CAPITAL STRUCTURE :CHAPTERS 15 AND 16
BUSINESS RISK AND FINANCIAL RISK
THE BUSINESS RISK OF A FIRM ( OR A PROJECT) RELATES TO THE
VOLATILITY OF THE RETURN ON THE EQUITY OF ITS
SHAREHOLDERS WHEN THE FIRM IS 100% EQUITY FINANCED, I.E.,
THE FIRM HAS NO DEBT AND HENCE UNLEVERED. FINANCIAL
RISK RELATES TO THE ADDITIONAL RISK OF BANKRUPTCY DUE TO
THE USE OF DEBT IN THE OPERATIONS. THUS, STOCK HOLDERS OF
A FIRM WITH DEBT WILL HAVE TO BEAR THE BUSINESS RISK AS
WELL AS THE FINANCIAL RISK DUE TO DEBT. BUSINESS RISK MAY
BE INFLUENCED BY THE
PRODUCT DEMAND VARIABILITY
PRODUCT SALES PRICE VARIABILITY
INPUT COST VARIABILITY
ABILTY TO ADJUST OUTPUT PRICES FOR CHANGES IN INPUT COSTS
ABILITY TO DEVELOP NEW PRODUCTS , TIMELY AND
COST-EFFECTIVELY
FOREIGN RISK EXPOSURE
EXTENT TO WHICH OPERATING COSTS ARE FIXED:
OPERATING LEVERAGE
FOR A DISCUSSION OF THE ABOVE REFER TO PAGE 513 OF TEXT
SINCE SUCH CHARACTERISTICS COULD VARY ACROSS INDUSTRIES
AND ACROSS FIRMS IN AN INDUSTRY, BUSINESS RISK VARIES
FROM INDUSTRY TO INDUSTRY AND AMONG FIRMS IN AN
INDUSTRY.
THE EFFECT OF OPERATING LEVERAGE AND RELATED CONCEPTS
ARE ILLUSTRATED THRU THE FOLLOWING EXAMPLE:
EXAMPLE TO ILLUSTRATE OPERATING LEVERAGE
WORSE
EXPECTED
BETTER
SALES (UNITS)
90,000
$ SALES (@ $50/UNIT)
4.5 M
VARIABLE COST (@ $30/UNIT) 2.7 M
CONTRIBUTION
1.8 M
FIXED COSTS
1M
______
EBIT
0.8 M
_______
CASE A (FIRM HAS NO DEBT)
100,000
5M
3M
2
1M
______
1M
______
110,000
5.5 M
3.3 M
2.2M
1M
______
1.2 M
_______
INTEREST
TAXABLE INCOME
TAX @ 40%
0
0.8 M
0.32 M
________
0
1M
0.4 M
______
0
1.2 M
0.48 M
_______
NET INCOME
0.48 M
_________
0.6 M
_______
0.72 M
_________
0.2 M
0.6 M
0.24 M
________
0.36 M
_________
0.2 M
0.8 M
0.32 M
_______
0.48 M
________
CASE B (FIRM HAS DEBT)
INTEREST
TAXABLE INCOME
TAX @ 40%
NET INCOME
0.2 M
1M
0.4 M
_______
0.6 M
_______
DEGREES OF LEVERAGE
DEGREE OF OPERATING LEVERAGE (DOL) = % CHANGE IN EBIT
% CHANGE IN SALES
DEGREE OF FINANCIAL LEVERAGE (DFL) = % CHANGE IN NI
% CHANGE IN EBIT
DEGREE OF TOTAL LEVERAGE (DTL) = % CHANGE NI
% CHANGE IN SALES
DTL = % CHANGE IN EBIT * % CHANGE IN NI
% CHANGE IN SALES
% CHANGE IN EBIT
= DOL * DFL
FOR CASE A (NO DEBT):
DOL = 20/10 =2
DFL = 20/20 =1
DTL = 20/10 = 2 (OR 2 * 1)
FOR CASE B (DEBT):
DOL = 20/10 =2
DFL = 25/20 = 1.25
DTL = 25/10 = 2.5 (OR 2 * 1.25)
CAPITAL STRUCTURE THEORY
MILLER & MODIGLIANI (M&M) ASSUMPTIONS
1. BUSINESSRISK CAN BE MEASURED AND FIRMS WITH THE
SAME BUSINESS RISK FALL IN A HOMOGENEOUS RISK CLASS
AND COMMAND THE SAME BUSINESS RISK PREMIUM
2. INVESTORS (PRESENT AND PROSPECTIVE) HAVE
HOMOGENEOUS EXPECTATIONS ABOUT EXPECTED
EARNINGS, RISK, ETC.
