Unlevering and Relevering Beta: The Step-by-Step Guide for IB Interviews

You've built your DCF, you've forecast free cash flow, and now you need a discount rate. To get the cost of equity, you need a beta. But the beta you pull for a comparable company reflects that company's debt load, not your target's. So what do you do?

You unlever the comps' betas to strip out the effect of their debt, then relever the result at your target's capital structure. That's the whole idea. It's one of the most common technical topics in IB interviews, and it's easy to nail once you see the logic and run through the numbers once.

Let's walk through it like we're sitting at a whiteboard together.

Why Beta Needs Adjusting in the First Place

Beta measures how much a stock moves relative to the overall market. A beta of 1.2 means the stock tends to move about 20% more than the market, in either direction.

The beta you see on Bloomberg or in a data provider is a levered beta (also called equity beta). It captures two kinds of risk at once:

• Business risk: how sensitive the company's operations are to the economy (think airlines vs. utilities)
• Financial risk: the extra volatility shareholders bear because the company has debt

Debt holders get paid first. The more debt a company has, the more its equity holders absorb the swings in operating results. So two companies with identical businesses can have very different levered betas just because one borrowed more.

The problem this creates

Say you're valuing a private company. It has no traded stock, so it has no observable beta at all. Your fix is to borrow betas from public comps.

But each comp has its own debt load. If you just averaged their levered betas, you'd be mixing business risk with a random assortment of capital structures. The result wouldn't reflect your target's actual risk.

Unlevering isolates pure business risk. Relevering adds back the financial risk that fits your target.

The Formulas You Need to Know

The standard formula used in banking (often called the Hamada formula) is:

Levered Beta = Unlevered Beta × [1 + (1 − Tax Rate) × (Debt / Equity)]

Rearrange it, and you get the unlevering version:

Unlevered Beta = Levered Beta / [1 + (1 − Tax Rate) × (Debt / Equity)]

A few things to notice:

• Unlevered beta is also called asset beta. It represents the risk of the business as if it had zero debt.
• The tax rate is there because interest is tax-deductible. The tax shield softens the impact of debt on equity risk.
• Debt / Equity uses market values, especially for equity (market capitalization, not book equity).
• If a company has positive debt, its unlevered beta will always be lower than its levered beta.

The hidden assumption

This version of the formula assumes the company's debt has a beta of zero, meaning debt carries no market risk. That's not perfectly true (risky debt does move with the market), but it's the standard simplification in most banking models. If an interviewer asks about it, you can mention that more complete versions include a debt beta, but practitioners usually set it to zero.

The Process in 4 Steps

Here's the workflow you'd follow in a real model:

1. Gather data for each comp: levered beta, market value of debt, market cap, and tax rate
2. Unlever each comp's beta using its own D/E and tax rate
3. Take the median (or mean) unlevered beta across the comp set
4. Relever that beta using your target's D/E and tax rate

Then plug the relevered beta into CAPM to get the cost of equity:

Cost of Equity = Risk-Free Rate + Beta × Equity Risk Premium

A Worked Example

Let's make this concrete. You're valuing a private manufacturing company. You've picked four public comps, and all of them face a 25% tax rate.

(These numbers are illustrative, chosen to make the math easy to follow.)

Step 1 and 2: Unlever each comp

Look at what happened. The levered betas ranged from 0.95 to 1.60, which looks like a wide spread. Once you strip out debt, the unlevered betas cluster tightly between about 0.88 and 0.96.

That's the point. Comp C looked riskiest only because it carried the most debt. Its underlying business risk is similar to the others.

Step 3: Take the median

Sorted unlevered betas: 0.884, 0.914, 0.946, 0.957

Median = (0.914 + 0.946) / 2 = 0.93

Bankers often prefer the median because one weird comp can skew the mean.

Step 4: Relever at the target's capital structure

Your target has a D/E of 0.40 and a 25% tax rate.

