446 Part Five Payout Policy and Capital Structure
bre44380_ch17_436-459.indd 446 10/05/15 12:52 PM
If you owned a portfolio of all the firm’s securities, you wouldn’t share the cash flows with
anyone. You wouldn’t share the risks with anyone either; you would bear them all. Thus the
firm’s asset beta is equal to the beta of a portfolio of all the firm’s debt and its equity.
The beta of this hypothetical portfolio is just a weighted average of the debt and equity
betas:βA = βportfolio = βD D__
V+ βE E__
V
Think back to our example. If the debt before the refinancing has a beta of .1 and the equity
has a beta of 1.1, thenβA = (^) ( .1 × ^30
10 0
(^) ) + (^) ( 1.1 × ^70
10 0
(^) ) = .8
What happens after the refinancing? The risk of the total package is unaffected, but both the
debt and the equity are now more risky. Suppose that the debt beta stays at .1. We can work
out the new equity beta:
βA = βportfolio = βD D__
V
- βE E
V
.8 = (^) ( .1 × __^40
10 0
(^) ) + (^) ( βE × ^60
10 0
(^) )
Solve for the formula for βE. You will see that it parallels MM’s proposition 2 exactly:
βE = βA + (βA − βD)D/V = .8 + (.8 − .1)(40/60) = 1.27
In fact one can derive MM’s proposition 1 directly from the capital asset pricing model
(CAPM).
Our example shows how borrowing creates financial leverage or gearing. Financial lever-
age does not affect the risk or the expected return on the firm’s assets, but it does push up the
risk of the common stock. Shareholders demand a correspondingly higher return because of
this financial risk.
You can use our formulas to unlever betas, that is, to go from an observed βE to βA. You
have the equity beta of 1.27. You also need the debt beta, here .1, and the relative market
values of debt (D/V) and equity (E/V). If debt accounts for 40% of overall value V, then the
unlevered beta is
βA = (^) ( .1 × ^40
10 0
(^) ) + (^) ( 1.27 × __^60
10 0
(^) ) = .8
This runs the previous example in reverse. Just remember the basic relationship:
βA = βportfolio = βD (^) ( D
V
(^) ) + βE (^) ( __E
V
(^) )
Watch Out for Hidden Leverage
MM did not say that borrowing is a bad thing. But they insisted that financial managers
stay on the lookout for the financial risk created by borrowing. That risk can be especially
dangerous when the borrowing is not in plain sight. For example, most long-term leases are
debt-equivalent obligations, so leases can hide debt. Long-term contracts with suppliers can
be debts in disguise when prices and quantities are fixed. For many firms pension liabilities
and liabilities for employees’ post-retirement health care are massive off-balance-sheet, debt-
equivalent obligations.
BEYOND THE PAGE
mhhe.com/brealey12e
Does MM apply to
banks?