When a project is considered more or less risky than the current risk profile of a company, we can adjust WACC to reflect the greater return that equity holders of the firm would expect for undertaking the riskier project.

We do this by using a *beta* specific to the risk of the project. We take the *beta,* equal to the projectâ€™s market risk, and plot it on the security market line (SML), which gives us the expected return of the investment. The intuition is that the investmentâ€™s risk and return should reflect how it contributes to the volatility of a well-diversified portfolio.

Where,

*r*_{o} = the expected return of the project or investment to the equity holders of an all-equity firm

*r*_{f} = the risk-free rate

*r*_{market} = the expected return of the market

B_{asset }= the beta of the project or investment

We can then adjust the all-equity expected return, r_{o}, for the expected return to equity holders of the levered firm using the following formula.

Where,

*r*_{s} = the expected return of the project or investment to the equity holders of a levered firm

*T*_{c} = the corporate tax rate

B = the proportion of the firm financed by bondholders

S = the proportion of the firm financed by shareholders

Once we have the expected return of the project to the equity holders of the levered firm, r_{s}, we can then use this amount in our calculation of WACC for discounting the project.

It is important to note that before we use this approach, we have to consider whether the risks of the project may be already reflected in its expected cash flows. For example, if expected cash flows are already adjusted for risk, then no adjustment is needed to the discount rate to reflect the riskiness of the project.

__How did we find beta for the project?__

Finding the beta for a project can be subjective. One approach is to find the average beta of other firms in the same industry as the new undertaking. This can be found by looking at market information for the different firms. Firms are leveraged by different amounts, so we use the following formula to get the correspnding asset-beta (or all equity beta) for each of the firms in the industry.

We can then take the average of these value for beta to estimate a suitable all-equity beta for our new project. However, we say this approach is subjective. That is because not all new projects fit neatly into one industry or another. Consider a company undertaking a project to allow consumers to shop directly through their television. Would this be a part of the e-commerce industry, the television industry, or the retail industry?