Chapter 15
Capital Structure Decisions:
Part I
1
Topics in Chapter





Overview of capital structure effects
Business versus financial risk
The impact of debt on returns
Capital structure theory, evidence, and
implications
Choosing the optimal capital structure:
An example
2
Basic Definitions





V = value of firm
FCF = free cash flow
WACC = weighted average cost of capital
rs and rd = costs of stock and debt
wce and wd = percentages of the firm that
are financed with stock and debt
3
Capital Structure and Firm Value
∞
V
=
∑
t=1
FCFt
(15-1)
(1 + WACC)t
WACC= wd (1-T) rd + wcers
(15-2)
4
Capital Structure Effects
Preview

The impact of capital structure on
value depends upon the effect of
debt on:
WACC
 FCF

5
The Effect of Debt on WACC

Debt increases the cost of equity, rs



Debt holders have a prior claim on cash flows
relative to stockholders.
Debtholders’ “fixed” claim increases risk of
stockholders’ “residual” claim.
Debt reduces the firm’s taxes



Firm’s can deduct interest expenses.
Frees up more cash for payments to investors
Reduces after-tax cost of debt
6
The Effect of Debt on WACC

Debt increases risk of bankruptcy


Causes pre-tax cost of debt to increase
Adding debt:



Increases percent of firm financed with
low-cost debt (wd)
Decreases percent financed with high-cost
equity (wce)
Net effect on WACC = uncertain
7
The Effect of Debt on FCF

 debt   probability of bankruptcy

Direct costs:



Legal fees
“Fire” sales, etc.
Indirect costs:



Lost customers
Reduction in productivity of managers and line
workers,
Reduction in credit (i.e., accounts payable)
offered by suppliers
8
The Effect of Additional Debt

Impact of indirect costs

 Sales &  Productivity



NOWC 



Customers choose other sources
Workers worry about their jobs
Suppliers tighten credit
NOPAT 
FCF 
9
The Effect of Additional Debt
on Managerial Behavior

Reduces agency costs:


Debt reduces free cash flow waste
Increases agency costs:

Underinvestment potential
10
Asymmetric Information
and Signaling

“Asymmetric Information” = insiders know
more than outsiders

Managers know the firm’s future prospects better
than investors.
Managers would not issue additional equity if
they thought the current stock price was less
than the true value of the stock
= Investors often perceive an additional
issuance of stock as a negative signal

Stock price 
11
Business Risk vs. Financial Risk

Business risk:



Uncertainty about future EBIT
Depends on business factors such as
competition, operating leverage, etc.
Financial risk:

Additional business risk concentrated on
common stockholders when financial
leverage is used
12
Business risk: Uncertainty about future
pre-tax operating income (EBIT).
Probability
Low risk
High risk
0
E(EBIT)
EBIT
Note: Business risk focuses on operating
income, ignoring financing effects.
13
Factors That Influence
Business Risk
1. Demand variability (uncertainty unit sales)
2. Sales price variability
3. Input cost variability
4. Ability to adjust output prices for changes
input costs
5. Ability to develop new products
6. Foreign risk exposure
7. Degree of operating leverage (DOL)
14
Operating Leverage


Operating leverage is the change in
EBIT caused by a change in quantity
sold.
> Fixed costs  > Operating leverage

