# Level 1 CFA® Exam:

Beta, Risk, & Flotation Costs

## Estimating Beta for CFA Exam – Market Model Regression of Stock Returns

star content check off when doneAs we know, beta is necessary when using the CAPM model. Hence, you need to estimate it.

In the case of public companies, we may use linear regression of the stock and market returns to estimate beta. However, you should know that the beta calculated with this model (aka. raw beta) may vary significantly depending on the assumptions and data used.

For example, the estimation period has a large impact on the size of beta. Typically, you use data from the period of two to nine years. You can apply a longer period of time only in the case of companies with a long operating history. A shorter period is taken into consideration in the case of younger companies or, for example, if the company has gone through restructuring.

What may also be problematic when calculating the beta with the aid of a market model regression of the stock returns is the choice of an appropriate index representing the market.

What is more, small-capitalization companies are characterized by greater risk and greater returns than large-capitalization companies, and that is why on average their betas will be higher than betas of large companies. Thus, some suggest that if you estimate a beta for a small company, you should customize it.

Additionally, beta tends to regress to the value of 1, e.g. if you estimate raw beta using linear regression to be 1.5, there is a high probability that in the future periods the beta will be lower and closer to 1, and vice versa. If you estimate raw beta using linear regression to be lower than 1, e.g. 0.7, there is a high probability that in the future periods the beta will be higher and closer to 1. Hence we often use adjustments, e.g. Blume adjustment:

\(\beta_{Blume}=\frac{2}{3}\times\beta_{raw}+\frac{1}{3}\times1\)

- \(\beta_{Blume}\) - Blume beta (adjusted beta)
- \(\beta_{raw}\) - raw beta (unadjusted beta)
- \(1\) - market beta (average-systematic-risk security beta)

Of course, a market model regression of the stock returns is well-suited for estimating betas of public companies. The problem arises when you need to estimate the beta for a thinly-traded or non-listed companies. In these cases, we can use the so-called pure-play method. In short, this method involves using the beta of a comparable publicly-traded company and adjusting the beta so that it takes into account the financial risk of a thinly-traded or nonpublic company.

Before we thoroughly explain the pure-play method algorithm and discuss formulas, we’re going to say what kinds of risk affect the beta and why the pure-play method makes sense.

Two main types of risk affect the size of a company’s beta:

- business risk, and
- financial risk.

(...)

The whole process starts with the selection of comparable companies listed on the stock exchange. When you have selected one or more of such companies, you estimate a beta which then you need to unlever by removing the effect of financial leverage. The unlevered beta reflects the business risk of the assets and thus is called the asset beta. The final step is to lever the beta by adjusting the asset beta to the financial risk of the company for which you want to calculate the beta. This beta is called the equity beta.

So, there are 2 betas:

- the asset beta, and
- the equity beta.

The asset beta is the beta of a company on the assumption that the company uses only equity financing. In contrast, the equity beta takes into account different levels of the company's debt. A company has one asset beta and, depending on its debt-to-equity ratio, it can have many different equity betas.

Let's look at the relationship between the asset and equity beta:

\(\beta_{U,comp} = \frac{\beta_{L,comp}}{[1+((1-t_{comp})\times \frac{D_{comp}}{E_{comp}})]}\)

- \(\beta_{U,comp}\) - asset beta (unlevered beta) of a comparable company
- \(\beta_{L,comp}\) - equity beta (levered beta) of a comparable company
- \(t_{comp}\) - marginal tax rate for a comparable company
- \(D_{comp}\) - market value of comparable company's debt
- \(E_{comp}\) - market value of comparable company's equity

(...)

A company operates in the pharmaceutical industry. This company has an asset-to-equity ratio of 3. The estimated asset beta for comparable companies is 1.1, and the tax rate is 20%. What is the company’s beta?

There is nothing simpler. All we need to do is to place all the data into the formula, right? We have all the data we need. But there is one small problem – an asset-to-equity ratio is given, and not a debt-to-equity ratio.

In that case, before we estimate the equity beta, we have to calculate the debt-to-equity ratio.

First of all, we know that the assets are equal to equity plus debt. If we know that the assets are 3 times larger than the equity, we can write this equation:

\(3=1+D\) >> \(D=2\)

So:

\(\frac{D}{E}=\frac{2}{1}=2\)

Therefore the equity beta for the company is equal to:

\(\beta_{L,nonP} = \beta_{U,comp}\times [1+((1-T_{nonP})\times \frac{D_{nonP}}{E_{nonP}})]=\\=1.1\times[1+(1-20\%)\times2]=2.86\)

A company planning to raise its capital is assisted by investment companies, which charge a fee in return for their services. This fee is referred to as the flotation cost.

There is no consensus as to whether this cost should be included in the cost of capital, or be considered as a negative cash flow in the project. However, remember that it is better to include the flotation costs, not in the cost of capital but incorporate it as a negative cash flow at the beginning of the investment.

But if you assume that you want to include flotation costs in the cost of capital, the cost of new shares will be calculated as follows:

- the cost of capital is equal to the next year's dividend divided by the current share price diminished by the flotation costs in nominal terms plus the dividend growth rate, or
- the cost of capital is equal to the next year's dividend divided by the current share price multiplied by 1 minus the flotation costs in percentage terms plus the dividend growth rate.

\(r_{e} = (\frac{D_{1}}{P_{0}-F})+g\)

- \(r_{e}\) - cost of external equity
- \(D_{1}\) - dividend of the next period
- \(P_{0}\) - current stock price
- \(F\) - flotation costs in monetary terms on a per share basis
- \(g\) - expected growth rate of dividends

\(r_{e} = (\frac{D_{1}}{P_{0}\times (1-f)})+g\)

- \(r_{e}\) - cost of external equity
- \(D_{1}\) - dividends expected next period on the index
- \(P_{0}\) - current stock price
- \(f\) - flotation cost as a percentage of the issue price
- \(g\) - expected growth rate of dividends

It is justified to include the flotation costs in the cost of capital:

- when it is problematic to determine financing costs, or
- when you want to show and compare the cost of equity capital of one project in two scenarios: when a company is financing the project using retained earnings, or if the funds come from the issue of new shares.

- In the case of public companies, we may use linear regression of the stock and market returns to estimate beta.
- Business risk is the risk associated with operating earnings which, in turn, depend on revenues.
- Financial risk is associated with the uncertainty of net income and cash flows.
- The asset beta is the beta of a company on the assumption that the company uses only equity financing.
- The equity beta takes into account different levels of the company's debt.
- A company planning to raise its capital is assisted by investment companies, which charge a fee in return for their services. This fee is referred to as the flotation cost.
- It is better to include the flotation costs, not in the cost of capital but incorporate it as a negative cash flow at the beginning of the investment.