What it means
Beta measures how strongly a share price tends to move when the market moves. A beta of 1 means the share moves broadly in line with the market, while a beta above 1 means it swings more.
The beta that is observed in the market for a company reflects two things: the risk of its business and the extra risk created by its borrowing. Debt raises the risk to shareholders because interest must be paid whatever happens to profits.
Two companies in the same industry can therefore have different betas simply because one has borrowed more. The Hamada equation, developed by the economist Robert Hamada, separates these effects.
The equation links the levered beta, which includes the effect of debt, to the unlevered beta, which reflects the business risk alone. It uses the debt to equity ratio and the tax rate, because interest is usually deductible and so reduces the true cost of debt.
Analysts can unlever the betas of comparable companies, average them, and then relever the result at the target company's own capital structure. This is useful in valuation and in capital budgeting.
A manager evaluating a new division, or a bank valuing a private business with no traded shares, can borrow betas from listed peers and adjust them with the equation. The relevered beta then feeds into the capital asset pricing model to produce a cost of equity.
The equation rests on assumptions that should be understood. It assumes that debt is risk free in terms of its beta, that the debt level stays constant in proportion to equity, and that the tax shield on interest is fully usable.
Real companies may break these assumptions, so the result is an estimate and not a precise measurement.
In practice
Real-world examples.
Example
An analyst values a private packaging company by collecting the betas of five listed rivals. She unlevers each beta using that rival's debt ratio and averages the results. She then relevers the average at the packaging company's own debt ratio to estimate its cost of equity.
Example
A retail chain plans to fund an expansion mostly with new borrowing. The treasurer uses the Hamada equation to see how the beta, and therefore the required return to shareholders, would rise as debt grows. She presents the result to the board alongside the tax benefit of the interest.
Example
A consultant is asked to set a hurdle rate for a new business unit in a different industry. He takes peer betas for that industry, unlevers them and relevers them using the target debt level for the unit. The hurdle rate is then lower than the group average because the new unit is less risky.
Formula
Calculation
Levered beta = unlevered beta x [1 + (1 - tax rate) x (debt / equity)]
Suppose a manufacturing company has an unlevered beta of 0.80, a tax rate of 25% and a debt to equity ratio of 0.50.
Levered beta = 0.80 x [1 + (1 - 0.25) x 0.50] = 0.80 x [1 + 0.375] = 0.80 x 1.375 = 1.10.
With a risk-free rate of 4% and a market risk premium of 5%, the cost of equity = 4% + (1.10 x 5%) = 4% + 5.5% = 9.5%.Case study
Seen in the real world.
Oakhaven Foods is a fictional company considering a major plant upgrade financed by borrowing. The finance director wanted to know how the added debt would change the return its shareholders would demand.
She started with an unlevered beta of 0.80 based on peers. At the current debt to equity ratio of 0.25 and a 25% tax rate, the levered beta was 0.80 x [1 + 0.75 x 0.25] = 0.95, and at the planned ratio of 0.75 it rose to 0.80 x [1 + 0.75 x 0.75] = 1.25.
The illustrative analysis showed that the cost of equity would climb noticeably, partly offsetting the cheaper debt. The board went ahead with a smaller borrowing plan that kept the ratio near 0.50.
Watch out
Common mistakes.
- Using the equation without adjusting for each peer company's own debt ratio, which gives a distorted average beta.
- Forgetting the tax rate, which changes the size of the adjustment.
- Treating the result as exact, when it relies on simplifying assumptions about the cost and riskiness of debt.
Questions
People also ask.
What does the Hamada equation do?
It converts between a beta that includes the effect of debt and a beta that reflects only business risk.
What is an unlevered beta?
It is the beta a company would have if it had no debt, showing its pure business risk.
Why does adding debt raise beta?
Because fixed interest payments make shareholder returns more sensitive to swings in profit.
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