I am sorry if this question seem stupid/simple, but still I'd greatly appreciate your help.

levered beta = Unlevered Beta * [1 + (1 - Tax Rate) * Debt / Equity ]

Unlevered Beta = something we see on Yahoo Finance

Could someone please take a shot and explain why we multiply by [1 + (1 - Tax Rate) * Debt / Equity ] and not something else? Was this formula discovered intuitively based on previous finance formulas, or was it more of "This is the law, learn it"?

### Levered and Unlevered Beta

The following was originally posted by @Max Margin. The post has been formatted and edited.

First, it is important to understand where unlevered beta falls short in projecting risk. Basically, unlevered(asset) beta represents pure business risk. It does not incorporate financial risk at all, using unlevered beta you pretend that the firm is entirely equity financed, and all cash flows are due only to the equity holder(s).

Say I'm the sole owner of my own large corporation, which has risk equal to the market risk i.e. a beta of exactly 1. The corporation will provide me with the expected return of the market, on the equity which I have invested in it, via the aftertax free cash flows accruing to me. In turn these cash flows are discounted back at the required rate of return (in this case the market return) shall lead us back to the market value of the corporation, lets say its \$1000MM, the standard deviations of the cash flows from my corporation will equal that of the market. Remember that this is the case because a beta of 1 means a companies risk is equal to market risk.

### What is Levered Beta?

definition from subjectmoney.com
Levered Beta, commonly referred to as "equity beta", is the beta of a firm with financial leverage. The levered beta of a firm is different than the unlevered beta as it changes in positive correlation with the amount of debt a firm has in its financial structure.

### Example of Levered Beta Calculation

Now say I decide to mix up the capital structure, I borrow \$500MM in the name of the corporation and pocket it, essentially the corporation now has 500MM of debt on its balance sheet and has bought half my equity stake with the debt ,leading to a D/E ratio of 1. The business risk/unlevered beta/asset beta remains the SAME as it always was, nothing about the corporation's operations have changed. The standard deviations of the operating cash flows are still the SAME. But relative to my equity stake now, the standard deviations of the cash flows are doubled, since my equity stake is twice as small. Again, equity stake is 500MM and debt is 500MM which makes it one to one. So the market risk is 1 plus your debt to equity ratio which also 1. This is where the 1 + D/E comes in, in our case 1+D/E = 2. (we'll get to taxes later)

Another way to think of this is that if half the cash-flows during the life of the corporation are now due to bondholders (debt), then I will demand that the firms expected cash flows must now double in value, for me not to get ripped off.

So if a company is replacing equity with debt or issuing new debt, I expect to get repaid for my equity stake in the case of the former, and expect the company's free cash flows to double in the case of the latter. If beta = 1 then I would expect 2 x market return relative to my stake in the company. The company is actually earning market return (beta = 1) on capital, but relative to where I'm sitting with half the capital, beta = 2 for me because of the change in capital structure (1 + D/E).

Thats why we have betaL = betaU(1 + D/E)

What about (1-T)? from an equity perspective? I will incur inflows from tax savings over the life of the corporation. Since D (debt) is the present value of these cash flows to debt holders, rest assured that (1-T)(D) in taxes will be saved, as long as the corporation retains same capital structure and continues to rollover debt.

Therefore if a company incurs a 1 D/E ratio out of the blue, I will first demand that its free cash flows double, but then I will realize that I will earn (1-T)D in cash over the life of the company, therefore I will demand that its cash flow increase by betaU(1+(1-t)D/E)) , as before we'll set betaU as 1 and t as .35,

we then have 1 + 1 - 1(.35)(1) = 1.65 = BetaL,

Therefore if a company with no debt takes on a debt load with D/E = 1, as an equity holder I will demand free cash flows increase by 2 in the case that interest is NOT tax deductible. On the other hand, I will demand that free cash flows increase by 1.65 in the case that interest is tax deductible!!

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### Comments (119)

I'm not sure if this is what you're looking for, but its essentially because of the idea of the "Tax Shield" nature of Debt, due to the fact that issuing debt and accruing interest allows you to offset some revenue, which saves on taxes (lower profit, therefore lower tax expense). A more intuitive way to think of the formula may be:

Levered= Unlevered + Unlevered(1- Tax Rate)(D/E)

I know this seems stupid, but its easier to see the effect of leverage on Beta. You can then see that Levered Beta is Unlevered + another factor that is related to the Tax Rate and the D/E ratio. Essentially Debt magnifies the Cash Flows (increases Beta). It also takes into account the Tax Shield discussed earlier (which lowers the beta in the way that the larger the Tax Rate, the lower the Beta). Does that make any sense? Its 3am and my brain is tired.

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Thanks Revsly, I was able to follow your ideas and whole levered = unlevered + ... now makes more sense. But why Debt/Equity? Why not Debt ^ 2 / Equity, etc.?

I guess my math background always taught me that new formulas are based on previous findings/research. In reality the entire math (integrals, derivatives, topologies, etc.) based on simple axioms.

