EFFECT
OF TAXES AND TRANSACTION COSTS
·
In
PCM, increasing a firm’s debt has no impact on firm value or stockholder
wealth => there is no marginal cost or marginal benefit to increasing
debt.
·
So
first we ask how taxes and transaction costs change things.
Do they result in any marginal cost or marginal benefit to issuing
debt?
IMPACT
OF CORPORATE TAXES
·
Assume
initially there are only corporate taxes (no personal taxes).
·
There
are two otherwise identical firms U and L.
They have the same assets and therefore the same EBIT.
The only difference is that L is partly debt financed, and therefore
makes some interest payments. Assume
L has issued $10,000 worth of debt at an interest rate of 8%.
So the annual interest = $800.
Firm
U
Firm L
EBIT
5,000
5,000
Interest
0
800
EBT
5,000
4,200
Tax
(35%)
1,750
1,470
N.I.
to s/h
3,250
2,730
Combined
income
to s/h and b/h
3,250
3,530
Interest
payments are tax deductible, and therefore generate tax savings. The amount of tax saved = interest * tax rate = 800*.35 =
$280. We call the tax shield provided by L’s debt.
Since L pays $280 less in taxes, it has $280 more available for its
b/h and s/h.
·
Assume
that L’s debt is perpetual debt. The
value of the debt is obtained by discounting interest payments at the 8%
interest rate: D = 800/.08 = 10,000.
The
debt will generate tax shields of $280 each year.
Assuming that the risk of the interest tax shields is the same as the
risk of the interest payments, we discount them at the same 8%: PV of tax
shields (PVTS) = 280/.08 = 3,500.
·
Note
that PVTS simply equals the tax rate times the value of debt:
Tc*D.
When
you issue debt, the combined income available to b/h and s/h increases by
the amount of the tax shields. Correspondingly,
the value of the firm increases by an amount equal to PVTS:
VL = VU + PVTS =
VU + Tc*D
·
The
more debt a firm issues, the higher its value.
The value of the cashflows generated by assets ($5,000 in this case)
does depend on how the cashflows are divided up.
If there’s no debt and the entire cashflows go to s/h they are
worth less (VU). If
there’s debt financing and the cashflows are divided up between b/h and
s/h, they are worth more (VL).
·
Why
does this happen? There’s an
invisible partner in any firm, the Govt.
The total value of debt + equity + taxes stays constant (unaffected
by financing decision). Debt
financing reduces the value of taxes, and hence increases D + E.
·
What
we have here is a situation where there’s a marginal benefit to issuing
debt (each dollar of debt you issue increases the value of the firm by 35c
due to tax shields). But there’s no marginal cost. So the more debt you issue, the better off you are.
·
Putting
it into cost of capital terms:
o
The
after-tax cost of debt = Rd (1 - Tc)
o
WACC
= (D/V)
Rd (1
- Tc)+
(E/V) Re = Ra (1
– [D/V]*
Tc)
o
Re
= Ra + (D/E)
(Ra - Rd) (1
- Tc)
Compared
to PCM:
o
cost
of debt shifts down
o
Cost
of equity increases more slowly than before, since the slope is reduced by
the term (1 - Tc)
o
WACC
slopes down instead of staying constant
IMPACT
OF CORPORATE AND PERSONAL TAXES
·
Tp
= marginal personal tax rate on ordinary income (e.g. interest or dividends)
·
Equity
income comes partly in the form of dividends and partly in the form of
capital gains. Recall from Ch.
16 that the effective tax rate for capital gains is lower than the tax rate
for dividends.
·
Tpe
= marginal personal tax rate on equity income as a whole < Tp
·
If
one dollar of operating income (EBIT) is paid out as interest, there are no
corporate taxes. The only tax
that comes into play is personal taxes at the rate Tp, so the net
after-tax income resulting from this payment = 1 - Tp.
·
If
that dollar of operating income (EBIT) was not paid out as interest, there
would be corporate tax at the rate Tc. Stockholders would
get 1 - Tc before personal taxes.
They would pay tax on this at the rate Tpe.
Tax = Tpe(1 - Tc); the net after-tax income
left = (1 - Tpe)(1 - Tc).
·
From
the tax point of view, the firm is better off borrowing when
1
- Tp > (1 - Tpe)(1
- Tc)
And
the value of the levered firm is given by
VL = VU + T’*D, where T’
= 1 – [(1 - Tpe)(1
- Tc)]/( 1 - Tp)
·
If
there are no personal taxes, or if Tpe = Tp, then T’
just simplifies to what we had before, namely Tc.
·
However,
since Tpe < Tp, this makes T’ < Tc.
