Unlevered Beta = Levered Beta / (1 + ((1 – Tax Rate) x (Debt/Equity)))

Levered Beta = Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))

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# Category: Discounted Cash Flow Analysis

## What are the formulas for unlevering and levering Beta?

## Which is less expensive capital, debt or equity?

## When using the CAPM for purposes of calculating WACC, why do you have to unlever and then relever Beta?

## What is Beta?

## How do you calculate the cost of equity?

## What is WACC and how do you calculate it?

## Walk me through a Discounted Cash Flow (“DCF”) analysis…

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Investment banking interview questions regarding discounted cash flow analysis and weighted average cost of capital (WACC)

Unlevered Beta = Levered Beta / (1 + ((1 – Tax Rate) x (Debt/Equity)))

Levered Beta = Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))

Debt is less expensive for two main reasons. First, interest on debt is tax deductible (i.e. the tax shield). Second, debt is senior to equity in a firm’s capital structure. That is, in a liquidation or bankruptcy, the debt holders get paid first before the equity holders receive anything. Note, debt being less expensive capital is the equivalent to saying the cost of debt is lower than the cost of equity.

In order to use the CAPM to calculate our cost of equity, we need to estimate the appropriate Beta. We typically get the appropriate Beta from our comparable companies (often the mean or median Beta). However before we can use this “industry” Beta we must first unlever the Beta of each of our comps. The Beta that we will get (say from Bloomberg or Barra) will be a levered Beta.

Recall what Beta is: in simple terms, how risky a stock is relative to the market. Other things being equal, stocks of companies that have debt are somewhat more risky that stocks of companies without debt (or that have less debt). This is because even a small amount of debt increases the risk of bankruptcy and also because any obligation to pay interest represents funds that cannot be used for running and growing the business. In other words, debt reduces the flexibility of management which makes owning equity in the company more risky.

Now, in order to use the Betas of the comps to conclude an appropriate Beta for the company we are valuing, we must first strip out the impact of debt from the comps’ Betas. This is known as unlevering Beta. After unlevering the Betas, we can now use the appropriate “industry” Beta (e.g. the mean of the comps’ unlevered Betas) and relever it for the appropriate capital structure of the company being valued. After relevering, we can use the levered Beta in the CAPM formula to calculate cost of equity.

Beta is a measure of the riskiness of a stock relative to the broader market (for broader market, think S&P500, Wilshire 5000, etc). By definition the “market” has a Beta of one (1.0). So a stock with a Beta above 1 is perceived to be more risky than the market and a stock with a Beta of less than 1 is perceived to be less risky. For example, if the market is expected to outperform the risk-free rate by 10%, a stock with a Beta of 1.1 will be expected to outperform by 11% while a stock with a Beta of 0.9 will be expected to outperform by 9%. A stock with a Beta of -1.0 would be expected to underperform the risk-free rate by 10%. Beta is used in the capital asset pricing model (CAPM) for the purpose of calculating a company’s cost of equity. For those few of you that remember your statistics and like precision, Beta is calculated as the covariance between a stock’s return and the market return divided by the variance of the market return.

To calculate a company’s cost of equity, we typically use the Capital Asset Pricing Model (CAPM). The CAPM formula states the cost of equity equals the risk free rate plus the multiplication of Beta times the equity risk premium. The risk free rate (for a U.S. company) is generally considered to be the yield on a 10 or 20 year U.S. Treasury Bond. Beta (See the following question on Beta) should be levered and represents the riskiness (equivalently, expected return) of the company’s equity relative to the overall equity markets. The equity risk premium is the amount that stocks are expected to outperform the risk free rate over the long-term. Prior to the credit crises, most banks tend to use an equity risk premium of between 4% and 5%. However, today is assumed that the equity risk premium is higher.

The WACC (Weighted Average Cost of Capital) is the discount rate used in a Discounted Cash Flow (DCF) analysis to present value projected free cash flows and terminal value. Conceptually, the WACC represents the blended opportunity cost to lenders and investors of a company or set of assets with a similar risk profile. The WACC reflects the cost of each type of capital (debt (“D”), equity (“E”) and preferred stock (“P”)) weighted by the respective percentage of each type of capital assumed for the company’s optimal capital structure. Specifically the formula for WACC is: Cost of Equity (Ke) times % of Equity (E/E+D+P) + Cost of Debt (Kd) times % of Debt (D/E+D+P) times (1-tax rate) + Cost of Preferred (Kp) times % of Preferred (P/E+D+P).

To estimate the cost of equity, we will typically use the Capital Asset Pricing Model (“CAPM”) (see the following topic). To estimate the cost of debt, we can analyze the interest rates/yields on debt issued by similar companies. Similar to the cost of debt, estimating the cost of preferred requires us to analyze the dividend yields on preferred stock issued by similar companies.

In order to do a DCF analysis, first we need to project free cash flow for a period of time (say, five years). Free cash flow equals EBIT less taxes plus D&A less capital expenditures less the change in working capital. Note that this measure of free cash flow is unlevered or debt-free. This is because it does not include interest and so is independent of debt and capital structure.

Next we need a way to predict the value of the company/assets for the years beyond the projection period (5 years). This is known as the Terminal Value. We can use one of two methods for calculating terminal value, either the Gordon Growth (also called Perpetuity Growth) method or the Terminal Multiple method. To use the Gordon Growth method, we must choose an appropriate rate by which the company can grow forever. This growth rate should be modest, for example, average long-term expected GDP growth or inflation. To calculate terminal value we multiply the last year’s free cash flow (year 5) by 1 plus the chosen growth rate, and then divide by the discount rate less growth rate.

The second method, the Terminal Multiple method, is the one that is more often used in banking. Here we take an operating metric for the last projected period (year 5) and multiply it by an appropriate valuation multiple. This most common metric to use is EBITDA. We typically select the appropriate EBITDA multiple by taking what we concluded for our comparable company analysis on a last twelve months (LTM) basis.

Now that we have our projections of free cash flows and terminal value, we need to “present value” these at the appropriate discount rate, also known as weighted average cost of capital (WACC). For discussion of calculating the WACC, please read the next topic. Finally, summing up the present value of the projected cash flows and the present value of the terminal value gives us the DCF value. Note that because we used unlevered cash flows and WACC as our discount rate, the DCF value is a representation of Enterprise Value, not Equity Value.