Download Corporate Finance: Modigliani and Miller

Corporate Finance:
Modigliani and Miller
Yossi Spiegel
Recanati School of Business
The M&M 1958 setting
 A firm operates for infinitely many periods
 Each period, the firm generates a random cash flow,
X, distributed over the interval [X0, X1] according to
some distribution function
 Assumptions:





A1 - No transactions costs for buying and selling securities
and no bid-ask spreads (i.e., buying and selling prices are
the same).
A2 - The capital market is perfectly competitive
A3 - No bankruptcy costs
A4- No corporate or personal taxes
A5 - All agents (firms and investors) have the same
information
Corporate Finance
2
The market value of an all-equity
firm
 Since the market is perfectly competitive:
Xˆ
Xˆ
Xˆ
Xˆ
VU 


 
2
3
1   1    1   
1 


1
1

 
1 
2
  1   
1


z
 Now
z
1
1
1
 1


z
2
1 
1   1   
1 


1
1

   1
1 
2
  1   
1


z
 Hence z 
1 

Corporate Finance
3
The market value of an all-equity
firm
 Since the market is perfectly competitive:
Xˆ
Xˆ
Xˆ



VU 
2
3
1   1    1   

Xˆ 
1
1


 
1 
2
1    1   1   

1   Xˆ
Xˆ



1 


Corporate Finance
4
The market value of an all-equity
firm – another derivation
 Since the market is perfectly competitive:
1
Xˆ
Xˆ
Xˆ
Xˆ





VU 

1   1   2 1   3
1  1 
 Xˆ

Xˆ

 

2
1   1   


VU
 Hence
V
Xˆ
 U
VU 
1  1 
 VU 
Corporate Finance
Xˆ

5
The market value of a leveraged
firm
 The market value of debt:
rD
rD
rD



BL 
2
3
1  r 1  r  1  r 

1
1
rD 


 
1 
2
1  r  1  r 1  r 

rD 1  r


D
1 r
r
 The market value of equity
EL 
Xˆ  rD
L
Corporate Finance
6
The market value of a leveraged
firm
 The total value of the firm:
VL  BL  EL  D 
Corporate Finance
Xˆ  rD
L
7
The M&M propositions
M&M Proposition 1
 Given Assumptions A1-A5, the market
values of U and L are equal: VU = VL
 The proof of M&M1 uses a noarbitrage argument
 Under Assumptions A1-A5, investors in U
can replicate the cash flows of investors
in L and vice versa so the prices of U and
L must be same
Corporate Finance
9
Proof of M&M1 – part 1
 Suppose by way of negation that VU > VL
 Consider an investor who holds a fraction 
of firm U
 The investor’s payoff is X and the market
value of his portfolio is VU
 Consider the following investment strategy:
“Sell the holdings in firm U and buy a
fraction of firm L's equity and debt”
Corporate Finance
10
Proof of M&M1 – part 1
 The investor’s payoff
  X  rD   rD  X
 The investor’s wealth:
VU  VL  0
 The strategy yields the same payoff but
a higher wealth so all investors should
follow it; but then, it’s no longer true
that VU > VL
Corporate Finance
11
Proof of M&M1 – part 2
 Suppose by way of negation that VU < VL
 Consider an investor who holds a fraction 
of firm L
 The investor’s payoff is (X-rD) and the
market value of his portfolio is VL
 Consider the following investment strategy:
“Sell the holdings in firm L and buy a
fraction of firm U's equity and borrow D
at an interest rate r”
Corporate Finance
12
Proof of M&M1 – part 2
 The investor’s payoff
 X  r D    X  rD 
 The investor’s wealth:
 EL  D   VU   EL  D    VU  0



VL
 The strategy yields the same payoff, but
a higher wealth, so all investors should
follow it; but then, it’s no longer true
that VU < VL
Corporate Finance
13
M&M Proposition 2
 Given Assumptions A1-A5, the
discount rate for a leveraged firm is

  r D
L   
EL
 The expression (-r)D/EL can be
thought of as a financial risk premium
Corporate Finance
14
Financial risk premium
 Why is the equity of a leveraged firm
“risky”?
 Consider an investment of 100 which yields
either 100 or 300 with equal probabilities
 Under all equity financing, the net return is
 prob. 50%: (100-100)/100 = 0%
 prob. 50%: (300-100)/100 = 200%
Corporate Finance
15
Financial risk premium
 Suppose now the firm issued debt with face value 80
 If r = 0, investors pay 80 for the debt so the firm
finance the remaining 20 with equity
 The net return is


prob. 50%: (100-80-20)/20 = 0%
prob. 50%: (300-80-20)/20 = 1000%
 The net return is much more volatile
 If investors do not like volatility they will require a
higher return as compensation
Corporate Finance
16
Proof of M&M2
 From the market value of equity:
EL 
Xˆ  rD
L
Xˆ  rD
 L 
EL
 By M&M1,
VL  VU 
 Hence
L 
Xˆ


 EL  D   rD
EL
Xˆ   EL  D 



VL

  r D

Corporate Finance
EL
17
The implications of the M&M
propositions
WACC
 In practice, investors often discount the cash flows
from projects using a weighted average cost of
capital:
D
EL
WACC  r    L 
VL
VL
 By M&M2,

D 
  r D  EL  EL  D 
 
WACC  r     


VL 
E L  VL
VL

L
 WACC is independent of capital structure (otherwise it
would have affected investment decisions)
Corporate Finance
19
The stock price reaction to
recapitalization

An all-equity firm with N outstanding shares priced at P0 issues
debt with market value D and uses the proceeds to repurchase M
shares for a price Pr. What’s the post-recapitalization price, P1?