The higher the proportion of fixed costs
within a firm’s overall cost structure, the
greater the operating leverage.
15
Figure
15.1
Illustration
of
Operating
Leverage
16
Higher operating leverage leads to more
business risk: small sales decline causes a
larger EBIT decline.
Rev.
$
Rev.
$
} EBIT
TC
TC
F
F
QBE
Sales
QBE
Sales
17
Strasburg Electronics Company
Input Data
Price
Variable costs
Fixed costs
Capital
Tax Rate
Plan A
Low FC
$2.00
$1.50
$20,000
$200,000
40%
Plan B
High FC
$2.00
$1.00
$60,000
$200,000
40%
18
Strasburg Expected Sales
Operating Performance
Data Applicable to Both Plans
Units
Dollar
Demand
Probability
Sold
Sales
Terrible
0.05
0
$0
Poor
0.2
40,000
$80,000
Average
0.5
100,000
$200,000
Good
0.2
160,000
$320,000
Wonderful
0.05
200,000
$400,000
Expected Values:
100,000
$200,000
Standard Deviation (SD):
49,396
98,793
Coefficient of Variation (CV):
0.49
0.49
19
Strasburg Plan A
Units
Sold
0
40,000
100,000
160,000
200,000
Exp. Values:
Std. Dev.:
Coef. of Var.:
Plan A: Low Fixed, High Variable Costs
Pre-tax
Net Op Profit
Return on
Operating
Operating
After Taxes
Invested
Costs
Profit (EBIT)
(NOPAT)
Capital
$20,000
($20,000)
($12,000)
-6.0%
$80,000
$0
$0
0.0%
$170,000
$30,000
$18,000
9.0%
$260,000
$60,000
$36,000
18.0%
$320,000
$80,000
$48,000
24.0%
$170,000
$30,000
$18,000
9.0%
$24,698
7.4%
0.82
0.82
Figure 15-1 Lower Panel
20
Strasburg Plan B
Units
Sold
0
40,000
100,000
160,000
200,000
Exp. Values:
Std. Dev.:
Coef. of Var.:
Plan B: High Fixed, Low Variable Costs
Pre-tax
Net Op Profit
Return on
Operating
Operating
After Taxes
Invested
Costs
Profit (EBIT)
(NOPAT)
Capital
$60,000
($60,000)
($36,000)
-18.0%
$100,000
($20,000)
($12,000)
-6.0%
$160,000
$40,000
$24,000
12.0%
$220,000
$100,000
$60,000
30.0%
$260,000
$140,000
$84,000
42.0%
$160,000
$40,000
$24,000
12.0%
49,396
14.8%
1.23
1.23
Figure 15-1 Lower Panel
21
Strasburg: Plans A & B
Plan A: Low Fixed Costs,
Low Operating Leverage
Plan B: High Fixed Costs,
High Operating Leverage
Revenues
Revenues and costs
VC
FC
$150,000
$100,000
$50,000
$0
Revenues and costs
$200,000
$200,000
Revenues
VC
$150,000
FC
$100,000
$50,000
$0
0
50000
100000
S ales (units)
0
50000
100000
Sales (units)
Figure 15-1 Upper Panel
22
Operating Breakeven: QBE
QBE = F / (P – V)
(15-4)

QBE
= Operating breakeven quantity

F
= Fixed cost

V
= Variable cost per unit

P
= Price per unit
23
Strasburg Breakeven
Q
A
BE
$20 ,000

 40 ,000 units
$2.00  $1.50
Q
B
BE
$60 ,000

 60 ,000 units
$2.00  $1.00
24
Strasburg: Plans A & B
Plan A: Low Fixed Costs,
Low Operating Leverage
Plan B: High Fixed Costs,
High Operating Leverage
Revenues
Revenues and costs
VC
FC
$150,000
$100,000
$50,000
$0
Revenues and costs
$200,000
$200,000
Revenues
VC
$150,000
FC
$100,000
$50,000
$0
0
50000
100000
S ales (units)
0
50000
100000
Sales (units)
25
Higher operating leverage leads to higher
expected EBIT and higher risk.
Low operating leverage
Probability
High operating leverage
EBITL
EBITH
26
Strasburg & Financial Risk

Strasburg going with Plan B



Riskier
Higher expected EBIT and ROIC
Financial risk:

Additional business risk concentrated on
common stockholders when financial
leverage is used
27
Strasburg - Extended


To date – no debt
Two financing choices:


