Giddy | Leverage and the required return on equity

Briefing
Leverage and Equity Returns

Prof. Ian Giddy, New York University

What happens to a company's required return on equity when it increases leverage, i.e. the proportion of debt in its total financing? Answer -- the required return increases. But how, and how much? This note tries to answer that question.

The Required Return on Equity
How does one look for the required return on equity, to use to discount the cash flows in a project?

The pure equity required rate of return, according to the Capital Asset Pricing Model, depends on how risky the firm or project is relative to the market (its Beta)

ROEU = PURE (UNLEVERED) ROE REQUIRED

= RISKFREE RATE + RISK PREMIUM (which depends on the Beta and the market risk premium)

ROEU = RF + Beta(RM - RF)

The Effect of Leverage
Leverage (debt) increases the expected rate of return on the equity. this is simply because leveraged investments are riskier than unleveraged ones.

ROEL = LEVERED ROE REQUIRED

= UNLEVERED ROE + RISK PREMIUM DUE TO LEVERAGE

ROEL = ROEU + D/E(ROEU - RF)

Since both the expected return and the risk increase, the net effect on the value of the project is unclear. More debt can penalize the present value of the future cash flows becuase they must be discounted at a more severe rate.

Introduce Taxes
Because interest is tax deductable, debt can provide a tax shield. The effect of the tax shield depends on the proportion of debt in the financing mix, and on the corporate tax rate. From the proposition that

Value of levered firm = Value of Unlevered Firm + Value of Tax Shield

we can derive the tax version of the Leveraged ROE equation:

ROEL = ROEU + D/E(1 - T)(ROEU - RF)

Find the Project's or Company's NPV
Use the levered, tax-adjusted required return on equity to find the present value of all future cash flows to equity. Test for the effect on the firm's/project's value of changing the variables under control, such as the proportion of debt financing, to find the optimal financing mix.

Change the assumptions as you see fit, either because they are wrong, or to perform sensitivity analysis.

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