# Unlevered Beta Calculator

By Wei Bin Loo
Last updated: Jun 14, 2021

With this unlevered beta calculator, you can easily deleverage the equity beta, or levered beta, and convert it into the unlevered beta. Unlevered beta is a very useful metric to assess the risk and volatility of a stock. It measures the movement of a company's stock against a broad market index, such as the S&P 500, and informs you how volatile the stock is compared to the index.

This article will help you understand what is unlevered beta and how to calculate it using the unlevered beta formula. We will also tell you the difference between levered beta and unlevered beta to help you understand the concept.

Now, before we dive into the calculation, let's talk about the definition of unlevered beta.

## What is unlevered beta?

Before we attempt to discuss unlevered beta, we need to first understand what is levered beta, which is also known as the beta of a stock. Beta is defined as slope coefficient when we perform a regression using a stock against a market index, such as the S&P 500. A beta of 1 signifies that the stock moves just like the index. If the market rises by 1%, the stock is expected to do the same. The farther beta is from 1, positively or negatively, the more volatile the stock is.

The volatility of a stock is primarily influenced by its capital structure. For example, companies that take on more leverage on debt will be more volatile than their otherwise less leveraged peers. Hence, to understand the "true" volatility of a business, we need to compare them on the same level. As different companies have different capital structures, we need to strip away any benefits or disadvantages incurred by the difference in capital structure. The unlevered beta is designed to serve this purpose.

## How to calculate unlevered beta using the unlevered beta formula?

Let's take Company Alpha as an example to help us understand the calculation of the unlevered beta.

Company Alpha reports the following information:

• Net income: \$800,000;
• Pre-tax income: \$1,000,000;
• Total debt: \$12,000,000;
• Total shareholders' equity: \$6,000,000; and
• Equity beta: 1.2.

Calculating the `unlevered beta` requires four steps:

1. Determine the levered beta / equity beta

Performing a regression of the stock's return against the market returns is usually rather complicated and time-consuming. But worry not, most companies' equity betas are published by various financial data providers such as the Financial Times and Bloomberg. Hence, to determine a company's equity beta, all you need to do is retrieve it from those websites.

In our example, the `equity beta` for Company Alpha is `1.2`.

1. Determine the corporate tax rate

As `corporate tax rate` is applied to the `pre-tax income`, you can calculate it using the formula below:

`corporate tax rate = 1 - net income / pre-tax income`

Hence, the `corporate tax rate` for Company Alpha is `1- (\$800,000 / \$1,000,000) = 20%`.

1. Calculate the debt-to-equity ratio (D/E ratio)

Next, we need to calculate the company's debt-to-equity ratio, also known as the `D/E ratio`. We can calculate it using the formula below:

`D/E ratio = total debt / total shareholders' equity`

The Company Alpha's `D/E ratio` can be calculated as `\$12,000,000 / \$6,000,000 = 2x`.

1. Calculate the unlevered beta

The last step is to calculate the company's `unlevered beta`. This can be calculated using the formula below:

`unlevered beta = equity beta / (1 + (1 - corporate tax rate) * D/E ratio)`

In this example, the Company Alpha's `unlevered beta` is `1.2 / (1 + (1 - 20%) * 2) = 0.4615`.

## The purpose of calculating unlevered beta

The results from our unlevered beta calculator can be used in different ways:

• Compare the systematic risks of different companies

As mentioned above, companies with different leverage will experience different earning volatilities. These earnings volatilities include both the business risks and the systematic risks of the companies. In short, business risks are risks that can be eliminated through diversification and systematic risks are risks that investors can't avoid. Hence, it makes sense to compare the systematic risks between companies as they reflect the "true" risks of the companies. Unlevered beta is the metric designed to do that.

• Calculate beta for non-public listed firms

As beta is defined as the slope coefficient of a stock's returns against the returns of a market, it is difficult to estimate beta for non-public listed firms since their share is not traded in public markets. One of the ways of estimating the beta for private firms is using the unlevered beta. The steps for calculating beta for private firms are:

1. Find the peers of the company.
2. Calculate their unlevered betas using the unlevered beta formula.
3. Take the average of the unlevered betas.
4. Convert it into levered beta, or equity beta, using the company's D/E ratio. By estimating the unlevered beta and re-lever it using the company's debt-to-equity ratio, we will be able to find out the beta for private firms.
Wei Bin Loo
Corporate tax rate
Net income
\$
Pre-tax income
\$
Corporate tax rate
%
Debt-to-equity ratio (D/E ratio)
Total debt
\$
Total shareholders’ equity
\$
D/E ratio
x
Unlevered beta
Levered beta (equity beta)
Unlevered beta
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