Remain at 0 debt
Move to $100,000 debt and $100,000
book equity
28
Table 15.1
Strasburg
Electronics
– Effects of
Financial
Leverage
29
Strasburg with No Debt
Debt
Book equity
Interest rate
Demand for
product
Probability
(1)
(2)
Terrible
0.05
Poor
0.2
Normal
0.5
Good
0.2
Wonderful
0.05
Expected value:
Standard deviation:
Coefficient of variation:
$0
$200,000
n.a.
EBIT
(3)
($60,000)
(20,000)
40,000
100,000
140,000
$40,000
Table 15-1 Section I
Interest
(4)
$0
0
0
0
0
$0
Pre-tax
income
(5)
($60,000)
(20,000)
40,000
100,000
140,000
$40,000
Taxes
(40%)
(6)
($24,000)
(8,000)
16,000
40,000
56,000
$16,000
Net
income
(7)
($36,000)
(12,000)
24,000
60,000
84,000
$24,000
ROE
(8)
-18.0%
-6.0%
12.0%
30.0%
42.0%
12.0%
14.8%
1.23
ROE = Net Income/Book Equity
Expected ROE = ROE under each demand X Probability
30
Strasburg with 50% Debt
Debt
Book equity
Interest rate
Demand for
product
Probability
(1)
(2)
Terrible
0.05
Poor
0.2
Normal
0.5
Good
0.2
Wonderful
0.05
Expected value:
Standard deviation:
Coefficient of variation:
$100,000
$100,000
10%
EBIT
(3)
($60,000)
(20,000)
40,000
100,000
140,000
$40,000
Table 15-1 Section II
Interest
(4)
$10,000
10,000
10,000
10,000
10,000
$10,000
Pre-tax
income
(5)
($70,000)
(30,000)
30,000
90,000
130,000
$30,000
Taxes
(40%)
(6)
($28,000)
(12,000)
12,000
36,000
52,000
$12,000
Net
income
(7)
($42,000)
(18,000)
18,000
54,000
78,000
$18,000
ROE
(8)
-42.0%
-18.0%
18.0%
54.0%
78.0%
18.0%
29.6%
1.65
31
Section I. Zero Debt
Debt
Book equity
Interest rate
Demand for
product
Probability
(1)
(2)
Terrible
0.05
Poor
0.2
Normal
0.5
Good
0.2
Wonderful
0.05
Expected value:
Standard deviation:
Coefficient of variation:
Net
income
(7)
($36,000)
(12,000)
24,000
60,000
84,000
$24,000
ROE
(8)
-18.0%
-6.0%
12.0%
30.0%
42.0%
12.0%
14.8%
1.23
Strasburg w/
Zero Debt
Section II. $100,000 of Debt
Debt
Book equity
Interest rate
Demand for
product
Probability
(1)
(2)
Terrible
0.05
Poor
0.2
Normal
0.5
Good
0.2
Wonderful
0.05
Expected value:
Standard deviation:
Coefficient of variation:
Net
income
(7)
($42,000)
(18,000)
18,000
54,000
78,000
$18,000
ROE
(8)
-42.0%
-18.0%
18.0%
54.0%
78.0%
18.0%
29.6%
1.65
Strasburg w/
50% Debt
Higher ROE
Higher Risk
32
Leveraging Increases ROE

More EBIT goes to investors:

Total dollars paid to investors:



Taxes paid:


I: NI = $24,000
II: NI + Int = $18,000 + $10,000 = $28,000
I: $16,000; II: $12,000
Equity $ proportionally lower than NI
33
Strasburg’s Financial Risk


In a stand-alone sense, stockholders
see much more risk with debt.

I: σROE = 14.8%

II: σROE = 29.6%
Strasburg’s financial risk = σROE - σROIC
= 29.6% - 14.8% = 14.8%
34
Capital Structure Theory

Modigliani & Miller theory








Zero taxes (MM 1958)
Corporate taxes (MM 1963)
Corporate and personal taxes (Miller 1977)
Trade-off theory
Signaling theory
Pecking order
Debt financing as a managerial constraint
Windows of opportunity
35
MM Results: Zero Taxes

If two portfolios (firms) produce the
same cash flows, then the two
portfolios must have the same value.
A firm’s value is unaffected by its capital
structure
36
MM (1958) Assumptions
1. No brokerage costs
2. No taxes
3. No bankruptcy costs
4. Investors can borrow and lend at the
same rate as corporations
5. All investors have the same information
6. EBIT is not affected by the use of debt
37
MM Theory: Zero Taxes
Firm U
Firm L
$3,000
$3,000
0
1,200
NI
$3,000
$1,800
CF to shareholder
$3,000
$1,800
CF to debt holder
0
$1,200
$3,000
$3,000
EBIT
Interest
Total CF
Notice that the total CF are identical.
38
MM Results: Zero Taxes

MM prove:




If total CF to investors of Firm U and Firm L are
equal, then the total values of Firm U and Firm L
must be equal:
VL = VU
Because FCF and values of firms L and U
are equal, their WACCs are equal
Therefore, capital structure is irrelevant
39
MM (1963): Corporate Taxes