Edit: actually it makes sense now. Assume Tax = 0. If we rise debt equal to equity/market cap, then levered beta = double unlevered, which makes sense because now company is "twice as risky"

I thought it was Modigliani and Miller, though I could be wrong. I know they worked with Value of Firms unlevered and levered, and it would make sense that beta would be a natural application. Yeah, you've got the idea.

Haha as a Math major too, I see where you're coming from (though its not quite as easy to believe in the complex plane lol)

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Why do we use Levered instead of Unlevered in cost of equity formula?

Cost of Equity = Risk-Free Rate + Equity-Risk Premuim * Levered + other premiums

My wrong intuition tells me that equity (market cap) is tied up with Unlevered Beta hence we should use unlevered beta.

After some research: "The cost of equity is the minimum rate of return that a business or organization must offer investors or owners to offset their wait for a return on investment and for assuming some level of risk." Do we use levered beta because we need to account for "some level of risk"? As soon as debt is issued, there is risk involved.

PussInBoots:

Why do we use Levered instead of Unlevered in cost of equity formula?

Cost of Equity = Risk-Free Rate + Equity-Risk Premuim * Levered + other premiums

My wrong intuition tells me that equity (market cap) is tied up with Unlevered Beta hence we should use unlevered beta.

After some research: "The cost of equity is the minimum rate of return that a business or organization must offer investors or owners to offset their wait for a return on investment and for assuming some level of risk." Do we use levered beta because we need to account for "some level of risk"? As soon as debt is issued, there is risk involved.

As you get more debt on your balance sheet, your cost of equity goes up. Think about this intuitively. Your equity investors are going to require a greater return if you have more debt, thus the cost of equity increases. This is reflected by beta in the formula mentioned above.

Also, as you have more debt, the financial risk of the company is greater - more interest payments to be made and repay principal.

So, equity investors will demand more return to bear this risk....

Think of it this way: As the company takes on more debt, theoretically the risk of it not repaying the debt increases and if it happens (not repay) and the company goes bankrupt, you lose ALL your equity.

To sum up, as you increase leverage, your financial risk is greater (more interest payments + generate cash flow to repay principal) and equity holders will demand "extra" return/reward to bear this risk - greater discount rate / CAPM (where leverage beta is one component).

That's why leveraging a company reduces its WACC up to a certain point. After that, the use of debt will increase your WACC (and the leverage beta is the variable that will drive this increase in CAPM and consequently WACC).

I realized I actually didn't answer your original question...
"Why we multiply by [1 + (1 - Tax Rate) * Debt / Equity ] and not something else? "

1. Debt/Equity = the most traditional way of measuring leverage (basic corp finance theory)
2. (1 - Tax rate) = as mentioned above, debt has a tax shield, so this item accounts for that
3. [1 + .... = anything in finance that is a rate and you want to turn it into a factor, you've got to add 1. Try to do this formula without summing up 1, it's going to give you a proportion of unlevered beta (because you would be multiplying a number to a percentage, whereas when you multiple a number by a factor, you obtain a number sensitiized by that factor)

Hope that helps.

3 internets to lui for helping poor monkey out :)

This levering formula that the OP has suggested is the most widely accepted.

However, most people seem to forget that it is only valid under two assumptions, which explain why it looks like that:

1) Debt is assumed to be risk free.

2) The Tax Shield has the same risk as the Debt.

In our current economic climate, with sovereign crises and constant downgrades, these assumptions might not be valid anymore and my guess is we will see a strong shift toward the use of more complete formulas.

The current formula will then not be accurate anymore and analysts will have to use something else.

I recommend reading Berk & DiMarzo for more on this topic.

Following UChicago methods, unlevered beta = levered beta * (MV of Equit/Enterprise Value)
where Enterprise Value = MV Equity + MV Debt - Excess Cash.

What does MV stand for? Marginal Value?

must be market value.

humble_dude:

must be market value.

Ha, of course. I feel slow now.

Best Response

Sry just stumbled on this thread, was just thinking about this formula..

Basically, unlevered(asset) beta represents pure business risk. It does not incorporate financial risk at all, using unlevered beta you pretend that the firm is entirely equity financed, and all cashflows are due only to the equity holder(s).

Say I'm the sole owner of my own large corporation, which has risk equal to the market risk i.e. a beta of exactly 1. The corporation will provide me with the expected return of the market, on the equity which I have invested in it, via the aftertax free cash flows accruing to me. In turn these cashflow's discounted back at the required rate of return (in this case the mkt return) shall lead us back to the market value of the corporation, lets say its \$1000MM, the standard deviations of the cashflows from my corp will equal that of the mkt. Now say I decide to mix up the capital structure, I borrow \$500MM in the name of the corp and pocket it, essentially the corp now has 500MM of debt on its BS and has bought half my equity stake with the debt leading to a D/E ratio of 1. The business risk/unlevered beta/asset beta remains the SAME as it always was, nothing about the corp's operations have changed. The standard deviations of the operatating CF's are still the SAME. But relative to my equity stake now, the standard deviations of the CF's are TWICE bigger, since my equity stake is twice smaller. This is where the 1 + D/E comes in, in our case 1+D/E = 2. (we'll get to taxes later)

Another way to think of this is that if half the cashflows during the life of the corporation are now due to bondholders, then I will demand that the firms expected cash flows must now double in value, for me not to get ripped off.

