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because
is perpetual. If it is not, then you would need to
carefully calculate the corresponding tax shields.
14 MM1 With No Taxes
To prove MM1 with no taxes, simply set TC = 0 in all of
To
the steps above.
The proof is identical!
The
You will conclude that: VU = VL (MM1 with no taxes)
You 15 The Two MM2 Propositions
MM Proposition 2 without taxes:
When TC = 0, then rS = r0 = WACC
When
WACC is independent of capital structure!
WACC
MM Proposition 2 with taxes:
When TC > 0, then rS = r0 + (r0rB)(B/S)(1TC)
More debt increases the required return on equity!
More
Prove MM2 with taxes (without is just a special case)
16 Proof of MM2 With Taxes
Start with MM1: VL = VU + TCB = S + B. The levered firm’s
B.
market value balance sheet is:
market
Assets
VU Liabs.&Equity
B TC B S Note that for a perpetuity: r PV = C (from PV = C/r)
Note
The expected annual cash flow from the lefthand side
of the balance sheet is: r0 VU + TC B rB
of
The expected annual cash flow to bondholders and
shareholders together is: rS S + rB B
shareholders
17 Proof of MM2 With Taxes
Because all cash flows are paid out as dividends in our nogrowth perpetuity model, the cash flows going into the firm
growth
equal those going to stakeholders. Hence:
r0 V U + TC B r B = r S S + r B B
But VL = S + B = VU + TC B , so VU = S + B  TC B
Plugging into previous equation and rearranging gives:
Plugging
rS = r0 + (r0rB)(B/S)(1TC) (MM2 with taxes) 18 Proof of MM2 Without Taxes
Simply repeat the previous proof setting TC =0, and you
will get
will
rS = r0 + (r0rB)(B/S) (MM2 with no taxes) 19 Implication for Equity Risk
Assets = $10,000 ; Return on debt = 10% ; No taxes
Let ROA and Capital Structure Vary State
ROA (%)
Earnings
Interest
NI
ROE (%) Allequity firm: S=10,000 & B=0
A
B
C
D
0
0 5
500 10
1000 15
1500 0
0 0
500 0
1000 0
1500 0 5 10 15
20 E
20
2000
0
2000
20 Implication for Equity Risk
Levered firm (D/V=.5): S=5,000 & B=5,000
A
B
C
D State
ROA (%)
Earnings
Interest
NI
ROE (%) 0
0 5
500 10
1000 15
1500 500
500 500
0 500
500 500
1000 10 0 10 20 E
20
2000
500
1500
30 Debt increases the sensitivity of ROE to changes in earnings.
This is the idea of financial leverage.
Financial leverage typically increases expected ROE, but also
increases the riskiness of these returns.
21 Implications of MM2 for WACC
As we on Lecture 5 (p. 1213), plugging the formula for
As
MM2 into the WACC formula you get: S + B (1 − T )
WACC =
r0
S+B Increasing debt lowers WACC (see Lecture 5)
Increasing
Without taxes: WACC = r0 Increasing debt does not affect WACC
Increa...
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This document was uploaded on 03/09/2014 for the course COMM 371 at UBC.
 Spring '13

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