(We’ll see this in a minute)
·
One
issue is whose tax rates should we plug into this formula? Different
investors have different marginal tax rates.
We really need the marginal tax rates for the marginal investor, the
one who is just indifferent between holding debt or equity.
·
We
don’t know for sure what the tax rates of the marginal investor might be,
but we can do an approximate calculation.
Assume that:
o
Tp
= 33% (marginal tax rate of marginal investor in muni market)
o
The
effective tax rate on capital gains is half the statutory rate of 20%.
o
Equity
income, on average, consists of 28% dividend income and 72% capital gains
income.
o
Then
Tpe = .28 * .33 + .72 * .10 = 0.16
o
T’
is then 1 – 0.84*0.65/0.67 = 19%
[When
the book computes 0.127 they are not computing T’.
They
compute (1 -Tp) - (1
- Tpe)(1 - Tc). That
divided by (1 - Tp) gives T’.]
·
Bottom
line:
o
Corporate
taxes are a benefit of issuing debt (interest payments are tax-deductible).
o
Personal
taxes are a disadvantage (since debt income has a higher tax rate than
equity income).
o
The
corporate tax effect outweighs the personal taxes effect.
o
There
is a net tax advantage to issuing debt, but it’s only about half the
benefit we had with corporate taxes alone.
The
same equations we wrote before still apply with T’ instead of Tc.
Similar
diagrams describe how the cost of debt, the cost of equity and WACC change
with leverage. (Will just have
a smaller deviation from the PCM case than before).
COSTS
OF FINANCIAL DISTRESS: BANKRUPTCY COSTS
o
Costs
of financial distress (COFD) are the costs that arise when a firm actually
goes bankrupt or gets into financial distress (i.e. faces a high probability
of bankruptcy in the near future)
o
Bankruptcy
process:
o
When
s/h issue debt, they promise to make certain payments to b/h
o
The
liability to make these payments is limited to the firm’s assets.
If the firm is unable to make a promised payment in full, s/h are not
personally liable to make up the difference.
S/h have limited liability.
o
When
the firm is unable to make a promised payment in full, we say it defaults on
its debt.
o
Bondholders
file for bankruptcy.
o
Firm’s
assets are sold.
o
Proceeds
are used first to pay off b/h. If
anything is left over, that goes to s/h.
o
Bankruptcy
in itself does not make capital structure relevant. Bankruptcies occur in PCM too.
But in PCM there are no transaction costs associated with bankruptcy.
The firm’s assets are liquidated at their market value (no distress
sale costs), and all of the proceeds go to pay b/h and s/h.
o
In
the real world, the bankruptcy transaction is costly. The firm typically realizes less than the fair market value
of the assets. Also, lawyers,
accountants, investment bankers, court fees have to be paid. This can add up to a tidy sum.
A company with $1 billion in assets will typically pay about $60
million in such costs (6%).
o
Apart
from such direct costs of bankruptcy, there are indirect costs too:
o
lost
business
o
employees
leave, and are hard to replace
o
suppliers
stop extending credit
o
bankruptcy
court supervision impedes business decisions
o
These
direct and indirect bankruptcy costs become a marginal cost of issuing debt that didn't exist in
PCM.
COSTS
OF FINANCIAL DISTRESS: AGENCY COSTS
·
When
a firm is in financial distress, there is a conflict of interest between
stockholders and bondholders which can lead to distorted investment decisions.
·
Normally
a firm will accept only positive NPV projects, and it will accept all
independent projects with positive NPV, since this is what increases s/h
wealth.
·
But
in financial distress, the firm may accept some negative NPV projects and
reject some positive NPV projects. This reduces the value of the firm. But managers, acting on behalf of s/h, do it anyway because
it reduces the value of debt more than it reduces the value of the firm.
This means that the value of equity increases.
For example, initially D = 60, E = 20 and VL = 80.
If VL drops by 10 to 70, and D drops by 15 to 45, then E
becomes 70 – 45 = 25. These
distorted investment decisions are bad for b/h and bad for the firm as a whole
but they benefit s/h.
·
Risk-shifting:
accepting negative NPV projects
o
Assume
a one-period world. There’s
only today (the beginning of the period) and tomorrow (the end).
o
Also
assume it’s a risk-neutral world. There
is no risk premium for bearing risk; one single discount rate applies to all
assets, namely 10%.
o
The
firm has a debt repayment of $100 tomorrow.
o
Existing
assets will generate $110 tomorrow with a probability of .3 and $30 tomorrow
with a probability of .7.
o
The
firm also has $40 in cash today. This
can be invested in T-bills to yield 5%.
o
Alternatively
they can invest the $40 in a risky project where there’s a small chance of
getting a large return and a big chance of losing money.
