Can someone please walk me through the calculation / reasoning behind unlevered beta? I know it has something to do with looking at the ratio of a company's debt to equity and their tax rate...

### What is Unlevered Beta?

Unlevered Beta is a metric that compares the risk of an unlevered company to the overall risk of the market. Levered is a term that implies the use of debt. Consequently, Unlevered beta, also called asset beta, removes debt from the equation.

### When to Use Unlevered Beta?

BABanker - Corporate Finance Director:
1. Levered beta measures both the business risk and the financial risk of the company. Business risk is essentially how the company will perform like sales, growth, i.e. how good of a company it is. The important distinction is the financial risk Financial risk is a company's capital structure, in other words, how much debt they have, or how leveraged they are.
2. So, a company with debt has a higher risk than a company with no debt because they have to divert some of their cash flows to paying the interest and eventually paying off the principal of the debt.

In order to apply a Beta to a different company, you need to remove the Financial Risk component of the Beta, so that you are only left with the Business Risk Component of the Beta.

3. Unlevered Beta- Beta that only measures the business risk of a company. This DOES NOT take into account how much debt a company has.
4. If you're still with me, now you need to do something with this Unlevered Beta (only business risk is included).

5. Relever the Beta- You have your company (for example, a private company) that you want to calculate a Beta for. You know what the company's future Debt to Equity Ratio will be (Capital Structure).

Use this future Debt/Equity Ratio and add it back into the Unlevered Beta, to come up with the LEVERED Beta for your company.

So now you have, a Beta which includes BOTH business risk and financial risk.

The following video goes takes an in depth look at levered and unlevered beta. The introduction also covers the debt tax shield. The presenter starts discussing beta and unlevered beta at 10:24.

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Unlevered Beta = levered beta / [1+(1-company tax rate)*company debt/equity ratio]

A beta is usually shown based on its actual capital structure. As such, if you want to show a beta based on an optimal capital structure, you must unlever it and then re-lever it.

Optimal capital structure is important when determining a discount rate (WACC)

wharton05:
Unlevered Beta = levered beta / [1+(1-company tax rate)*company debt/equity ratio]

A beta is usually shown based on its actual capital structure. As such, if you want to show a beta based on an optimal capital structure, you must unlever it and then re-lever it.

Optimal capital structure is important when determining a discount rate (WACC)

Can someone explain the parts of the formula and why the formula is what it is (what part does adding the (1-taxrate) do, and why multiply it by the debt/equity ratio)?

I understand theoretically what it does, but don't understand how the formula achieves that.

Wouldn't you use an unlevered beta for APV in the CAPM calculation before DPS? I thought levered beta (historical basis) would be used for WACC.

It's been a long day, but let me give this one a try...

When we value a business we review historical cash flows and we forecast future cash flows. However, we need to discount future cash flows to their present value because \$1 today is worth more than a \$1 tomorrow. Therefore, we discount future cash flows using a discount rate that most accurately reflects the

Beta is a pivotal component of the CAPM model which we use to derive our discount rate or WACC. Why do we care about WACC? Well, because investors have choices and an investor wants to gauge his opportunity cost. Debt and equity carries certain rates of return and WACC represents the "hurdle rate" at which both debt and equity investors will be happy... get it? Say a company just announced earnings and said that it enjoyed a 20% return on its business. e.g. if your investment was \$100 and the WACC was calculated to be 10%, then the company just added 10 cents of value to each dollar it invested and everyone's happy.

This is why we have to tear beta apart a little bit... You know that beta captures risk, blah blah blah.

The risk we're specifically talking about is the risk of generating operating cash flows from a business.

In business valuations all future FCF's need to be adjusted for risk. Remember, FCF's are after-tax. So we need to tax affect the beta too... hence the "(1-T)".

We're valuing cash and cash has no risk right? We need to measure cash separate from other assets. Therefore, we need to make an adjustment. We unlever beta by dividing the levered beta by a tax affected rate. We multiply the tax affected rate by the D/E ratio because we're attempting to capture the capital structure. Remember, we could be valuing a private company and comparing it to its publicly traded peer group for which data is readily available. Using a D/E ratio is useful because the capital structure of the subject company could be misleading and the optimal capital structure derived from a set of guideline companies would be more reasonable.

(Confused? Me too... it's easier to calculate this stuff vs. explain it)

• 4

Yeah, definitely still lost. Thanks for trying to explain it though.

But, as you say, as long as I know how to calculate it, I should be okay.

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Why do you need to unlever a beta when valuating a private company? Is it because since a private company is not public that you need to unlever a public company's beta and use that as a substitute for beta for the private company?

The previous explanation was too complicated to understand, that's why I'm asking.