Relaxed assumption of no corporate
taxes
Interest may be deducted, reducing taxes
paid by levered firms
More CF goes to investors, less to taxes
when leverage is used
Debt “shields” some of the firm’s CF from
taxes
40
MM Result: Corporate Taxes

MM show that the value of a levered firm
= value of an identical unlevered form +
any “side effects.”
VL = VU + TD

(15-7)
If T=40%, then every dollar of debt adds
40 cents of extra value to firm
41
MM relationship between value and debt
when corporate taxes are considered.
Value of Firm, V
VL
TD
VU
Debt
0
Under MM with corporate taxes, the firm’s value
increases continuously as more and more debt is used.
42
MM relationship between capital costs and
leverage when corporate taxes are considered
Cost of
Capital (%)
0
rs
20
40
60
80
WACC
rd(1 - T)
Debt/Value
100
Ratio (%)
43
Miller (1977): Corporate and
Personal Taxes

Personal taxes lessen the advantage of
corporate debt:
 Corporate taxes favor debt financing


Interest expenses deductible
Personal taxes favor equity financing
No gain is reported until stock is sold
 Long-term gains taxed at a lower rate

44
Miller’s Model with Corporate
and Personal Taxes
(1 - Tc)(1 - Ts)
VL = VU + 1−
(1 - Td)
D
(15-8)
Tc = corporate tax rate.
Td = personal tax rate on debt income.
Ts = personal tax rate on stock income.
45
Tc = 40%, Td = 30%,
and Ts = 12%
(1 - 0.40)(1 - 0.12)
VL = VU + 1−
(1 - 0.30)
= VU + (1 - 0.75)D
D
= VU + 0.25D
Value rises with debt; each $1 increase in
debt raises Levered firm’s value by $0.25.
46
Trade-off Theory


MM theory assume no cost to bankruptcy
The probability of bankruptcy increases as
more leverage is used



At low leverage, tax benefits outweigh
bankruptcy costs.
At high levels, bankruptcy costs outweigh tax
benefits.
An optimal capital structure exists
(theoretically) that balances costs and
benefits.
47
Figure 15.2
Effect of Leverage on Value
48
Signaling Theory


MM assumed that investors and
managers have the same information.
Managers often have better information
and would:



Sell stock if stock is overvalued
Sell bonds if stock is undervalued
Investors understand this, so view new
stock sales as a negative signal.
49
Pecking Order Theory

Firms use internally generated funds first (1):



If more funds are needed, firms then issue
debt (2)



No flotation costs
No negative signals
Lower flotation costs than equity
No negative signals
If more funds are still needed, firms then
issue equity (3)
50
Pecking Order Theory
INTERNAL EXTERNAL
2
DEBT
EQUITY
1
3
51
Debt Financing & Agency Costs


Agency problem #1: Managers use
corporate funds for non-value
maximizing purposes
Financial leverage:



Bonds commit “free cash flow”
Forces discipline on managers to avoid
perks and non-value adding acquisitions.
LBO = ultimate use of debt controlling
management actions
52
Debt Financing & Agency Costs

Agency problem #2: “Underinvestment”
 Debt increases risk of financial
distress
 Managers may avoid risky projects
even if they have positive NPVs
53
Investment Opportunity Set and
Reserve Borrowing Capacity

Firms should normally use more
equity, less debt than optimal
 “Reserve borrowing power”
 Especially important if:
Many investment opportunities
 Asymmetric information issues cause
equity issues to be costly

54
Windows of Opportunity
Managers try to “time the market” when
issuing securities.
Issue
When
And
Equity
Market is “high” Stocks have “run up”
Debt
Market is “low”
Interest rates low
S/T Debt
Term structure is upward sloping
L/T Debt
Term structure is flat
55
Empirical Evidence

Tax benefits are important



Bankruptcies are costly


$1 debt adds  $0.10 to value
Supports Miller model with personal taxes
Costs can =10% to 20% of firm value
Firms don’t make quick corrections
when Δstock price  Δdebt ratios

Doesn’t support trade-off model
56
Empirical Evidence

After stock price , debt ratio , but firms
tend to issue equity not debt




Inconsistent with trade-off model
Inconsistent with pecking order
Consistent with windows of opportunity
Firms tend to maintain excess borrowing
capacity


Firms with growth options
Firms with asymmetric information problems
57
Implications for Managers

