Market Risk and Financial Leverage If a firm has no debt, the market risk of its common stock is the same as

Market Risk and Financial Leverage If a firm has no debt, the market risk of its common stock is the same as

the market risk of its assets. This is to say the beta of its equity, β equity , is the same as the beta of its assets, β asset .

Financial leverage is the use of fixed payment obligations, such as notes or bonds, to finance a firm’s assets. As we will demonstrate in Chapter 18, the greater the use of debt obligations, the more financial leverage and the greater the risk associated with cash flows to owners. So the effect of using debt is to increase the risk of the firm’s equity. If the firm has debt obligations, the market risk of its common stock is greater than its assets’ risk (that is, β equity > β asset ), due to financial lever- age. Let’s see why.

Consider the an asset’s beta, β asset . This beta depends on the asset’s risk, not on how the firm chose to finance it. The firm can choose to finance it with equity only, in which case β asset = β equity . But what if, instead, the firm chooses to finance it partly with debt and partly with equity? When it does this, the creditors and the owners share the risk of the asset, so the asset’s risk is split between them, but not equally because of the nature of the claims. Creditors have seniority and receive

a fixed amount (interest and principal), so there is less risk associated with a dollar of debt financing than a dollar of equity financing of the same asset. So the market risk borne by the creditors is different than the market risk borne by owners.

Let’s represent the market risk of creditors as β debt and the market risk of owners as β equity . Because the asset’s risk is shared between credi- tors and owners, we can represent the asset’s market risk as the weighted average of the firm’s debt beta,

β 2 debt , and equity beta, β equity : 2 The process of breaking down the firm’s beta into equity and debt components is attributed to Robert S. Hamada [“The Effect of the Firm’s Capital Structure on the

Systematic Risk of Common Stocks,” Journal of Finance (May 1972) pp. 435–452].

Capital Budgeting and Risk

equity  debt + equity  But interest on debt is deducted to arrive at taxable income, so the

asset

debt ---------------------------------

debt + equity

claim that creditors have on the firm’s assets does not cost the firm the full amount, but rather the after-tax claim. Therefore, the burden of debt financing is actually less due to interest deductibility. Let τ repre- sent the marginal tax rate. The asset beta is:

 -------------------------------------------------- ( 1 β – = β τ )debt

equity 

-------------------------------------------------- ( 1 – τ )debt equity +  equity  ( 1 – τ )debt equity +  If the firm’s debt does not have market risk, β debt = 0. This means

asset

debt 

that the returns on debt do not vary with returns on the market. We generally assumed this to be true for most large firms. Therefore, the market risk of a firm’s equity is affected by both the assets’ market risk and the nondiversifiable portion of firm’s financial risk. If β debt = 0,

β asset = β -------------------------------------------------- equity equity = -------------------------------------- β 1

( 1 – τ )debt equity +

equity 1 + ---------------------------- ( 1 – τ )debt equity

This means that an asset’s beta is related to the firm’s equity beta, with adjustments for financial leverage. 3 You’ll notice that if the firm does not use debt, β asset = β equity and if the firm does use debt, β asset < β equity . Therefore, we can translate a β equity into a β asset by removing the firm’s financial risk from its β equity . As you can see from the above, to do this we need to know:

■ the firm’s marginal tax rate; ■ the amount of the firm’s debt financing; and ■ the amount of the firm’s equity financing.

3 This means that we can also specify the firm’s equity beta in terms of its asset beta: β equity = β

( asset  1 + ---------------------------------------------------------------------- – 1 marginal tax rate )debt   equity  The greater a firm’s use of debt (relative to equity), the greater its equity’s beta and

hence the greater its equity’s market risk.

LONG-TERM INVESTMENT DECISIONS

If the firm’s β equity , is 1.2, its marginal tax rate is 40%, and it has $4 million of debt and $6 million of equity, and its asset risk is 0.8571:

1.2 -------------------------------------------------------------- asset 1 = = ( 1.2 0.7143 ) = 0.8571

1 + ( ---------------------------------------------------- – 1 0.40 )$4 million

$6 million

The process of translating an equity beta into an asset beta is referred to as “unlevering” since we are removing the effects of financial leverage from the equity beta, β equity , to get a beta for the firm’s assets, β

. asset 4