So if a company is replacing equity with debt or issuing new debt, I expect to get repaid for my equity stake in the case of the former, and expect the company's FCF to double in the case of the latter( if beta = 1 then I would expect 2 x mkt return relative to my stake in the company, the company is actually earning mkt return on capital, but relative to where im sitting with half the capital, beta = 2 for me)

Thats why we have betaL = betaU(1 + D/E)

what about (1-T)? from an equity prespective, I will incure inflows from tax savings over the life of the corporation. Since D is the PV of these cashflows to debtholders, rest assured that (1-T)(D) in taxes will be saved, as long as the corporation retains same cap structure and continues to rollover debt.

Therefore if a company incurse a 1 D/E ratio out of the blue, I will first demand that its FCF double, but then i will realize that I will earn (1-T)D in cash over the life of the company, therefore I will demand that its cashflow increase by betaU(1+(1-t)D/E)) or betaU + betaU - betaU(t)(D/E), as before we'll set betaU as 1 and t as .35,

we then have 1 + 1 - 1(.35)(1) = 1.65 = BetaL,

therefore If a company with no debt takes on a debt load with D/E = 1, as an equity holder I will demand FCF increase by 2 in the case that interest is NOT tax deductible

And I will demand that FCF increase by 1.65 in the case that interest is tax deductible!!

I was thinking about this earlier and writing it out helps me understand it, sorry for such a long essay

PondFish:

Sry just stumbled on this thread, was just thinking about this formula..

Basically, unlevered(asset) beta represents pure business risk. It does not incorporate financial risk at all, using unlevered beta you pretend that the firm is entirely equity financed, and all cashflows are due only to the equity holder(s).

Say I'm the sole owner of my own large corporation, which has risk equal to the market risk i.e. a beta of exactly 1. The corporation will provide me with the expected return of the market, on the equity which I have invested in it, via the aftertax free cash flows accruing to me. In turn these cashflow's discounted back at the required rate of return (in this case the mkt return) shall lead us back to the market value of the corporation, lets say its \$1000MM, the standard deviations of the cashflows from my corp will equal that of the mkt. Now say I decide to mix up the capital structure, I borrow \$500MM in the name of the corp and pocket it, essentially the corp now has 500MM of debt on its BS and has bought half my equity stake with the debt leading to a D/E ratio of 1. The business risk/unlevered beta/asset beta remains the SAME as it always was, nothing about the corp's operations have changed. The standard deviations of the operatating CF's are still the SAME. But relative to my equity stake now, the standard deviations of the CF's are TWICE bigger, since my equity stake is twice smaller. This is where the 1 + D/E comes in, in our case 1+D/E = 2. (we'll get to taxes later)

Another way to think of this is that if half the cashflows during the life of the corporation are now due to bondholders, then I will demand that the firms expected cash flows must now double in value, for me not to get ripped off.

So if a company is replacing equity with debt or issuing new debt, I expect to get repaid for my equity stake in the case of the former, and expect the company's FCF to double in the case of the latter( if beta = 1 then I would expect 2 x mkt return relative to my stake in the company, the company is actually earning mkt return on capital, but relative to where im sitting with half the capital, beta = 2 for me)

Thats why we have betaL = betaU(1 + D/E)

what about (1-T)? from an equity prespective, I will incure inflows from tax savings over the life of the corporation. Since D is the PV of these cashflows to debtholders, rest assured that (1-T)(D) in taxes will be saved, as long as the corporation retains same cap structure and continues to rollover debt.

Therefore if a company incurse a 1 D/E ratio out of the blue, I will first demand that its FCF double, but then i will realize that I will earn (1-T)D in cash over the life of the company, therefore I will demand that its cashflow increase by betaU(1+(1-t)D/E)) or betaU + betaU - betaU(t)(D/E), as before we'll set betaU as 1 and t as .35,

we then have 1 + 1 - 1(.35)(1) = 1.65 = BetaL,

therefore If a company with no debt takes on a debt load with D/E = 1, as an equity holder I will demand FCF increase by 2 in the case that interest is NOT tax deductible

And I will demand that FCF increase by 1.65 in the case that interest is tax deductible!!

I was thinking about this earlier and writing it out helps me understand it, sorry for such a long essay

That's probably the best explanation I've ever seen, and I was a 4.0 in my finance classes. If I had an SB I'd give you one. Well done.

PondFish:

Sry just stumbled on this thread, was just thinking about this formula..

...

I was thinking about this earlier and writing it out helps me understand it, sorry for such a long essay

Really great post. Helped a lot. My last SB for you.

PondFish:

Sry just stumbled on this thread, was just thinking about this formula..

Basically, unlevered(asset) beta represents pure business risk. It does not incorporate financial risk at all, using unlevered beta you pretend that the firm is entirely equity financed, and all cashflows are due only to the equity holder(s).

