors pertaining to the company and the environment. Finally, the authors discuss capital budgeting techniques, risk-assessment/risk-adjustment and capital budgeting policies.

The **risk **premium for evaluating public projects, **Klein, M. (1997). ***Oxford review of economic policy***, ***13***(4), 29-42. **This paper discusses the risk premium on government-financed projects. The government has access to open-ended credit insurance of formidable proportions in the form of taxpayers. However, taxpayers receive no remuneration for assuming the risks of tax-financed projects. Providing remuneration to taxpayers would strip the government finance of the cost advantages that it currently enjoys.

Use of the CAPM to **discount **property-liability loss reserves, **D’Arcy, S. P. (1988). ***Journal of Risk and Insurance***, 481-491. **According to the Tax Reform Act of 1986, insurers of property-liability are required to evaluate tax liabilities by discounting loss reserves at a set rate. On the other hand, insurers are seldom permitted to discount loss reserves. When appropriately applied, discounting of loss reserves results in a present value for loss reserves that is adjusted for risk in keeping with the monetary value of these liabilities.