3. CAPITAL MARKETS ARE PERFECT (NO BROKERAGE COSTS)
4. ANY AMOUNT OF BORROWING AND LENDING CAN BE
TRANSACTED AT THE SAME INTEREST RATE –RISK-FREE
RATE- BY INDIVIDUALS AND FIRMS
5. BORROWING DECISION IS A ONE-TIME DECISION
6. FIRMS HAVE NO GROWTH AND ALL CASH FLOWS ARE
PERPETUITIES
7. EBIT IS NOT AFFECTED BY DEBT
8. BANCRUPTCY IS POSSIBLE, BUT THERE ARE NO BANKRUPTCY
COSTS
9. AGENCY PROBLEM MAY BE PRESENT BUT THERE ARE NO
AGENCY COSTS
WITH THE ABOVE ASSUMPTIONS, M&M EXAMINED WHETER
VL = VU
VL < VU
VL > VU
THEY EXAMINED THE ABOVE RELATIONSHIPS UNDER:
A. NO CORPORATE TAXES AND NO PERSONAL TAXES
B. NO PERSONAL TAXES, BUT CORPORATE TAXES EXIST
LATER, MILLER EXAMINED THE RELATIONSHIPS UNDER:
BOTH CORPORATE AND PERSONAL TAXES EXIST
WITHOUT
TAXES (NO CORPORATE OR PERSONAL TAXES)
VL = VU = EBIT/ rSU
rSL = rSU + RISK PREMIUM
= rSU + (rSU-rD) * (D/S)
(16-1)
(16-2)
WACCL = WACCU = rSU
REFER TO FIG. 16-1 (LEFT)
PROBLEM 16-2
a. VU =
EBIT
rsU
=
b. rsU = 10.0%.
$2 million
0.10
= $20 million.
(Given)
rsL = rsU + rsU - rd)(D/S)= 10%+(10%-5%)($10/$10)=
15.0%.
c. SL =
EBIT  rd D
$2  0.05($10)
=
= $10 million.
0.15
rsL
SL + D = VL = VU + TD.
$10 + $10 = $20 = VL = $20 + (0)$10 = $20
million.
d. WACCU = rsU = 10%.
For Firm L, we know that WACC must equal rsU =
10% according to Proposition I.
But, we can
demonstrate this as follows:
WACCL
= (D/V)rd + (S/V)rs
= ($10/$20)5% +($10/$20)15%
= 2.5% + 7.5% = 10.0%.
e. VL = $22 million is not an equilibrium value
according to MM.
Here’s why.
Suppose you
owned 10 percent of Firm L’s equity, worth
0.10($22 million - $10 million) = $1.2 million.
You could (1) sell your stock, (2) borrow an
amount (at 5%) equal to 10 percent of Firm L’s
debt, or 0.10($10 million) = $1 million, and
(3) end up with $1.2 million + $1 million =
$2.2 million.
You could spend $2 million to
buy 10% of Firm U’s stock, and invest $200,000
in risk-free debt. Your cash stream would now
be 10 percent of Firm U’s flow, or 0.10(EBITU)
= 0.10($2 million) = $200,000, plus the return
on the $200,000 of risk-free debt, minus the
0.05($1 million) = $50,000 interest expense for
$150,000 plus the return on the extra $200,000.
Before the arbitrage, your return was 10
percent of the $2 million - 0.05($10 million) =
$1.5 million, or $150,000. Investors would do
this arbitrage until VL = VU = $20 million.
WITH CORPORATE TAXES ONLY (NO PERSONAL TAXES)
VU = EBIT*(1-T)/ rSU
(16-5)
VL = VU + T*D
(16-4)
rSL = rSU + RISK PREMIUM
= rSU + (rSU-rD) * (1-T) * (D/S)
(16-6)
WACCL < WACCU
REFER TO FIG. 16-1 (RIGHT)
PROBLEM 16-3
$2(1  0.4)
EBIT (1  T )
=
= $12 million.
0.10
rsU
a. VU =
VL = VU + TD = $12 + (0.4)$10 = $16 million.
VL = D + SL OR
SL = VL – D = 16 – 10 = 6 Million
b. rsU = 0.10 = 10.0%.
rsL
= rsU + (rsU - rd)(1 - T)(D/S)
= 10% + (10% - 5%)(0.6)($10/$6) = 10% + 5%
= 15.0%.
c. SL =
( EBIT  rd D)(1  T)
[$2  0.05($10)]0.6
=
= $6 million.