Say I'm the sole owner of my own large corporation, which has risk equal to the market risk i.e. a beta of exactly 1. The corporation will provide me with the expected return of the market, on the equity which I have invested in it, via the aftertax free cash flows accruing to me. In turn these cashflow's discounted back at the required rate of return (in this case the mkt return) shall lead us back to the market value of the corporation, lets say its \$1000MM, the standard deviations of the cashflows from my corp will equal that of the mkt. Now say I decide to mix up the capital structure, I borrow \$500MM in the name of the corp and pocket it, essentially the corp now has 500MM of debt on its BS and has bought half my equity stake with the debt leading to a D/E ratio of 1. The business risk/unlevered beta/asset beta remains the SAME as it always was, nothing about the corp's operations have changed. The standard deviations of the operatating CF's are still the SAME. But relative to my equity stake now, the standard deviations of the CF's are TWICE bigger, since my equity stake is twice smaller. This is where the 1 + D/E comes in, in our case 1+D/E = 2. (we'll get to taxes later)

Another way to think of this is that if half the cashflows during the life of the corporation are now due to bondholders, then I will demand that the firms expected cash flows must now double in value, for me not to get ripped off.

So if a company is replacing equity with debt or issuing new debt, I expect to get repaid for my equity stake in the case of the former, and expect the company's FCF to double in the case of the latter( if beta = 1 then I would expect 2 x mkt return relative to my stake in the company, the company is actually earning mkt return on capital, but relative to where im sitting with half the capital, beta = 2 for me)

Thats why we have betaL = betaU(1 + D/E)

what about (1-T)? from an equity prespective, I will incure inflows from tax savings over the life of the corporation. Since D is the PV of these cashflows to debtholders, rest assured that (1-T)(D) in taxes will be saved, as long as the corporation retains same cap structure and continues to rollover debt.

Therefore if a company incurse a 1 D/E ratio out of the blue, I will first demand that its FCF double, but then i will realize that I will earn (1-T)D in cash over the life of the company, therefore I will demand that its cashflow increase by betaU(1+(1-t)D/E)) or betaU + betaU - betaU(t)(D/E), as before we'll set betaU as 1 and t as .35,

we then have 1 + 1 - 1(.35)(1) = 1.65 = BetaL,

therefore If a company with no debt takes on a debt load with D/E = 1, as an equity holder I will demand FCF increase by 2 in the case that interest is NOT tax deductible

And I will demand that FCF increase by 1.65 in the case that interest is tax deductible!!

I was thinking about this earlier and writing it out helps me understand it, sorry for such a long essay

Brilliant explanation.

Thanks guys,

I was very sleep deprived writing that, so in addition to a few spelling errors (incur/incurs) and minor inconsistencies, I made the mistake of stating that the equity holder earns (1-t)D in tax savings, its ofcourse tD. Which leads us to the final equation of betaL = betaU + betaU(D/E) - betaU(t)(D/E) = betaU[1+(1-t)(D/E)]

I can't edit my original post for some reason...

I'm new to finance too, for me the hardest part is to understand why is tax shield D(1-t). I thought only interest has tax shield effect, so wouldnt the real savings be a lot smaller? Say (1-t * interest rate)?

Bong bong tango:

I'm new to finance too, for me the hardest part is to understand why is tax shield D(1-t). I thought only interest has tax shield effect, so wouldnt the real savings be a lot smaller? Say (1-t * interest rate)?

WACC calculates a percentage/interest rate. You are reducing the interest rate (D) by the tax deductible portion (1-t). So, in effect, the weighted cost of debt is just the net interest rate (taken after tax savings).

You are thinking about it in Dollar (or other currency) terms, not with respect to the rate.

Treat the debt as being rolled over in perpetuity. This then becomes a perpetual cash flow stream, like in basic finance. Whats the value of 4% on 100\$ when the required rate of return/riskiness/discount of such debt is 4%? The value of that perpetual cash flow stream will be \$100. So even though you are paying \$4 each term, and saving \$4t in taxes each time, taken in perpetuity you end up saving the sum of these \$4t increments which ends up being \$100t

The Phantom:

I am sorry if this question seem stupid/simple, but still I'd greatly appreciate your help.

levered beta = Unlevered Beta * [1 + (1 - Tax Rate) * Debt / Equity ]

Unlevered Beta = something we see on Yahoo Finance

Could someone please take a shot and explain why we multiply by [1 + (1 - Tax Rate) * Debt / Equity ] and not something else? Was this formula discovered intuitively based on previous finance formulas, or was it more of "This is the law, learn it"?

Disagree with that formula. If the debt to value ratio of the firm is going to be constant then you should not unlever (or relever) with a *(1-T). The intuition is that the cash flows from the tax savings has the same beta as the overall firm. It is not until you have a constant debt level that the stream of tax savings have the same risk as the debt itself. So infact in a firm with constant capital structure the cash flows from the tax savings are as risky as the cash flows from the firm in general. I.E. if the firm cannot pay its debt, debtholders can claim assets etc. But the tax shield that accrues to equity cant (so it is riskier than the debt itself).

Thoughts?

