AAPL's live leverage inputs for unlevering
The formula that unlevers an observed beta
β Unlevered = β Levered / [1 + (1 − Tax) × (D/E)]
The unlever, average, relever sequence
| Step | What You’re Doing | Formula |
|---|---|---|
| 1. Unlever | Remove financial risk from peer betas | βu = βL / [1 + (1−T)(D/E)] |
| 2. Average | Take median unlevered beta of peers | Median(βu) |
| 3. Relever | Add target company’s financial risk back | βL = βu × [1 + (1−T)(D/E)] |
Why an industry unlevered beta beats the target's own
Using an industry unlevered beta and relevering to your target’s capital structure is more reliable than using the target’s own levered beta, which is noisy and unstable.
Unlever a peer group's betas
Separating business risk from leverage in beta
Why unlevering enables apples-to-apples comparison
Re-levering a peer beta to a target structure
Why the relever formulas encode debt-policy assumptions
Going deeper (optional). Up next: why the three relever formulas are debt-policy assumptions in disguise — an advanced aside you can skip on first pass and come back to anytime. Continue when you're curious.
Going Deeper — the three relever formulas differ by DEBT-POLICY assumption, not by algebra preference. This module relevers with the Hamada equation, but practitioners choose among three formulas, and the choice is a statement about how the company manages its debt. (1) Hamada: βL = βU × [1 + (1 − T) × D/E]. It presumes the company holds a FIXED dollar amount of debt forever, so the tax shields are as predictable as the debt itself — that is where the (1 − T) dampening term comes from. (2) Harris-Pringle: βL = βU × [1 + D/E]. It presumes debt is REBALANCED continuously to a target ratio, so the tax shields rise and fall with firm value and carry the same risk as the business — no (1 − T) dampening, and the same D/E produces a higher relevered beta than Hamada. (3) Miles-Ezzell sits between the two: debt is rebalanced annually, so the first year's tax shield is locked in and only the later ones are risky. Practical guidance: match the formula to the company's actual debt policy, not to habit. A stable-leverage compounder that manages to a target rating or a target debt-to-capital ratio fits the rebalancing assumptions (Harris-Pringle or Miles-Ezzell). An LBO-style structure with a fixed, amortizing debt schedule fits Hamada. Whichever you pick, use the SAME formula to unlever the peers and to relever the target — mixing families quietly shifts the beta. AI prompt: 'For this ticker, does management hold a roughly fixed dollar amount of debt or rebalance to a target leverage ratio? Which relever formula matches that policy, and how different would the relevered beta be under the other one?'
Sit with the ideas.
Three restaurant chains have: (A) Beta 1.2, D/E 0.5x; (B) Beta 1.5, D/E 1.0x; (C) Beta 0.95, D/E 0.1x. Tax rate is 25% for all. What are their unlevered betas, and what do they tell you?