0.15
rsL
VL = SL + D = $6 + $10 = $16 million.
d. WACCU
WACCL
= rsU = 10.00%.
= (D/V)rd(1 - T) + (S/V)rs
= ($10/$16)5%(0.6) + ($6/$16)15%
= 7.50%.
WITH
CORPORATE AND PERSONAL TAXES
VU = EBIT*(1-TC) * (1-TS)
rSU * (1-TS)
(16-8)
VL = VU + {1- [(1-TC) * (1-TS)/(1-Td]}* D
(16-12)
PROBLEM 16-4
a. VU =
EBIT (1  TC )(1  Ts )
EBIT (1  TC ) $2(0.6)
=
=
= $12
0.10
rsU (1  Ts )
rsU
million.
b.

VL = VU + 1 

(1  TC )(1  Ts ) 
D
(1  Td )


(0.6)( 0.8) 
= $12 + 1 
$10
(0.72) 

= $12 + [1 - 0.67]$10 = $12 + 0.33($10)
= $15.33 million.
VL = $15.33 million.
Gain from leverage = $3.33 million.
c. The
gain
from
leverage
under
Miller
is
0.33($10) = $3.33 million.
The gain from
leverage in Problem 16-3 is 0.4($10) = $4
million.
Thus, the addition of personal tax
rates reduced the value of the debt financing.
d. VU = VL = $20 million.
Gain from leverage = $0.00.
e. VU = $12 million. VL = $16 million.
Gain from leverage = $4 million.
f. VU = $12 million.
VL = $16 million.
Gain from leverage = $4.0 million.
Note that
the gain from leverage is the same as in Part
(e) and will be the same value, as long as
Td = Ts.
CAPITAL STRUCTURE THEORY, HAMADA MODEL
AND PURE PLAY APPROACH
bL = bU[1 + (1 - T)(D/S)]
rsU = rRF + (rM - rRF)bU
rsL = rsU + (rsU - rRF)(1 - T)(D/S)
PROBLEM 16-1
a. bL = bU[1 + (1 - T)(D/S)].
bU =
bL
1.8
1 .8
=
=
= 1.125.
1 .6
1  (1  T )( D / S)
1  (1  0.4)( 0.5 / 0.5)
b. rsU = rRF + (rM - rRF)bU
= 10% + (5%)1.125 = 10% + 5.625% = 15.625%.
c. $2 Million Debt:
VL = VU + TD
= $10 + 0.25($2) = $10.5 million.
rsL = rsU + (rsU - rRF)(1 - T)(D/S)
= 15.625% + (15.625% - 10%)(0.75)($2/$8.5)
= 15.625 + 5.625% (0.75)($2/$8.5) = 16.62%.
$4 Million Debt:
VL = $10 + 0.25($4) = $11.0 million.
rsL = 15.625% + 5.625%(0.75)($4/$7) = 18.04%.
$6 Million Debt:
VL = $10 + 0.25($6) = $11.5 million.
rsL= 15.625% + 5.625% (0.75)($6/$5.5) = 20.23%.
CAPITAL STRUCTURE THEORY
THE TRADE-OFF MODEL
THE MODELS OF M&M WITH CORPORATE TAXES AND THE MILLER
MODEL WITH CORPORATE
AND PERSONAL TAXES IMPLY THAT
DEBT IS BENEFICIAL AND CAPITAL STRUCTURE SHOULD BE
CLOSE TO 100% DEBT FOR FIRM VALUE MAXIMIZATION.
HOWEVER, WITH THE EXCEPTION OF A FEW FIRMS, THE
OBSERVED DEBT LEVEL IS BETWEEN 0% AND 100% ALSO,
DIFFERENT INDUSTRIES HAVE DIFFERENT AVERAGE DEBT
LEVELS. HOW CAN THIS BE EXPLAINED? MODELS USING
FINANCIAL DISTRESS (BANKRUPTCY) COSTS AND AGENCY
COSTS OF DEBT ALONG WITH TAX BENEFITS OF DEBT (DUE TO
TAX DEDUCTIBILITY OF INTEREST) ARE CALLED TRADE-OFF
MODELS.