Edit
This has nothing to do with cash flows but the risk of the cash flows. What is the risk of the tax savings? The value of the cash flows themselves come from the reduced CoD in the WACC calculation.

That's a great thread. Really helpful.

Just a short addition is that the best intuitive way to think of the formula is:

Levered= Unlevered(E/E) + Unlevered(1- Tax Rate)*(D/E)

Than it's totally transparent for understanding.

levered beta = Risk of Equity

Unlevered Beta = Risk of Entire Firm (Assets)

Unlevered Beta is basically a weighted average of the levered Beta and the debt Beta. Typically, the debt beta is thought to be 0, although it isn't always.

Ub = [(1-L)Eb + (L)DB ]/ (1 - TL)

That's the general formula for conversion, with Ub being the unlevered (or Asset) beta, Eb being the levered (or equity) beta, and Db being the debt beta. L is the leverage ratio. From this equation, you can see the "weighted average" quality of asset beta.

Basically, there is a ton of information about the relation between levered and unlevered betas. For valuation purposes, I think it is important to know that when using the betas of comparable companies to find a beta for your private company, you would want to unlever them to make them "free" of the comparable companies' capital structure. After doing this, you would then take the average (or whatever) and relever it using your company's leverage ratio to find the appropriate equity beta, and thus amount of return that you need to get on your equity (using CAPM).

you use cap-struct indifferent [unlevered] FCF's thus, you always start with NOPAT... don't know where you learned that other way, unless you invented it yourself. The other [proper] way to do it is CFO + tax-affected interest - capex, which is probably used more often since these are the metrics most broker reports give.

you need to take the levered beta in its current state (what Yahoo finance would give you) and adjust it for post-transaction cap-struct. thus, you always unlever to industry level than relever to pf cap-struct.

Didn't invent it...

http://www.investopedia.com/terms/f/freecashflow.asp
and EBIT(1-T) is the way they explain it in vault (which I know everyone thinks is garbarge, but for those of us not in banking yet, its one resource to use).

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NOPAT = EBIT (1-T)

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.

Thank you Star, if you use EBIT(1-T) to calculate the unlevered FCF for your DCF, is that going to result in enterprise value, or equity value?

Sorry if these seem simple, its the simple ones I can't afford to botch.

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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.

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

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

A lot of people don't understand the difference, nor can they offer you an informed, clear explanation, as b2's retarded answer shows. Guess some people get so used to BSing they forget when they don't have to! That kid must have forgotten the simple basics of finance because none of his staffers trust him with any important work. At least he's immaculate when it comes to spreading those comps and preparing those pibs!

When valuing the firm we take unlevered cash flows (ie, cash flow before the effects of financing ie interest payments, etc.). We account for the capital structure and its effects on value later in the discount rate.

This is the proper method, though some banks may change things because they 1. don't care explaining why not this/that to their busch league analysts (b2) or 2. none of their clients ultimately care about the theory. They're there for a sales pitch. Either way its worth knowing it if you have a genuine interest in learning the intuition behind it.

unlevered cash flow, or "Free Cash Flow to The Firm"

FCFF = EBIT(1-T) + Dep./Amort. - change in non-cash NWC - capex

Oh yeah, some people don't understand that NOPAT = EBIT(1-T), just so there's no confusion. And the proper way is to consider non-cash net working capital needs, because things like cash are non-operating assets. We're concerned with valuing the operating assets of the firm, and can then add back any non-operating assets like cash later, after we've discounted these cash flows (since including cash in this calculation and discounting it by the cost of capital doesn't make sense).

As for the other one, I've seen that too, but remember:

Net Income + D/A = NET cash flow. We don't really use this because it is a levered cash flow. That is, it is effected by the financing mix of the firm (if we have more debt, we're probably paying more interest, hence changing the figure. If we used this when valuing the firm, we'd be double counting the financing effects.

Now, that said, we DO use NI as a proxy for cash flow when we are trying to find the free cash flow to equity holders, or the levered cash flows (cash flow left to equity holders after all non-equity claims have been paid), which can be simply stated:

FCFE = Net Income + D/A - change in non-cash NWC - capex + (new debt issued - debt repayment)

This is the cash flow that is available to paid out as dividends to common equity holders. Of course, for any number of reasons, it rarely is. You can change this formula here and there for firms with unique debt repayment schedules, financing mixes, etc., but this is the general model)

As for beta:

You never discount cash flows by using unlevered beta in the discount rate (though this changes for APV-adjusted present value, but that's not really what you're asking I don't think). The beta you find on finance sites/bloomberg/etc. are levered. So, the effects of the capital structure are included in the beta you or the fin. services firms get by taking the statistical figure from monthly returns, etc. Whether you need to unlever and relever it depends: the best practice is that when valuing a firm, you take the betas of the comps, unlever these betas at their firm's unique capital structures, and then take that pure-play, raw, unlevered, equity beta, or whatever else you want to call it, and relever using the capital structure you have for the firm you are valuing, or using the capital structure you expect your valuation target to have. So, when you plug that into the CAPM and the cost of equity into your cost of capital for the DCF, you are using a levered beta once again.