Best Response

1) levered beta measures both the business risk and the financial risk of the company. Business risk is essentially how the company will perform like sales, growth, i.e. how good of a company it is. ***** The important distinction is the financial risk ***** Financial risk is a company's capital structure, in other words how much debt they have, or how leveraged they are.

So, a company with debt has a higher risk than a company with no debt because they have to divert some of their cash flows to paying the interest and eventually paying off the principal of the debt.

In order to apply a Beta to a different company, you need to remove the Financial Risk component of the Beta, so that you are only left with the Business Risk Component of the Beta.

2) Unlevered Beta- Beta that only measures the business risk of a company. This DOES NOT take into account how much debt a company has.

If you're still with me, now you need to do something with this Unlevered Beta (only business risk is included).

3) Relever the Beta- You have your company (for example, a private company) that you want to calculate a Beta for. You know what the company's future Debt to Equity Ratio will be (Capital Structure).

Use this future Debt/Equity Ratio and add it back into the Unlevered Beta, to come up with the LEVERED Beta for your company.

So now you have, a Beta which includes BOTH business risk and financial risk.

Alexey Kirilov:
1) levered beta measures both the business risk and the financial risk of the company. Business risk is essentially how the company will perform like sales, growth, i.e. how good of a company it is. ***** The important distinction is the financial risk ***** Financial risk is a company's capital structure, in other words how much debt they have, or how leveraged they are.

So, a company with debt has a higher risk than a company with no debt because they have to divert some of their cash flows to paying the interest and eventually paying off the principal of the debt.

In order to apply a Beta to a different company, you need to remove the Financial Risk component of the Beta, so that you are only left with the Business Risk Component of the Beta.

2) Unlevered Beta- Beta that only measures the business risk of a company. This DOES NOT take into account how much debt a company has.

If you're still with me, now you need to do something with this Unlevered Beta (only business risk is included).

3) Relever the Beta- You have your company (for example, a private company) that you want to calculate a Beta for. You know what the company's future Debt to Equity Ratio will be (Capital Structure).

Use this future Debt/Equity Ratio and add it back into the Unlevered Beta, to come up with the LEVERED Beta for your company.

So now you have, a Beta which includes BOTH business risk and financial risk.

Was going to try and explain this one but you answered it right on with simplicity.

Alexey Kirilov, thank you for clarifying that for me. I appreciate your reponse big time, pal.

Since you're intelligent upon the subject (a little ass-kissing doesn't hurt here), I wanted to know why the DTS (discounted tax shield) gives more value than an all-equity firm when you calculate the value of the firms through Discounted Cash Flow analysis. I thought all along that the tax shield benefits a leveraged firm with both debt and equity. Interest expense is tax deductible which lowers such a firm's income and taxes relative to an all-equity firm without such a cap structure. Why then does the tax shield give an all -equity firm more value than a company with both debt and equity when valuating companies through free cash flows?

taurus:
Alexey Kirilov, thank you for clarifying that for me. I appreciate your reponse big time, pal.

Since you're intelligent upon the subject (a little ass-kissing doesn't hurt here), I wanted to know why the DTS (discounted tax shield) gives more value than an all-equity firm when you calculate the value of the firms through Discounted Cash Flow analysis. I thought all along that the tax shield benefits a leveraged firm with both debt and equity. Interest expense is tax deductible which lowers such a firm's income and taxes relative to an all-equity firm without such a cap structure. Why then does the tax shield give an all -equity firm more value than a company with both debt and equity when valuating companies through free cash flows?

I'm not sure I understand what you are asking exactly. Can you be a little clearer as to what is not working out in your example?

I was out the past couple days due to sickness, excuse the delay. Anyway, I'm going to re-clarify what I meant in my last post: When you calculate the free cash flows of an all equity firm, you must integrate in that valuation the DTS (Debt Tax Shield). Doing so adds value to the terminal value of that all equity firm. Why would that be? It's an all equity firm that doesn't fund its business in debt. Why then does this raise such a company's value?

In comparison, when valuating a leveraged company, the DTS is not integrated into the equation and so doesn't add value to its termial value.

Let me take a crack at this:

If we're dealing with an all equity firm, then there is no DTS (by construction). Similarly, the levered beta will equal the unlevered beta (just look at the formula).

I think you might be confusing the APV method with WACC.

With APV your discount rate originates from the CAPM using the unlevered Beta.

You discount your FCF with this discount rate to get the value of an all equity firm. Then, if your firm uses leverage you add in the debt tax shield. For a frim with perpetual debt, this dts approximates (tax rate)* (amount borrowed).

So that APV = (FCFs/Cost of equity) + (Amount borrowed*tax rate)

The APV method is much more flexible in dealing with dynamic debt loads, as the WACC factors in a single %debt and a single %equity (target rates usually). Thus APV can be used for LBOs.

Your dcf using APV and WACC should equate (but usually don't).

