( . Interest Payment rDebt . Debt ) 1 + E(rDebt) The cost of capital
on the second term (but not the first term) may or may not be correct.
Because the second term is small, it rarely makes much difference if
E(rFirm) is used instead of E(rDebt). APV: App
capital structure, the DF capital structure created just under $6 in present
value. solve now! Q 17.3 A $1 million construction project is expected
to return $1.2 million in 1 year. Your company is in a 45% combined
federal and state marginal income tax b
neutrality is just for convenience, not because it makes any difference.)
There are two ways to prove the proposition that it makes no difference
as to whether the firm is financed with debt or equity: The full
restructuring (takeover) argument: Assume th
just payoffs of $20,000 and $100,000 to work out. The figure shows that
the shape of the lines may have changed, but most of the intuition has
not. Because it is always possible that the firm will be worth nothing, it
is now impos- Here is what you should
FORMAL WAY 581 scenario, and $0.94 in the good scenariotwo
equations, two unknowns: Bad Luck d . $55 + e . $5 = $0.60 d 0.0106
Good Luck d . $55 + e . $105 = $0.94 e 0.0034 If you purchase 0.0106
LD bonds and 0.0034 of the LD equity, you will end up with
suitably lowering the cost of debt capital. Method #3 is called flow-toThe next section explains a third method to value the tax benefits. This
flow-toequity. equity method constructs the financials for the firm in
the new hypothetical capi- Valuing after
future tax savings relative to 616 CHAPTER 17 THE WEIGHTED
COST OF CAPITAL AND ADJUSTED PRESENT VALUE IN AN
IMPERFECT MARKET WITH TAXES an all-equity-financed firm is
the amount of corporate income tax that the firm will not have to pay on
the interest. E
E Rate of Return (E(r) 10% 6% Step 3: Discount the expected cash
flows by the appropriate cost of capital demanded Discount the expected
payoffs on the overall project and on the debt. by the capital providers:
Financing Financing Scheme AE Scheme DE Bond
remains the same, regardless of how it is financedwhether it is 100%
equity financed, 50% equity financed, or 30% equity financed. This is
because the world is perfect. Any capital structure would Table 16.1
shows the only logical possibility for a firm w
saves on taxes when it distributes its earnings in the form of interest
payments. For example, if PepsiCos operations really produced $100,
and if $100 in interest was owed to creditors, then Uncle Sam would get
nothing and the creditors would get the ent
action.) Thus, a firm with the bad capital structure that requires changing
management every week could simply not exist. Again, you would not
be the only one to recognize that this creates value. Therefore, in this
perfect world, firms not only end up wi
now know that you cannot add too much value by fiddling around with
how you finance your projects if your financial markets are reasonably
close to perfect. 16.4 THE WEIGHTED AVERAGE COST OF
CAPITAL (WACC) 583 solve now! Q 16.5 Under what assumptions
does
multiperiod setting if convenient and intuitive WACC is often difficult
to apply. the cost of capital, the firms debt ratio, and the firms tax rate
all stay constant. In this case, a present value formula would look
something like PV = E(CTime 1) cfw_1 +
it was worth. This is M&M precisely. It is the very same argument.
Another way is to think of M&M financing as a decision that can be
made inde- M&M view #2: Additivity of pendent of the underlying
projects. In this case, net present values are additive.
proof. that you can relever the claims yourselfyou do not need to own
the entire firm to do it. The idea is that you do not buy 100% of the firm,
but only 1% of the firm. If you buy 1% of all the firms claims, you
receive 1% of the projects payoffs. You c
to firms just as it did to buildings. derlying project. Although we
continue calling this project a building (to keep correspondence with
Section 6.4), we now extend the metaphor. Consider the corporation to
be the same as an unlevered building, the mortg
example from page 589 if the debt promises $75,000 and E(rDebt) =
8.64%. Confirm that the weight of the debt in the capital structure is
77.14%. Q 16.15 Compared to hypothetical firm B, hypothetical firm A
has both a higher cost of capital for its debt an
generally 16.4 THE WEIGHTED AVERAGE COST OF CAPITAL
(WACC) 589 influence individual securities costs of capital. So return
now to the debt-and-equityonly numerical example. Everything
included, we just worked out: Medium leverage. Scheme AE Scheme
DE Bond
all equity) versus if they promise $28,125 to bondholders and retain
only the levered equity (scheme DE for debt and equity). Naturally, in
each state, the bond and the levered equity together must own the entire
building: Financing Financing Scheme AE Sc
when the world is not risk neutral, lets repeat the building with
mortgage example from Section 6.4. However, we Splitting building
payoffs into debt and equity, Section 6.4, p. 155 now allow riskier claims
to have higher expected rates of return. We can
opinions are universally shared. Other arbitrageurs would compete, too.
The only price at which no one will overbid you for the right to purchase
the firms current claims is $100. But notice that this means that the
value of the old claims is instantly bi
off to provide the necessary funds. To convey that notion within my
allotted 10 seconds I said: The M&M dividend proposition amounts to
saying that if you take money from your left-hand pocket and put it in
your right-hand pocket, you are no better off. O
considerably higher price 16.2 MODIGLIANI AND MILLER: THE
INFORMAL WAY 577 than the whole milk would bring. (Selling cream
is the analog of a firm selling low-yield and hence high-priced debt
securities.) But, of course, what the farmer would have left wo
The perfect market provided two aspects important to the M&M
argument: 1. The capital market is perfectly elastic. All financial claims
that the firm could dream up would be snatched up by a perfect capital
market at an appropriate price. 2. There is no l
could depend on its capital structurein a perfect world, this should not
be possible. However, there is an important caveat to this homemade
restructuring proof: Beware: This homemade restructuring argument
ignores control rights. Homemade leverage only a
the firms WACC. For example, if the risk-free rate is 5% and a firm
with a 10% cost of capital were to increase its debt to 95% of the firms
value, the residual equity would have a seemingly astronomical cost of
capital, 5% . E(rEquity) + 95% . 5% = 10% E
exploit the help of the IRS. It earns $280 on an investment of $200. At a
30% corporate income tax rate, it will pay corporate income taxes of
30% . $80 = $24. It can then pay out the remaining $56 in dividends.
17.2 FIRM VALUE UNDER DIFFERENT CAPITAL STR