3.4. Estimating β

The estimation of β is based on the statistical calculate the standard error which show the extent of possible mismeasurement. Next step is to set up a confidence interval of the estimated value plus or minus standard errors. Fortunately, the estimation error in our case is impossibly. That is why we turn to industry betas. Notice that the estimated industry β is somewhat reliable. This shows up in the lower standard error. The industry betas provide a rough guide to the risk in various lines of business.⁵ Sometime we are going to invest or to have a deal with new kind of business not as usual to justify using a company cost of capital. In this case we should remember some things before we are making decision.

1. We have to avoid fudge factors. Don’t add fudge factors to discount rate to offset things could go wrong with the proposed investment. Firstly we have to adjust forecasted cash flows.

2. Do not forget about the determinants of asset risk. The characteristics of high-beta and low-beta assets can be observed when the β itself cannot be.

3. Do not forget diversifiable risk

3.4.1. Operating leverage and β

Sometime we do not have a β, or we get β estimates that are statistical garbage. In those cases, we can assess project’s operation leverage (its ratio of fixed to variable cost) and we can ask whether the project’s future cash flows will be unusually sensitive to the business cycle. Cyclical projects with high operating leverage have high betas. But it is important not to confuse diversifiable risk with market risk. Diversifiable risk does not increase the cost of capital. Many businesspeople associate risk with the variability of book, or accounting, earnings. But much of this variability reflects unique or diversifiable risk. What really counts is the strength of the relationship between the firm’s earnings and the aggregated on all real assets. We can measure this either by the accounting β or by the cash-flow β. We would predict that firms with high accounting or cash-flow betas should also have high project (contract) betas. There are firms whose revenues and earning are strongly dependent on the state of the business cycle – tend to be high-beta firms.

A business facility with high fixed costs, relative to variable cost, is said to have the high operating leverage. High operating leverage means high risk. The cash flows generated by any productive asset can be broken down into revenue, fixed costs, and variable cost:

Cash flow = revenue – fixed cost – variable cost (2.7)

We can break down the asset’s present value in the same way:

PV (asset) = PV (revenue) – PV (fixed cost) – PV (variable cost) (2.8)

We can figure out how the asset’s β is related to the betas of the values of revenue and costs. The β of PV (revenue) is weighted average betas of its component parts:

(2.9)

3.5. The risk and discount rates for international projects

Betas vary from project to project. They can also vary over time. Some projects are riskier in youth than in old age, for example, and we may need a higher discount rate for the start-up stage of a project. But in most case financial managers assume that project risk is the same in every future period and use a single risk-adjusted discount rate for all future cash flows. We will use certainty equivalents to illustrate how risk accumulates over time for ordinary projects.

In international projects the basic principles of estimation the risk and discount rate are the came, but of course there are complications. The risk of project and discount rate may depend on who’s investing. For example, a Swiss investor would calculate a lower β than an investor in U.S. Conversely, the U.S. investor would calculate a lower β for Swiss than Swiss investor. Both investors see lower risky abroad because of the less-than-perfect correlation between the two countries market. The most investors have a strong home-country bias. Perhaps some investors stay at home because they regard foreign investment as risky. But the truth is they mix up total risk and market risk.