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22 Implications of MM2 for CAPM
SML: r0 = rF + βU(rM-rF)
Assume debt beta is zero (i.e., rB = rF), and substitute into
rS = rF + βU(rM-rF) + βU(rM-rF)(1-T)(B/S)
= rF + βU[1+(1-T)(B/S)](rM-rF)
We also know that rS = rF + βL(rM-rF)
Therefore β L = β U [1+(1-T)(B/S)]
In our previous notation, this is just βS = βA [1+(1-T)(B/S)]
23 Implications of MM2 for CAPM (new 23)
From CAPM: r0 = rF + βU(rM – rF) or r0 – rF = βU(rM – rF) (1)
MM2 when βD = 0 (rB = rF): rS = r0 + (r0 – rF)(1 – t)B/S (2)
(1) into (2): rS = rF + βU(rM – rF) + βU(rM – rF)(1 – t)B/S
rS = rF + βU[1 + (1 – t)B/S](rM – rF) (3) From CAPM: rS = rF + βL(rM – rF)
From (4). Plug (4) into (3): rF + βL(rM – rF) = rF + βU[1 + (1 – t)B/S](rM – rF)
Thus, βL = βU[1 + (1 – t)B/S]
In our previous notation, this is βS = βA[1 + 24 – t)B/S]
In 25 Summary of MM Propositions
MM1 with taxes VU + TCB = VL
Since firm value always increases in leverage, the
optimal capital structure is 100% debt!
MM2 with taxes rS = r0 + (r0-rB)(B/S)(1-TC)
It implies that WACC decreases in leverage, thus
increasing firm value. Same conclusion!
MM1 with no taxes VU = VL
Capital structure is irrelevant!
MM2 with no taxes rS = r0 + (r0-rB)(B/S)
It implies that WACC is not affected by leverage, thus not
changing firm value. Same conclusion!
changing The Static Tradeoff Theory
MM2 leaves us far away from a theory of capital structure:
the optimal would be 100% debt
But we do not observe this in reality…
We are missing the costs of having higher levels of
There are several important costs associated with debt
financing. Though more difficult to quantify, these are no
less relevant than the tax effects of debt.
A trade-off between benefits and costs of debt will give us
a theory of optimal capital structure, rather than more debt
is always better.
27 The Static Tradeoff Theory
What are these costs of debt? Look behind the MM
Main issue is that in practice capital structure may affect
the cash flows to the firm
The original theory talks about costs of financial distress
– Direct Costs: legal, administrative and accounting
(about 3% o...
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