Unlevered beta

Start with the leverage formula. Under the standard assumptions of the Hamada / Modigliani-Miller-with-taxes setup, debt bears effectively no market risk and tax shields are as safe as the debt itself. Levered and unlevered betas then connect like this:

βL = βU × [1 + (1 − t) × D/E]            (relever: business risk → equity risk)
βU = βL / [1 + (1 − t) × D/E]            (unlever: equity risk → business risk)

βL = levered (equity) beta — what a regression measures
βU = unlevered (asset/business) beta — risk of the operations themselves
D/E = debt ÷ equity, BOTH at market values
t  = marginal tax rate (the shield makes debt slightly cheaper to bear)

Why that shape? With no debt, βL = βU, because equity holders bear the business's risk and nothing more. Each unit of D/E stacks the whole business's swings onto a thinner equity slice, which scales risk up linearly. That (1−t) haircut is there because the tax shield absorbs a sliver of the pain. You should know about a competing convention, Harris-Pringle, which drops the (1−t) term under different tax-shield assumptions. Both are defensible. We standardize on the (1−t) version, which is Damodaran's and the practitioner default. Pick one, disclose it, never mix them in one analysis.

How do you unlever and relever beta, step by step?

Here's the recipe. It's the core motor skill of the whole build:

1. Define the business(es). Read the segment note, which Phase 1 trained you to do. A single-business firm takes one sector. A multi-business firm gets a value-weighted blend, as in Worked Example 1.
2. Assemble the peer set. Take every listed firm in that business, aiming for 8 to 30 names. The more the better. Use domestic peers plus global ones, because business risk travels. A cement plant's operating leverage is the same physics everywhere.
3. Unlever each peer with its own regression beta, its own market D/E, its own marginal tax rate. Or skip straight to Damodaran's pre-computed sector tables, which come up below.
4. Average the unlevered betas. A simple average works, or the median if there are outliers. Averaging is what beats any single regression. Standard errors of independent estimates shrink with √n when you average them. Twenty-five peers at ±0.25 each give an average that carries ±0.25/√25 = ±0.05. You've turned a rumor into a measurement.
5. Relever at the target's own market D/E and marginal tax rate. Use the current capital structure by default. Use a stated target structure if management is credibly migrating toward it. A de-levering promise is credible when the cash flows and covenants say so. Hearing the CFO say "comfortable" doesn't make it credible.

Worked example: an Indian cement leader

Now try a worked computation on an Indian cement major, built bottom-up. All the inputs are illustrative and modeled on ~FY25 scale. Pull actual filings and current betas before real use. Your target is an UltraTech-style cement leader with a market cap of ₹3,20,000 crore, total debt of ₹20,000 crore and a marginal tax rate of 25%. These are the peers, with their regression betas and market D/E:

For the drill, t = 25% for all of them. In practice you'd use each peer's own rate. Now look at what the unlevering did. Raw betas ranged from 0.95 to 1.25, and much of that spread was just balance sheets. Unlevered, they cluster between 0.85 and 0.98, which is the business risk of making cement, isolated. Call it βU ≈ 0.93, with an averaging-shrunk standard error that no single regression could touch.

Then relever to the target, where D/E = 20,000/3,20,000 = 0.0625. That gives βL = 0.93 × [1 + 0.75 × 0.0625] = 0.93 × 1.0469 = 0.97.

A lightly levered leader in a cyclical, high-fixed-cost business ends up with a beta just under 1. And now the number has a story. Demand is cyclical, which is layer 1. The kilns and plants are layer 2, and a conservative balance sheet is layer 3.

A regression slope never gives you that.

Where do you find sector betas, and what about conglomerates?

In practice you'll use a shortcut most weeks. Damodaran publishes levered and unlevered betas by industry on his data page, with US, global, and emerging-markets datasets (India is included). You'll find them under Current Data → "Levered and Unlevered Betas by Industry", in the betas and totalbeta spreadsheets, refreshed each January. In the standard workflow you read the sector's unlevered beta from the table matching where your company operates, then do only step 5 yourself. Build the full peer-set version when the company is unusual or the sector bucket is too coarse. And build it at least once by hand, which the practice set makes you do, so the table stays a convenience and never becomes a crutch.

Multi-business firms need one more step. Their unlevered beta is a value-weighted average of the segments' sector betas. Estimate each segment's value and weight the betas by it. Then relever the blend at the consolidated D/E. When segments aren't separately listed, the standard proxy for value is segment revenue × sector EV/Sales. Worked Example 1 runs a Reliance-style three-business blend end to end.

What if the company holds a lot of cash?

One refinement is worth knowing about, for when cash is huge. The firm you regress includes its cash pile, and cash has β ≈ 0. So for cash-heavy firms such as Indian IT, the business beta is understated unless you strip the cash out: βU(business) = βU(firm) / (1 − cash/firm value). Damodaran's tables publish an "unlevered beta corrected for cash". Prefer that column.