HOW WE ANALYZE THE CAPITAL STRUCTURE DECISION
·
The
capital structure decision (as we are unfortunately about to find out) involves
some pretty complicated analysis. To
focus on the fundamental issues in the simplest possible way, we consider the
simplest possible choice – between ordinary equity and ordinary debt.
(More complicated financing possibilities – such as preferred stock,
convertible debt, warrants, etc – are ignored.)
·
And we
ask: if a firm chooses to use some debt financing (instead of remaining an
all-equity firm) how does that affect s/h wealth?
·
The
firm’s assets generate a stream of cashflows.
The capital structure decision boils down to deciding how that stream
should be divided up.
o
All
equity firm => entire stream goes to s/h
o
Partly
debt-financed firm => stream is divided between stockholders and bondholders
(b/h). B/h get the safer part of
the stream, s/h get the riskier part of the stream
·
The
question will become: is the value of the stream affected by how the stream is
divided up?
IMPLICATIONS OF A PURE CAPITAL STRUCTURE CHANGE
·
Up to
now we have said maximizing s/h wealth means maximizing stock price.
A higher stock price leads to greater s/h wealth.
·
When
we consider the capital structure decision, maximizing s/h wealth translates
into something different.
·
Consider
a pure capital structure change – holding assets constant we increase the
firm’s debt. This means we issue
new debt. What happens to the money
that is raised? Can’t be retained within the firm, because that would
change the firm’s assets. So if
we are to keep the assets constant and increase the debt ratio, the money raised
must be paid out to s/h. We assume
it’s paid as a dividend.
·
So a
“pure capital structure change” necessarily involves a dividend policy
change. We can’t separate the
capital structure decision from the dividend decision.
·
When
we consider the capital structure decision, we assume that dividend policy is
irrelevant. (If it is not,
increasing debt ratio will have whatever effects we identify in our discussion
of capital structure plus whatever effects result from paying a higher
dividend.)
·
Consider
a firm which initially has debt worth $25 and equity worth $50.
They make a pure capital structure change by issuing $10 worth of new
debt and paying out this $10 to s/h. The
value of the debt becomes $35 (there are some issues here that we are ignoring,
but we’ll consider these issues in Chapter 18).
Let’s say the value of the equity becomes X.
·
Original
wealth of s/h = 50; final wealth of s/h = 10 + X
=>
increase in s/h wealth = (10 + X) – 50 = X - 40
·
Original
value of firm = VU = 75; final value of firm = VL
= 35 + X
=>
increase in the value of the firm = (35 – X)
- 75 = X - 40
·
Maximizing
s/h wealth is the same as maximizing the value of the firm.
So the capital structure decision boils down to comparing VU
and VL.
o
VU
is the value of the cashflows generated by the firm’s assets when the
cashflows are not divided up
o
VL
is the value of the cashflows generated by the firm’s assets when the
cashflows are divided up into 2 streams
o
If the
value of the cashflows is not affected by how they are divided, capital
structure is irrelevant.
o
If
dividing up the cashflows increases their value, then s/h wealth is higher with
debt financing (and the firm should adopt the highest possible debt ratio)
IMPACT
OF PURE CAPITAL STRUCTURE CHANGE IN PCM: M&M PROPOSITION 1
Assume
U and L are identical except for their capital structure.
(They are 2 possible incarnations of the same firm.
We are taking a given firm. If
it chooses to stay unlevered, it becomes U.
It if choses to become levered, it becomes L.)
For
the unlevered firm, U, we have VU = EU
For
the levered firm, L, we have VL = EL + DL
Let
Y = net cashflows (as conventionally computed, ignoring interest)
Let
I = interest on the debt of the levered firm
The
stockholders of U get Y; the stockholders of L get Y-I.
·
The
basic argument is an equal access argument.
Stockholders are not going to care whether their firm chooses to be
levered or unlevered because they can mimic or undo the effects of any changes
in the firm’s capital structure.
·
It
might seem that a s/h who prefers less risk would prefer the firm to be
unlevered. (Equity in an unlevered
firm is less risky. There’s only
business risk, no financial risk.) However,
such a s/h can construct the same investment no matter which firm he is
presented with U or L.
