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