Take advantage of tax benefits by
issuing debt, especially if the firm
has:
High tax rate
 Stable sales
 Less operating leverage

58
Implications for Managers

Avoid financial distress costs by
maintaining excess borrowing capacity,
especially if the firm has:




Volatile sales
High operating leverage
Many potential investment opportunities
Special purpose assets (instead of general
purpose assets that make good collateral)
59
Implications for Managers

If manager has asymmetric information
regarding firm’s future prospects, then:


Avoid issuing equity if actual prospects are
better than the market perceives
Consider impact of capital structure
choices on lenders’ and rating agencies’
attitudes
60
The Optimal Capital Structure





Maximizes shareholder wealth
Maximizes firm value
Maximizes stock price
Minimizes WACC
Does NOT maximize EPS
61
Estimating the Optimal Capital
Structure: 5 Steps
1. Estimate the interest rate the firm will
2.
3.
4.
5.
pay (cost of debt)
Estimate the cost of equity
Estimate the WACC
Estimate the free cash flows and their
present value (value of the firm)
Deduct the value of debt to find
Shareholder Wealth  Maximize
62
Choosing the Optimal Capital
Structure: Strasburg Example



Currently all-equity financed
Expected EBIT = $40,000
10,000 shares outstanding
rs
= 12%
P0
= $25
T
= 40%
b
= 1.0
rRF
= 6%
RPM = 6%
63
Step 1:
Estimates of Cost of Debt
TABLE 15.2
64
The Cost of Equity at Different Levels
of Debt: Hamada’s Equation


MM theory  beta changes with
leverage
bU = the beta of a firm with NO debt


Unlevered beta
b = bU [1 + (1 - T)(D/S)]
D = Market value of firm’s debt
S = Market value of firm’s equity
T = Firm’s corporate tax rate
65
Step 2:
The Cost of Equity for wd = 50%


Use Hamada’s equation to find beta:
b = bU [1 + (1 - T)(D/S)]
= 1.0 [1 + (1-0.4) (50% / 50%) ]
= 1.60
Use CAPM to find the cost of equity:
rs= rRF + bL (RPM)
= 6% + 1.60 (6%) = 15.6%
66
TABLE 15.3
Strasburg’s optimal Capital Structure
67
Step 3: Strasburg’s WACC &
Optimal Capital Structure
Table 15-3 Strasburg's Optimal Capital Structure
Percent
financed
with debt, wd
(1)
0%
10%
20%
30%
40%
50%
60%
Market
Debt/Equity,
D/S
(2)
0.00%
11.11%
25.00%
42.86%
66.67%
100.00%
150.00%
After-tax
cost of debt,
(1-T) rd
(3)
4.80%
4.80%
4.86%
5.10%
5.40%
6.60%
8.40%
Estimated
beta, b
(4)
1.00
1.07
1.15
1.26
1.40
1.60
1.90
Cost of
equity, rs
(5)
12.0%
12.4%
12.9%
13.5%
14.4%
15.6%
17.4%
WACC
(6)
12.00%
11.64%
11.29%
11.01%
10.80%
11.10%
12.00%
Value of
operations,
Vop
(7)
$200,000
$206,186
$212,540
$217,984
$222,222
$216,216
$200,000
Note: The Capital Structure that MAXIMIZES firm value is
the one that MINIMIZES WACC
68
Notes to Table 15-3
Notes:
a
The D/S ratio is calculated as: D/S = wd / (1-wd).
b
The interest rates are shown in Table 15-2, and the tax rate is 40%.
c
The beta is estimated using Hamada’s formula in Equation 15-8.
d
The cost of equity is estimated using the CAPM formula: rs = rRF + (RPM)b,
where the risk free rate is 6 percent and the market risk premium is 6 percent.
e
The weighted average cost of capital is calculated using Equation 15-2: WACC =
wce rs + wd rd (1-T), where wce = (1-wd).
f
The value of the firm's operations is calculated using the free cash flow valuation formula in
Equation 14-1, modified to reflect the fact that Strasburg has zero growth: Vop = FCF / WACC.
Since Strasburg has zero growth, it requires no investment in capital, and its FCF is equal to its
NOPAT. Using the EBIT shown in Table 15-1:
FCF = NOPAT + Investment in capital = EBIT(1-T) + 0
= $40,000 (1-0.4) = $24,000.
69
Figure 15.3
Strasburg’s Required Rate of Return on Equity
70
Figure 15-4: Effects of Capital
Structure on Cost of Capital
20%
Cost of Equity
15%
WACC
10%
After-T ax
Cost of Debt
5%
0%
0%
10%
20%
30%
40%
50%
60%
Percent Financed with Debt
71
Step 4:
Corporate Value for wd = 0%