THESE MODELS SEEK TO EXPLAIN THE OPTIMUM
CAPITAL STRUCTURE AS THE DEBT LEVEL AT WHICH THE
TAX-SHELTERING BENEFITS OF DEBT ARE OFFSET BY THE
FINANCIAL DISTRESS (BANKRUPTCY) AND AGENCY COSTS THAT
ARISE DUE TO DEBT AND INCREASE WITH DEBT LEVEL:
VL = VU + TAX BENEFITS OF DEBT (SAY,T*D)
- PV OF EXPECTED FINANCIAL DISTRESS COSTS
- PV OF EXPECTED AGENCY COSTS
REFER TO FIG. 15-1
HERE ONLY FINANCIAL DISTRESS COSTS ARE SHOWN.
IT IS EASY TO INCLUDE THE EFFECTS OF AGENCY COSTS IN
THE DIAGRAM
Also refer to power point slides 40-50 as well as
discussion in chapter 15 of text (pages 519-530)
FINDING OPTIMUM CAPITAL STRUCTURE WITH
BANKRUPTCY AND AGENCY COSTS
1. FIND VU
2. ESTIMATE BANKRUPTCY COSTS AND THEIR PRESENT VALUE
3. ESTIMATE THE PROBABILITY OF BANKRUPTCY AT
DIFFERENT DEBT LEVELS
4. ESTIMATE THE EXPECTED PV OF BANKRUPTCY COSTS AT
DIFFERENT DEBT LEVELS AS (2) * (3)
5. ESTIMATE PV OF EXPECTED AGENCY COSTS AT DIFFERENT
DEBT LEVELS
6. FOR EACH DEBT LEVEL FIND
VL = VU + T*D – (4) – (5)
7. THE OPTIMUM CAPITAL STRUCTURE (DEBT LEVEL) IS
WHERE VL IS MAXIMUM
PROBLEM
LLL IN. IS CURRENTLY UNLEVERED, WITH A VALUE OF $30
MILLION. IT WILL CONTINUE TO BE IN THE 40% TAX
BRACKET. THE COMPANY HAS ESTIMETED THAT THE PV OF ITS
BANKRUPTCY COSTS WOULD BE $8 MILLION. LLL INC. HAS
ESTIMATED THE PROBABILITIES OF BANKRUPTCY AND
EXPECTED PV OF AGENCY COSTS AT DIFFERENT DEBT LEVELS
AS FOLLOWS:
DEBT $ MILLION
PROB. OF BANKRUPTCY
EXPECTED PV OF AGENCY
COSTS ($ MILLION)
0
0
0.25
5
.1
10
0.3
20
0.5
30
35
0.8 0.95
0.5 0.75
1.0
1.5
3.0
FIND THE OPTIMUM LEVEL OF BORROWING (OPTIMUM CAPITAL
STRUCTURE) FORR LLL INC.
SOLUTION
1. VU = $ 50 MILLION (GIVEN)
2. PV OF BANKRUPTCY COSTS = $ 8 MILLION (GIVEN)
3. PROBABILITY OF BANKRUPTCY AT DIFFERENT DEBT
LEVELS IS GIVEN ABOVE IN THE PROBLEM
4. EXPECTED PV OF BANRUPTCY COSTS AT DIFFERENT DEBT
LEVELS
DEBT $ MILLION
0
5
10
20
30 35
PROBABILITY OF BANKRUPTCY 0
0.1 0.3 0.5 0.8 0.95
EXPECTED PV OF BANKRUPTCY
COSTS=(2)*(3)$ MILLION
0
0.8 2.4 4.0 6.4 7.60
5. EXPECTED PV OF AGENCY
COSTS $ MILLION
0.25 0.5 0.75 1.0 1.5 3.0
6.FIND VL = VU + T*D – (4) – (5)
(1)
DEBT
VU
(2)
T*D
(3)
(4)
EXPECTED EXPECTED
PV OF
PV OF
BANKRUPTCY AGENCY
COSTS
COSTS
(5)
VL=(1)+(2)
-(3)-(4)
0
50
0
0
0.25
49.75
5
50
2
0.8
0.50
50.70
10
50
4
2.4
0.75
50.85
20
50
8
4.0
1.00
53.00
30
50
12
6.4
1.50
54.10
35
50
14
7.6
3.00
53.40
SINCE VALUE IS A MAXIMUM OF $54.10 MILLION AT A DEBT
LEVEL OF $30 MILLION, OPTIMUM LEVEL OF BORROWING
(OPTIMUM CAPITAL STRUCTURE) IS $30 MILLION