Relevered Beta = 0.93 × [1 + 0.75 × 0.40] = 0.93 × 1.30 = 1.21

Step 5: Plug into CAPM

Assume a 4.0% risk-free rate and a 5.5% equity risk premium (again, illustrative).

Cost of Equity = 4.0% + 1.21 × 5.5% = 4.0% + 6.66% = about 10.7%

That's your cost of equity, which then feeds into WACC.

Which Capital Structure Should You Relever At?

This is a judgment call, and interviewers like to probe it. You have a few options:

• The target's current capital structure: fine if it's stable and reasonable
• A target or "optimal" capital structure: what management plans to run long-term
• The industry median D/E from your comps: useful when the target's current structure is temporary or unusual

The key is consistency. The D/E you use to relever beta should match the debt and equity weights you use in WACC. If you relever at 0.40 D/E, your WACC weights should reflect that same mix (0.40 D/E means debt is about 28.6% of total capital and equity about 71.4%).

Common Mistakes That Cost People Points

1. Confusing D/E with D/(D+E)

This is the big one. The formula uses Debt / Equity, not debt as a percentage of total capital.

If you're told a company is "30% debt," that's D/(D+E). The D/E is 0.30 / 0.70 = 0.43, not 0.30. Plugging in 0.30 would understate the relevered beta.

2. Using book value of equity

Book equity can be wildly different from market cap, especially for companies with big buybacks or accumulated losses. Use market cap for equity. For debt, book value is often used as a proxy because market value is harder to find and usually close for investment-grade debt.

3. Forgetting the tax rate

Leaving out (1 − t) treats debt as more punishing than it is. If you're asked to do this on the spot, make sure the tax term is in there.

4. Unlevering with the target's D/E

Each comp gets unlevered with its own D/E and tax rate. The target's numbers only come in at the relevering step.

5. Mixing gross and net debt inconsistently

Some banks use net debt (debt minus cash) in the formula. Either approach can work, but pick one and apply it the same way to every comp and to the target. One quirk to know: if a company has more cash than debt, its net D/E is negative, which makes its unlevered beta higher than its levered beta.

How This Shows Up in Interviews

Here are questions you should be ready to answer cleanly.

"Why do we unlever and relever beta?" Because comps have different capital structures, and their observed betas mix business risk with financial risk. Unlevering isolates business risk so we can compare apples to apples, and relevering applies the financial risk that matches our target's capital structure.

"If a company takes on more debt, what happens to its beta?" Levered beta goes up, because equity holders bear more financial risk. Unlevered beta stays the same in theory, since the underlying business hasn't changed. Cost of equity rises as a result.

"What happens to WACC when a company adds debt?" Initially, WACC tends to fall because debt is cheaper than equity and interest is tax-deductible. But as leverage keeps rising, both the cost of debt and the cost of equity increase, and eventually the risk of financial distress pushes WACC back up. That's why there's an "optimal" capital structure somewhere in the middle.

"Is unlevered beta higher or lower than levered beta?" Lower, as long as the company has positive debt (or positive net debt, if you're using net debt). Debt adds risk for shareholders, so removing it reduces beta.

"Walk me through calculating cost of equity for a private company." Pick comps, unlever their betas, take the median, relever at the target's capital structure, and plug the result into CAPM with a risk-free rate and equity risk premium. Bonus points if you mention adding a size premium or company-specific premium for smaller private firms, which some practitioners do.

Quick Recap

• Levered beta = business risk + financial risk. Unlevered beta = business risk only.
• Unlever: Levered Beta / [1 + (1 − t) × D/E]
• Relever: Unlevered Beta × [1 + (1 − t) × D/E]
• Unlever each comp with its own numbers, take the median, then relever at the target's structure.
• Use market values, use D/E (not D/(D+E)), and keep your relevering D/E consistent with your WACC weights.

Practice the worked example above once or twice on paper without looking. Once you can do the unlever-median-relever sequence from memory and explain why each step exists, this question goes from intimidating to an easy win in your interview.