One thing you've gotta' remember is if you don't wanna end up in the depressing 65th percentile like b2 here, make sure you understand the methodology beyond the formula. This may be difficult if you wasted college studying some BS like art history and realized at the last minute you wanted to enter the world of finance when you realized the kids in your mansion-neighborhood were all going into banking and you wanted to "be one of the big boys" too, but I don't think you're as bad off as b2 yet man, so good luck, hope I didn't confuse anything there. Hope this helps! I think as always, damodaran or ibanking FAQ have the clearest, non-ranty explanations. Refer to those sources.

Alphaholic:

Whether you need to unlever and relever it depends: the best practice is that when valuing a firm, you take the betas of the comps, unlever these betas at their firm's unique capital structures, and then take that pure-play, raw, unlevered, equity beta, or whatever else you want to call it, and relever using the capital structure you have for the firm you are valuing, or using the capital structure you expect your valuation target to have. So, when you plug that into the CAPM and the cost of equity into your cost of capital for the DCF, you are using a levered beta once again.

I believe that "raw beta" refers to levered beta.

Other names that I've heard for levered beta include "observed" and "historical"

hope that helps.

@Star... you just copy/paste plagiarize from ibankingfaq.com? :(
@the other retard... HAHAHHAHA, discount by CAPM beta... HAHAHAHHA... wow, I seriously hope no one takes your retarded advice. No wonder you still don't have a job.

I keep my explanations brusque b/c anyone with reasonable intelligence and finance skills should be able to understand. I don't feel like teaching kindergarten finance to tier-3 idiots.

Obviously you never got the chance to work with an APV, where you value the firm in chunks. The unlevered value of the firm is discounted at the unlevered cost of equity, using an unlevered beta. APV is a variant sometimes used in private equity but you wouldn't have a clue about that, because you never have and never will get to enjoy the prestige it offers you. Your prestige doesn't go beyond the cheeto-crumb scattered desk you're forced to sit at because no one invites you to go to lunch. I feel bad for you, I truly do! Don't worry little buddy, I'm sure your parents haven't changed the Aladdin bed sheets you never quite grew out of! Your career is brusque, bro. Almost as depressing as the low-income dead-end jobs your genetic-cesspool parents have back in New England!

Do you think they use APV in banking???? HAHAHAHHAHAHAHHAHAHA wow... Yes, I learned that stupid theory in finance101 also - no you're not special - yes, your interviewer would "LMAO" at you once you mention those three letters.... hahahahahhaha... get back to the back of the unemployment line!

Dude, playing with your head makes it worth listening to more and more of your sad story leak out in nuance: from your shitty life with your poor, clearly neglecting parents to your sad attempts to justify yourself as a prestigious banker! Love it man, keep it coming. I can't see you crying in denial on my computer, but god knows, I wish I could.

a 65th thinking that he cna "play with" a 99th? hahahahahha, I pay more for my apartment in a month than you make in an entire year! go cash your welfare check!

So how about you take your bickering to myspace or something... thanks for the help, but both of you are acting like you are in third grade.

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I use the 'Raw Beta' number from Bloomberg extracted through the Excel plug-in.

Hmm...I use the "Adjusted Beta" from Bloomberg.

there are thousands of ways to estimate betas

go check Vasicek(this one might be better for FI rates tho) or Blume. it all depends on the spare time(and geekyness) that the guy who does it has.

Reading this forum is making me realize how much I hate this job.

"Why can't you just unlever target company beta and relever it?"

Wouldn't that just get you the same levered beta you started with? I guess that leads to the questions of why you can't just use the beta given on Yahoo Finance, etc.

You would be doing that if your target is a private company... whose beta you don't have. How can you unlever the target's beta if its private? So you take the comps betas unlever it then relever it with your private companies cap structure.

ok, so if your valuing a public company for a merger, you dont have to unlever and average comparable betas? you can jsut unlever the company beta and relever it at teh target d/e ratio?

i guess you unlever to get rid of risk of debt but i dont get why we relever...........when you unlever, are you unlevering a company comparables (industry) beta (where is the D/E coming from, the comparable comanpanies or the company we are actually looking to value?)?..........wheras when you relever, do you just use the D/E of the company which you are valuing

You unlever the observed betas of your comparable companies using the comparable company's capital structure; you relever them with either an average capital structure from your comps, or the capital structure for the company you are trying to value.

There have been many great comebacks throughout history. Jesus was dead but then came back as an all-powerful God-Zombie.

You are trying to make beta apple to apples because different debt levels affect beta.

Do what you want not what you can!

Second Edomerp's explanation
When you want to value of the company, you would like to value the business of the company, and not corrupt it by the financial strategy of the company e.g. if you are trying to value of a cement manufacturer, you want to get the beta to understand the risks in the cement manufacturing business, and remove the effect of any risk introduced by a cement manufacturer because they took on more debt, or more equity etc. So you unlever the beta of all the comparables, find the average, and then relever it for average leverage for the sector or the target leverage of the company you want to value

Yes, you need to get a portfolio of comparable companies (same business risk...), delever them to get the beta of their assets, calculate the average (whether weighted or not), and then relever the average beta to your company's capital structure

tzn007:

Equity Beta=Levered Beta which can be found by regressing the returns of the company's stock on the returns of a broad based market index. Additionally it's also available on sites such as yahoo finance. Equity Beta should generally be expected to be lower than unlevered Beta bc of debt interest saving affect, assuming the company's capital structure is not overly leveraged.
So am i getting this right??