P1= Pr, otherwise all shareholders tender or no shareholder does

D must cover the cost of recapitalization:
D  M  Pr  M  P1

The value of the shares that are not tendered:
E L   N  M  P1

The post-recapitalization value of the firm:
VL  D  E L  M  P1  N  M  P1  N  P1
Corporate Finance
20
The stock price reaction to
recapitalization
 By definition, the initial value of the firm is
VU  N  P0
 By M&M1,
VU  VL  N  P1
 The last two equations imply that P1 = P0
 In an M&M world, a firm cannot boost its stock prices
by repurchasing equity
 Why? Equityholders can create leverage by borrowing
money personally, so they will not agree to pay more
for the firm's equity just because the firm did
something that they could have done themselves
Corporate Finance
21
The expected EPS response to
recapitalization

Expected EPS for an all-equity firm:
Xˆ
EPSU 
N

Post-recapitalization EPS:

Since D must cover the cost of recapitalization and since P1
= P0 :

Xˆ  rD
EPS L 
N M
Xˆ  rMP0
EPS L 
N M
Moreover:
VU 
Xˆ

 NP0
Xˆ
 P0 
N
Corporate Finance
22
The expected EPS response to
recapitalization
 Altogether then:
ˆ
X
ˆ  rM
X
Xˆ  rMP0
N Xˆ  N  rM 
EPS L 

 
N M
N M
N  N  M 
 Using the EPS for an all-equity firm:
 N  rM 
EPS L  EPSU 



N
M

 

 Hence, EPSL >EPSU
Corporate Finance
1
23
The expected EPS response to
recapitalization
 To see why EPSL > EPSU note that by definition
p0 
EPSU
p1 

 Since P1 = P0:
EPSU


EPS L
L
EPS L
L
 By M&M2, L > , so EPSL > EPSU
 Equityholders must be compensated for the
added risk they take, by having higher EPS
Corporate Finance
24
M&M and EPS-price ratios
 Practitioners often compare earnings-price ratios
across firms in the same industry and use the
rule: "buy firms with higher EPS-price ratios"
 The logic: stocks with higher EPS-price ratios
yield a higher returns and must be better
 Since firms are in the same industry, their risks
are presumably the same
 What is ignored is financial risk: leverage raises
EPS but not prices so it raises EPS-price ratios
even of values are the same
Corporate Finance
25
M&M 1963: corporate taxes
M&M with corporate taxes
 Instead of Assumption A4, assume now
that there’s a corporate tax rate tc
 The market value of an all-equity firm:
Xˆ 1  tc  Xˆ 1  tc  Xˆ 1  tc 
Xˆ 1  tc 
VU 


 
2
3
1 

1    1   
Corporate Finance
27
M&M Proposition 1 with corporate
taxes
 Proposition: VL = VU+tcD
 To prove the proposition, consider anall-equity firm and a leveraged firm
which are identical, save for their
capital structures
 The market values are VU and VL =
EL+D
Corporate Finance
28
Proof of M&M1 – part 1
 Consider two investments:
 Buy a fraction  of firm U
 Buy a fraction  of firm L’s equity and a
fraction (1-tc) of firm L’s debt
 The annual payoff from investment 1:
X 1  tC 
 The annual payoff from investment 2:
  X  rD 1  tC   rD1  tC   X 1  tC 
Corporate Finance
29
Proof of M&M1 – part 1
 Since the two investments yield the
same payoff, they must have the same
value:
VU  EL  D1  tC   VU  EL  D  tC D

VL
 Intuition: with leverage, the firm saves
on corporate taxes, so its value
increases by the present value of the tax
shield on future interest payments
Corporate Finance
30
M&M Proposition 2
 Proposition:

  r D1  tC 
L   
EL
 By definition:
Xˆ 1  tC 

VU
L

Xˆ  rD 1  t

C

EL
 Combining the two:
 VU


 rD 1  tC 
1  tC
VU  rD1  tC 



L 
EL
EL
Corporate Finance
31
M&M Proposition 2
 By M&M1: VL = VU + tCD
VL
 


  EL  D  tC D   rD1  tC 


VU  rD1  tC 

 
L 
EL
EL

D1  tC   rD1  tC 
EL

  r D1  tC 

EL
Corporate Finance
32
Interpretation of M&M Proposition 2
 We can rewrite L as follows:

  r D1  tC   EL  tC D     r D  tC rD
L   

EL
EL
 (EL-tCD) – a return  on invested
equity
 -r)D – financial risk premium
 tCrD – per-period tax saving
Corporate Finance
33