# Capital Budgeting under Risk- Certainty Equivalent Approach and Risk Adjusted Discount Rate

**Capital Budgeting:** Capital budgeting (or investment appraisal) is the planning process used to determine whether an organization’s long term investments, such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing. When taking on this planning process, managers must take into account the potential risks of the investment not panning out the way they plan for it to, for any number of reasons. In order to discuss this further, we should look into defining the concept or risk.

**Risk: **Risk is the potential that a chosen action or activity (including the choice of inaction) will lead to a loss (an undesirable outcome). The notion implies that a choice having an influence on the outcome exists (or existed). Potential losses themselves may also be called “risks.”

**There are numerous kinds of risks to be taken into account when considering capital budgeting including:**

- Corporate risk
- International risk (including currency risk)
- Industry-specific risk
- Market risk
- Stand-alone risk
- Project-specific risk

Each of these risks addresses an area in which some sort of volatility could forcibly alter the plan of firm managers. For example, market risk involves the risk of losses in position due to movement in market positions.

There are different ways to measure and prepare to deal with risks as well. One such way is to conduct a sensitivity analysis. Sensitivity analysis is the study of how the uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input.

A related practice is uncertainty analysis which focuses rather on quantifying uncertainty in model output. Ideally, uncertainty and sensitivity analysis should be run in tandem. Another method is scenario analysis, which involves the process of analyzing possible future events by considering alternative possible outcomes.

For example, a financial institution might attempt to forecast several possible scenarios for the economy (e.g., rapid growth, moderate growth, slow growth), and it might also attempt to forecast financial market returns (for bonds, stocks, and cash) in each of those scenarios. It might consider sub-sets of each of the possibilities. It might further seek to determine correlations and assign probabilities to the scenarios. Then it will be in a position to consider how to distribute assets between asset types (i.e., asset allocation). The institution can also calculate the scenario-weighted expected return (which figure will indicate the overall attractiveness of the financial environment). It may also perform stress testing, using adverse scenarios.

**CERTAINTY EQUIVALENT APPROACH**

The certainty equivalent is a guaranteed return that someone would accept rather than taking a chance on a higher, but uncertain, return. To put it another way, the certainty equivalent is the guaranteed amount of cash that would yield the same exact expected utility as a given risky asset with absolute certainty, and represents the opportunity cost of risk.

Investments must pay a risk premium to compensate investors for the possibility that they may not get their money back

**Certainty Equivalent and Cash Flow**

The idea of certainty equivalent can also be applied to cash flow. The certainty equivalent cash flow is the risk-free cash flow that an investor or manager considers equal to a different expected cash flow which is higher, but also riskier. The formula for calculating the certainty equivalent cash flow is as follows:

Certainty equivalent cash flow = expected cash flow / (1 + risk premium)

The risk premium is calculated as the risk-adjusted rate of return minus the risk-free rate. The expected cash flow is calculated by taking the probability-weighted dollar value of each expected cash flow and adding them up.

**RISK ADJUSTED DISCOUNT RATE**

The risk-adjusted discount rate is based on the risk-free rate and a risk premium. The risk premium is derived from the perceived level of risk associated with a stream of cash flows for which the discount rate will be used to arrive at a net present value. The risk premium is adjusted upward if the level of investment risk is perceived to be high. When a high risk-adjusted discount rate is applied to a stream of cash flows, the net present value of those cash flows will be greatly reduced. Conversely, a low risk-adjusted discount rate will result in a higher net present value. A proposed investment with a higher net present value is more likely to be accepted. Thus, the discount rate is used to judge whether a proposed investment is acceptable. Other types of risks must also be considered, such as currency risk when a foreign investment is being evaluated.

Though the use of a risk-adjusted discount rate initially appears to be a highly regimented and quantitatively sound approach to evaluating risky investments, it is subject to one significant flaw, which is how the risk premium is derived. Managers could break the system by first calculating the maximum discount rate that will still result in their project being approved, and lobby in favor of the application of that discount rate – irrespective of the actual risk profile of the project.

The main advantages of the risk-adjusted discount rate are that the concept is easy to understand and it is a reasonable attempt to quantify risk. However, as just noted, it is difficult to arrive at an appropriate risk premium, which can render the results of the analysis invalid. This approach also assumes that investors are risk-averse, which is not always the case. Some investors will accept a high level of risk if they perceive a potentially large payoff from an investment in the future.

**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 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.

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