Correct me if I'm wrong, but levered betas should be higher than unlevered betas purely because if you're levering up your capital structure, you're inherently going to swing higher/lower each time the market moves up or down.

Think of it this way ... \$100 company that's all equity, assuming it tracks the market.

Market up 10%, \$100 -> \$110, beta of 1

\$100 company that's half equity half debt, ceteris paribus.

Market up 10%, \$100 -> \$110, equity goes from \$50 -> \$60, return of 20%, beta of 2.

Equity would only go up to 55\$ if the the market is up 10%.

ChildPlease:

Equity would only go up to 55\$ if the the market is up 10%.

Apologies - "market" is a misnomer, I meant total revenues, which I'm assuming is directly 1:1 correlated with spending increases - think about it this way ... if spending (or GDP or revenue) rises by 10%, it's okay to assume that TEV rises by 10%, not equity value.

Also, to tzn, cost of capital goes down to a certain point because debt is fundamentally cheaper than equity - if you're levering up, you're funding with more debt, and a greater proportion of your WACC is under the interest tax shield (that (1-Tc) term in the WACC calculation), therefore cost of capital decreases until a certain point.

sounds reasonable. But isn't it also true that generally when you add debt to company's capital structure, it's cost of capital goes down (up to optimal point). And that debt and eq market generally go opposite directions, hence diversification of capital structure reduces risk measured in Beta. Or is that off base?

Beta represents the leverage-adjusted risk. So if you buy into a company who's underlying assets have an spx beta of 0.7 and the company is levered 2:1, under CAPM, the company is expected to have a beta of 1.4. Of course, in reality, beta is calculated by regressing daily stock price moves against the SPX.

Typically, your professor will give you two numbers- the risk free rate and the market-risk premium. The risk-free rate is pretty self-explanatory and the market-risk premium is the expected rate of return for the SPX or base index and the risk free rate.. The cost of capital is risk-free-rate + market risk premium *beta.

First, you have to take the levered beta's of all your comparable companies, then you unlever them. Then, you take the median of the set and Re-Lever that figure based on your pro-forma capital structure to reflect the true risk of the company....so levered beta!

I think the raw tables should give you a levered beta unless it states it's adjusted.

I believe its correct to say that raw (levered beta) is sometimes called the equity beta.

1) CAPM probably uses the equity beta because if you take the raw feed and get beta (levered beta), and you want to buy ordinary stock (aka ordinary equity), you'd use that figure in the CAPM calculation of equity's cost. To use another number misrepresents what the market prices the beta at.

2) a) If you were to unlever it first it would give you a result without leverage modifiers (I think this is from the company's debt betas) which ignores that you're investing into ordinary shares (which have the respective debt betas included when they are performing on the market, remember since CAPM prices equity from market readings per illiniprogrammer's post).
b) Using it without leverage modifying the beta is unrealistic as it would not account for the capital structure and the tax effects.
c) It looks unrealistic to me as this 'pure' beta is not available on-market directly from the company in question.

I'm not certain how to work unlevered beta other than in comps like what londonib1 said.

At a stab, I suspect you'd use unlevered betas in assets-without-leverage calculations. So seems possible if you want to invest in an asset the company has without any debt components... I dunno when that would happen. Maybe when starting your own business and you want to duplicate the assets of a certain company... and find out how much its going to cost you before borrowing? Beats me.

Which site says you use unlevered beta in capm?

Interested in this as well.

It's levered. Unlever by dividing levered beta by (1+(1-T)*(D/E)). That's your asset beta. You do it this way to take into account the tax benefit from debt (the interest payments are tax deductible).

To go a step further, if you're valuing a company, you would take the industry average and relever the beta to forecast earnings in the future (particularly for the terminal value).

Might want to confirm with your text book, it's been awhile since I've done this and I don't use it anymore.

Hi guys,

I was wondering, how do we get the equity value we need to re-lever our unlevered beta? Isn't it the final target of the valuation?

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market cap

yep market value

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always use market value for any part of valuation Enterprise Value if you can get your hands on them easily.

Say both ways.

"One should recognize reality even when one doesn't like it, indeed, especially when one doesn't like it." - Charlie Munger

you should use 2 methods and play around depending what "target" price you have in mind. Lower beta for "sell-side" and higher for "buy-side". Method 1 offers you more flexibility, you can pick your comps.

yes, get it off terminals. they are calculated via method 2 i guess.

great thanks for the info

1 and #2 are the exact same method... how the hell do you think they calculate beta for the public comps?

lol

they mean the same thing but gives different number. for method 1 you can adjust the comp accordingly. Method 2 you can adjust the market index and dates accordingly... They mean the same thing but I dont think you can get the exact numbers using method 1 and 2 separately.