Specifically, with a probability of .3 the investment will generate
$100 tomorrow and with a probability of .7 it will generate only $10.
o
Exp
CF from the project = .3*100 + .7*10 = $37 < the $40 investment, so clearly
the project has negative NPV
o
If
the firm invests the cash in T-bills, we have:
Prob
Total CF
CF to b/h CF to s/h
0.3 110
+ 42 = 152
100
52
0.7
30 + 42 = 72
72
0
In
other words, with a probability of 0.7 the firm will default on the payment to
b/h. (Hence the firm is in
financial distress – facing the prospect of bankruptcy.)
Under this investment strategy, the value of equity is
0.3*52/1.1 = $14.20
o If the firm invests the cash
in the project, we have:
Prob Total CF
CF to b/h CF to s/h
0.3 110
+ 100 = 210 100
110
0.7
30 + 10 = 40
40
0
Under this investment strategy, the value of equity is
0.3*110/1.1 = $30
Clearly s/h have made themselves better off by investing in
this high risk negative NPV project.
o The key here is the project’s cashflows are highly correlated with
existing cashflows. Compared to
investing in T-bills, the project increases CF when the CF are already high
enough to pay b/h in full, so s/h get all the benefit.
It decreases CF when the entire CF are in any case going to b/h, so the
decrease only hurts b/h not s/h. B/h
are bearing the cost of this investment, s/h are reaping the benefit.
In effect, s/h substituted a risky project that yields CF mainly to s/h
for a safe project that yielded CF to both s/h and b/h.
· Underinvestment:
rejecting positive NPV projects
o This time the situation will
be that s/h have to put up the investment for a new positive NPV project, but
most of the CF from the project goes to b/h
o The firm has a debt
repayment of $100 tomorrow. The
cost of equity is 10%.
o Existing assets will
generate $30 tomorrow with a probability of .3 and $110 tomorrow with a
probability of .7. The firm has
no cash. It’s a risk-neutral
world with a 10% discount rate.
o They have a project with an
investment of $40. With a
probability of .3 the investment will generate $100 tomorrow and with a
probability of .7 it will generate $40.
o Exp CF from the project =
.3*100 + .7*40 = $58.
o NPV = 58/1.1 – 40 = $12.73
o Without the new project we
have:
Prob Total CF
CF to b/h CF to s/h
0.3 30
30
0
0.7
110 100
10
The
value of equity = .7*10/1.1 = $6.36
o If s/h contribute the $40
investment to undertake the project, we have:
Prob
Total CF
CF to b/h CF to s/h
0.3
130 100
30
0.7
150 100
50
S/h stared with equity worth $6.36 and they contributed
another $40 in cash. The value of
their equity at the end = (.3*30 + .7*50)/1.1 = 40.
So their wealth has actually declined by $6.36.
o Why
did this happen? The value of
debt must have increased by 12.73 + 6.36 = 19.09. (B/h got all of the positive
NPV from the project and also a “wealth transfer” from s/h of $6.36.)
Initial value of debt = (0.3*30 + .7*100)/1.1 = 79/1.1 =
71.82
Final value of debt = 100/1.1 = 90.91
Sure enough, the increase = 19.09.
o What
happens here is that when s/h contribute $40 and take the project, b/h CF go
up (with a probability of .3 they get $70 more). S/h put up the entire investment, but b/h get some of the
benefit. Here they get enough of
the benefit to make it a negative NPV project for s/h: the PV of the extra CF
s/h get is less than their investment.
· Implications
of these distorted investment decisions:
o If a firm remains an
all-equity firm, its value includes a PVGO term based on accepting all
positive NPV projects.
o When a firm issues debt,
even though it is not in financial distress today, the market recognizes there
is some probability of financial distress in the future.
So there is some probability of rejecting some positive NPV projects in
the future. The market reduces
PVGO accordingly. There is also
some probability of accepting negative NPV projects in the future.
The market adds a negative term to PVGO, reducing it further.
o Bottom line: debt financing
causes firm value to drop to the extent that future investment decisions will
be distorted. We call this cost
the agency cost of debt.
· Bankruptcy
costs and agency costs together are called “Costs of Financial Distress” (COFD).
They represent a marginal cost of issuing debt.
The more debt you issue, the more likely you are to go bankrupt or make
distorted investment decisions. So
the marginal COFD is not constant, but increases as you issue more and more
debt.