·
If he
is presented with firm U, he buys 1% of the shares of U.
o
Investment
= 0.01*VU
o
Dollar
return = 0.01*Y
·
If he
is presented with firm L, he buys 1% of the shares of L and 1% of the debt.
o
Investment
= 0.01*EL + 0.01*DL = 0.01*VL
o
Dollar
return = 0.01*(Y-I) + 0.01*I = 0.01*Y
·
Both
investments offer the same payoff, so they must have the same cost.
This means 0.01*VU must equal 0.01*VL.
Or the value of the firm is not affected by leverage.
Capital structure is irrelevant.
·
(Note
that once VL equals VU, both investments are
identical – same investment, same return.
So he doesn’t care which firm he is offered.)
·
Similarly,
consider a s/h who prefers more risk. If
she is presented with firm L, she buys 1% of the shares of L.
o
Investment
= 0.01*EL = 0.01*(VL - DL)
o
Dollar
return = 0.01*(Y-I)
·
If he
is presented with firm U, she will simply borrow an amount equal to 0.01*DL
and buys 1% of the shares of U. Assuming
her interest rate is the same as that of the levered firm,
o
Investment
= 0.01*VU - 0.01*DL =
0.01*(VU - DL)
o
Dollar
return = 0.01*Y - 0.01*I = 0.01*(Y-I)
·
Just
like before, identical payoffs imply identical investment amounts.
Not only does VL equal VU once again,
but both investments are identical again, so she doesn’t care which firm she
is offered.
·
The
bottom line is that stockholders can mimic or undo the
effects of any changes in the firm’s capital structure.
For that reason, they don’t care what capital structure the firm
adopts. In PCM, capital structure
is irrelevant.
·
It is
good to remind ourselves at the end of the assumptions we made:
o
Dividend
policy is irrelevant
o
Stockholders
can borrow at the same rate as the firm
PCM: LEVERAGE, BETAS, REQUIRED RETURN
·
Our discussion in Chapter 9 of betas and required returns
actually related to PCM. So it is in PCM that we have the following formulae:
ba
= (D/V) bd + (E/V) be
be= ba + (D/E) (ba - bd)
WACC = (D/V) Rd + (E/V) Re = Ra
re = ra + (D/E) (ra - rd)
·
In PCM, as you increase leverage the asset beta stays
constant even though the debt beta and equity beta both increase.
Or equivalently, WACC stays constant, even though the cost of debt and
the cost of equity both increase.
·
In fact, proposition 1 can be re-stated in terms of WACC.
o
Recall
that cashflows are computed ignoring interest charges (Y in the discussion
above)
o
If
a project was 100% equity financed, the cashflows Y would be discounted at ra (the required
return corresponding to the asset beta)
o
If
a project is actually debt-financed, the same cashflows are discounted at WACC
o
The
same principle applies when we think of a firm rather than a project.
§
Unlevered firm: to compute VU, take the cashflows
generated by the assets and discount them at ra
§
Levered firm: to compute VL, take the cashflows
generated by the assets and discount them at WACC (we don’t change the cashflows; the impact of
leverage is captured through WACC)
o
When
proposition 1 says the value of a firm is unaffected by leverage, it’s
basically saying WACC always equals ra (i.e. WACC stays constant).
·
Note that in PCM maximizing firm value is the same as
minimizing WACC. But once we make
more realistic assumptions, and allow for taxes, transaction costs, etc. this
will no longer be true. (It’s
true only as long as leverage does not affect the cashflows generated by assets;
i.e. only as long as Y stays constant. In
Chapter 18 we see that this does not always hold.)
NUMERICAL
EXAMPLE
·
Conceptually, we can compute values as follows:
o
VU:
discount net cashflows Y at ra (which is the same as re)
o
VL:
discount net cashflows Y at WACC (which will equal ra in PCM)
o
DL:
discount cashflows to b/h at rd
o
EL:
discount cashflows to s/h at re
·
However re = ra +
(D/E) (ra - rd). So
you can’t compute re without knowing EL in the first
place. If you don’t know EL,
the only way to compute it is by going VL - DL
·
Suppose a firm has operating cashflows of $15,000/year
forever. The asset beta = 0.8.
Riskfree rate = 2%, RPm = 8%. It’s
issued perpetual debt (no maturity; just pays interest forever) with interest
payments of $2,000/year forever. The
debt beta is 0.15.