If you're reasonably certain that the company's structure will change, then you should use the target structure.

You unlever and then relever

this helps. thanks

Awesome thanks guys

do your own homework

"After you work on Wall Street it's a choice, would you rather work at McDonalds or on the sell-side? I would choose McDonalds over the sell-side." - David Tepper

Unlevered Beta = levered beta/(1+(1-Tax rate)(D/E)) then to re-lever: Levered Beta=Unlevered(1+(1-Tax rate)*(D/E))

Then for cost of equity use new levered beta and = (Risk Free)+(Levered Beta*(Market Return-Risk Free))

I did it for the practice but won't give you the answer! I will tell you if you're wrong or right though.

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If you somehow got the wrong answer, use OS D/E to relever beta. Best of luck plugging in the numbers.

Yes the assumption is that Debt is no volatility.

The dragon dozes off in the spirit which is its dwelling.

You should use net debt. If you know how much cash the firm needs for operations (i.e. the remainder is excess cash) you should only subtract excess cash, but that's tough to know so just subtracting all cash is pretty common.

Thanks! But can I ask why net debt is used? Is it because it reflects the firm's financial situation more accurately?

Kind of. One reason is that the firm could easily retire its debt with its excess cash. Another is that the cash doesn't have anything to do with the firm's sensitivity to market returns (which is what beta measures). For a company like Apple, you want to be measuring the sensitivity of its operations to the market, not its cash. If you didn't use net debt in that case, Apple's relevered beta would be way too low since all its cash dampens that correlation. Let me know if that makes sense.

That makes sense thanks!

Interested as well

If you are determining a 100% equity value (i.e., debt excluded from your FCFs and discount rate), you will definitely want to incorporate an unlevered beta within your model. levered beta, as the name implies, incorporates debt within the subject company's target capital structure.

If you were to use a levered beta to conclude on an equity value, you would effectively be discounting debt-free FCF with a debt-inclusive discount rate. You want to make sure that the numerator and denominator of the discounting calculation match-up (in this case, debt-free FCF should be discounted at a debt-free discount rate. Doesn't matter whether the company has debt or not - what matters is that you are attempting to derive a 100% Equity Value.

Asset beta is the risk of the assets (D+E, not factoring in the proportion of D/E).
Equity beta is the risk of the equity, which is inherently dependent on the leverage ratio (more leverage = more risk).
You cannot compare one company's equity beta to another if one of the company has 90% debt and the other has 0% debt (because, all things equal, the 90% levered company's equity is far riskier).

Hope this helps.

^That's a pretty good explanation. The basic idea behind unlevering and then relevering your betas is that your comparable companies will have varying capital structures. Unlevering their betas allows you to directly compare them by removing the effect of different levels of leverage.

D/E is used because it shows the capital structure of a firm

Doesn't Debt to TEV show the capital structure of the firm too..? You just substract TEV-Debt to see the equity?

Unlevering the beta removes any beneficial effects gained by adding debt to the firm's capital structure. You are trying to take out debt. So you need to use D/E since D/TEV has debt in denominator.

"The way to make money is to buy when blood is running in the streets."

-John D. Rockefeller

so i never actually bothered learning the theoretical reason behind this because i personally think CAPM is pretty bullshit, but honestly, I don't understand why D/TEV doesn't work. It might have debt in the denominator by proxy, but unless there's financial distress, theoretically, TEV isn't captial dependent...

The derivation of this formula is in Hamada (1972).

Yeah. I assume you know what Beta is. So what you need to do is put it in terms that a 7 year old would understand by explaining it with things they would understand. If you need to read a few examples, go check out Reddit's ELI5 subreddit. Come up with how you want to phrase it and you can ask if we think it needs tweaking. Explain it to us like we were seven year old kids and if we think it's spot on, then I'm sure people will tell you so.

If the kid's dad works in finance, tell the kid to just look at his dad for an example of the ultimate beta.

I think that you would be hard pressed to come up with a simplistic example that perfectly explains beta to a 7 year old. If it was possible, then that's probably how beta would be defined in the first place. As long as you convey the sense that you know what you're talking about you should be fine. I'm a big fan of using lemonade stands for questions like this.

Say you have a lemonade stand set up at the end of your driveway year round. You sell three things: lemonade with ice, hot chocolate and hot dogs. You want to figure out how much people will pay for things based on what the temperature is; in other words, what the is beta of the price they will pay you compared to the temperature.

When are people going to pay more for the ice cold lemonade, when its cold and snowing during the winter, or when its 100 degrees out during the summer? Obviously the hotter it is the more they will want to drink the cold lemonade. You do some testing and find out that for each degree hotter that it is outside you can charge 5 cents more per cup of lemonade.

Now you look at the hot chocolate. You know that people really love it during the winter when it is cold, and not so much when its hot so you reason that you can charge people 10 cents less per cup for each degree colder it is outside.

Now the hotdog. You don't think that the temperature will affect how much they will pay for the hot dog so we can say it has a beta of 0 compared to the weather. The price they will pay depends on other things, like how much they like hotdogs, how hungry they are, etc.

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