I'll just reiterate in case this is a little confusing--an all equity firm has no debt, and therefore, no dts. Debt, being cheaper than equity, raises the value of a firm (to a certain extent). Using the WACC, this manifests in the lower discount rate (again to a certain extent, more leverage increases financial risk and therefore your levered beta and cost of equity). Using APV this manifests in the greater tax shield.

Manny07, thanks for the reply. You said that when dealing with an all equity firm that there is no debt, therefore, no DTS. I agree that thereâ€™s no debt involved. But, I disagree that there is no DTS involved. This is because in the book, â€œVaultâ€™s Guide to Finance Interviewsâ€, it clearly states that APV is used for all equity valuation, whereas, WACC is used to valuate leveraged firms. It also says that in using APV in valuating all equity firms, DTS is added to and raises the valuation of such a company.

taurus:
Manny07, thanks for the reply. You said that when dealing with an all equity firm that there is no debt, therefore, no DTS. I agree that thereâ€™s no debt involved. But, I disagree that there is no DTS involved. This is because in the book, â€œVaultâ€™s Guide to Finance Interviewsâ€, it clearly states that APV is used for all equity valuation, whereas, WACC is used to valuate leveraged firms. It also says that in using APV in valuating all equity firms, DTS is added to and raises the valuation of such a company.

No.

In the APV method (which is not used very much by the way), there are 2 distinct steps.

Step 1: Value the equity. Same process as a DCF, just the discount rate is the Cost of Equity only! There is no factor for the cost of debt here.

Step 2: Value the Debt Tax Shield (DTS).

Takeaway: Using APV, Step 1 is exactly the same for a leveraged firm or an all-equity firm. You are valuing the EQUITY ONLY!!! Thus if you have Company A (Leveraged) and Company B (all-equity) with the same cash flows excluding interest and tax savings, the Step 1 valuation for both companies will be EXACTLY THE SAME.

Step 2 is where the difference is. Company A (leveraged) actually has debt, so you calculate the value of the tax shield and add it to the Step 1 valuation.

Company B (all-equity) has NO DEBT. So there is nothing to calculate. No debt, no interest rate, NOTHING! So, the valuation of Company B (all-equity) is just the Step 1 value. Whereas Company A (leveraged) is Step 1 value (equity) PLUS Step 2 value (DTS).

The ABOVE explains APV ONLY!

Now let's look at WACC.

Using the WACC method there is only 1 Step. (Remember in APV Step 1 = equity value and Step 2 = Debt Tax Shield value).

We only have one step in WACC, so we somehow need to account for the value of the debt tax shield (Step 2 in an APV).

The difference is in the discount rate we use. In APV, the discount rate is the SAME for Company A and Company B. In APV, the discount rate is ALWAYS the cost of equity.

In WACC, the discount rate is the weighted average cost of BOTH EQUITY and DEBT!!!!

Company A (leveraged) WACC = Cost of Equity + Cost of Debt.

Company B (all-equity) WACC = Cost of Equity only (since there is no debt)

Implications:

1) For Company B (all-equity) the value using APV or WACC will be EXACTLY THE SAME!!! Why? Because the discount rate for Company B is the same in both methods. Because the WACC of an all-equity firm is simply the cost of equity.

2) For company A (leveraged), the WACC will be lower than company B (all-equity) because cost of debt is LOWER than cost of equity. Thus the firm value of Company A (leveraged) will also be higher, because the lower the discount rate, the higher the valuation. Note that this mechanical lowering of the discount rate is how the WACC method accounts for the value of the debt tax shield. Whereas, in APV you calculate the value of the Debt Tax Shield independently.

3) For Company A (leveraged), APV and WACC methods will NOT yield the same valuation. They should be close, but not the same. Because the two methods take different approaches at valuing the Debt Tax Shield, the numbers don't come out the same.

FINALLY: the vast majority of the time in banking, people use the WACC method as opposed to APV, but it's good to have it your back pocket just in case.

Hope that helps, let me know if you need further clarification.

Why is it necessary to calculate the optimal debt ratio to value a private company? How do you calculate it? Thanks!

What is the logic behind unlevering beta? (Originally Posted: 07/15/2016)

Is there any type of mathematical proof for this? Does this actually come from anywhere or is it just an attempt to lower the beta to adjust for the added risk of debt and since you do the same thing for every company, the results are consistent?

For levering/unlevering Beta, there isn't really a mathematical proof as to why it works. Essentially, the reason you need to unlever beta in the first place is that you are using Beta to measure the risk for the Equity capital, and if the Beta measurement you have isn't unlevered, this therefore includes risk for both Equity capital and Debt. However, if you unlever it, you are accounting for purely the Equity capital as this is what you need.

Then, after using the unlevered Beta, you of course need to re-lever for the specific company your working with since capital structure obviously differs greatly between firms.

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