PUTTING
IT ALL TOGETHER: THE TRADE-OFF THEORY OF CAPITAL STRUCTURE
· Let’s
re-trace things step by step:
o In
perfect capital markets, there’s no marginal benefit (MB) or marginal cost
(MC). So VL = VU
and capital structure is irrelevant.
o With
just corporate taxes, there is a constant MB (equal to TC) and no
MC. VL > VU
and keeps increasing as you issue more and more debt.
o With
corporate and personal taxes, there is a constant MB (equal to T’, which is
less than TC) and no MC. VL
> VU and keeps increasing as you issue more and more debt (but
at a slower rate than before).
o There’s
one more factor to consider before we bring in COFD. As you issue more and more debt, you are less and less likely
to be able to utilize your interest tax shields (will not have enough taxable
income to shield). So really,
with corporate and personal taxes, the MB may equal T’ initially, but it
won’t stay constant at T’. At
some point it will decline all the way to zero.
Correspondingly, VL will not increase at a constant rate. It
will increase at a decreasing rate, and eventually level off.
· Now
we integrate everything: corporate and personal taxes, the limit to
utilization of tax shields, and COFD. So
MB is initially constant at T’ and then declines to zero. MC is initially zero and increases as you issue more and more
debt.
· As
long as MB > MC, you keep issuing more debt, and VL keeps
increasing. VL is
maximum when MB = MC, and beyond this it starts decreasing as MC > MB.
Thus each firm has an optimal debt ratio determined by the intersection
of its MB and MC. Different firms have different MB and MC curves, so therefore
different optimal debt ratios.
· Some
factors that affect how high or low a firm’s optimal debt ratio will be:
o How
capital intensive the firm is. More
capital intensive firms generate higher depreciation charges, leaving less
taxable income for utilizing interest tax shields. So for more capital intensive firms, MB declines faster,
bringing down the optimal debt ratio.
o How
variable the cashflows are (total risk of cashflows). More variable cashflows typically imply a higher likelihood
of bankruptcy, increasing MC. This
again reduces the optimal debt ratio.
o Relative
proportion of intangible assets. When
a firm goes bankrupt, the losses on intangible assets are much higher than
the losses on tangible assets. A
higher proportion of intangible assets => larger bankruptcy costs, so this
once again increases MC and reduces the optimal debt ratio.
THE
PECKING ORDER THEORY
· The
trade-off theory is a quantitative theory.
(In Ch. 18, we focused on understanding it at the theoretical level; in
Ch. 19 we turn to applying it in practice, to compute the value of a levered
firm and the total NPV of a debt-financed project. So we haven’t sent the computational side yet, but we
will.)
· The
pecking order theory is a qualitative theory that is based partly on issue
costs and partly on the implications of managers having inside information.
· The
inside information argument:
o Due
to inside information, managers know when their shares are overpriced and when
they are under-priced.
o Issuing
shares when they are under-priced hurts s/h, so managers will be willing to
issue shares only when they are overpriced.
o The
market, however, recognizes this. A
firm whose shares are overpriced is willing to issue shares at the current
inflated price. But the moment
you put up your hand and say “I want to issue shares” the market
recognizes you to be an overpriced stock.
o In
other words, the announcement that you plan to issue shares conveys negative
information to the market. Your
stock price drops accordingly. So
the overpriced firm is not actually going to be able to issue shares at the
inflated price.
o By
choosing to issue shares you reveal to the market that you are overpriced, and
s/h wealth falls. By choosing to
issue debt instead, you don’t reveal yourself to be overpriced, and s/h
wealth stays unchanged.
o So
neither the under-priced firm nor the overpriced firm wants to raise new
capital by issuing shares. It
becomes their last choice; the lowest in the pecking order.
· Based
on this argument, and also invoking issue costs, the pecking order theory
proposes the following hierarchy:
o The
first choice is internal finance (retained earnings). This avoids both inside information problems and issue costs,
and is therefore the cheapest source of financing.
o If
internally generated funds are insufficient, and external finance must be
raised, then firms prefer to go with debt.
This avoids the inside information problems associated with issuing
equity. It also entails lower
issue costs than issuing equity.
o New
equity is generally issued only as a last choice, when a firm’s debt ratio
is too high to issue more debt (the firm has reached its “debt capacity”).
· There
is no optimal debt ratio in this theory.
Internal equity is at the top of the pecking order, external equity is
at the bottom. The debt ratio a
firm should have simply depends on how much capital it needs, and how much of
that need can be met from internal sources.
· One
implication of the pecking order theory: it is valuable to have “financial
slack”. If your internally
generated funds exceed capital requirements today, don’t pay out the
difference to s/h or use it to buy back debt.
Keep the excess internal capital (e.g. in the form of marketable
securities). If you have future
shortfalls, then you will not need to resort to external financing.
You can use the internal capital you held on to (and avoid issue
costs).