Vop = FCF(1+g) / (WACC-g)

g=0, so investment in capital is zero



FCF = NOPAT = EBIT (1-T)
NOPAT = ($40,000)(1-0.40) = $24,000
Vop = $24,000 / 0.12 = $200,000
72
Step 4: Strasburg’s Firm Value
Table 15-3 Strasburg's Optimal Capital Structure
Percent
financed
with debt, wd
(1)
0%
10%
20%
30%
40%
50%
60%
Market
Debt/Equity,
D/S
(2)
0.00%
11.11%
25.00%
42.86%
66.67%
100.00%
150.00%
After-tax
cost of debt,
(1-T) rd
(3)
4.80%
4.80%
4.86%
5.10%
5.40%
6.60%
8.40%
Estimated
beta, b
(4)
1.00
1.07
1.15
1.26
1.40
1.60
1.90
Cost of
equity, rs
(5)
12.0%
12.4%
12.9%
13.5%
14.4%
15.6%
17.4%
WACC
(6)
12.00%
11.64%
11.29%
11.01%
10.80%
11.10%
12.00%
Value of
operations,
Vop
(7)
$200,000
$206,186
$212,540
$217,984
$222,222
$216,216
$200,000
Note: The Capital Structure that MAXIMIZES firm value is
the one that MINIMIZES WACC
73
Implications for Strasburg




Firm should recapitalize (“recap”)
Issue debt
Use funds to repurchase equity
Optimal debt = 40%


WACC = 10.80%
Maximizes Firm Value
74
Anatomy of Strasburg’s Recap:
Before Issuing Debt
Value of Operations
+ Short Term investments
Total Value of the Firm
− Market Value of Debt
Value of equity (S)
Number of shares
Stock Price per Share
$200,000
0
$200,000
0
$200,000
10,000
$20.00
Value of stock
+ Cash distributed in
repurchase
Wealth of shareholders
$200,000
0
$200,000
75
Issue Debt (wd = 40%), But
Before Repurchase



WACC decreases to 10.80%
Vop increases to $222,222
Short-term funds = $88,889


Temporary until it uses these funds to
repurchase stock
Debt is now $88,889
76
Anatomy of a Recap: After
Debt, but Before Repurchase
Value of Operations
+ Short Term investments
Total Value of the Firm
− Market Value of Debt
Value of equity (S)
Number of shares
Stock Price per Share
Value of stock
+ Cash distributed in
repurchase
Wealth of shareholders
Before Debt
Issue
(1)
$200,000
0
$200,000
0
$200,000
10,000
$20.00
After Debt Issue,
But Before
Repurchase
(2)
$222,222
88,889
$311,111
88,889
$222,222
10,000
$22.22
$200,000
$222,222
0
$200,000
0
$222,222
Vop  $222,222
Debt
= $88,889
S/T funds = $88,889
Stock Price  $22.22
Shareholder wealth 
$222.222
77
The Repurchase:
No Effect on Stock Price


Announcement of intended repurchase might
send a signal that affects stock price
The repurchase itself has no impact on stock
price.
 If investors think the repurchase would:


 stock price, they would purchase stock the
day before, which would drive up its price.
 stock price, they would all sell short the stock
the day before, which would drive down the
stock price.
78
Remaining Number of Shares
After Repurchase



D0 = original amount of debt
D = amount after issuing new debt
If all new debt is used to repurchase shares,
then total dollars used equals:



(D – D0) = ($88,889 - $0) = $88,889
n0 = number of shares before repurchase,
n = number after repurchase.


n = n0 – (D – D0)/P = 10,000 - $88,889/$22.22
n = 10,000 – 4,000 = 6,000
79
Anatomy of Strasburg’s Recap:
After Repurchase
Value of Operations
+ Short Term investments
Total Value of the Firm
− Market Value of Debt
Value of equity (S)
Number of shares
Stock Price per Share
Value of stock
+ Cash distributed in
repurchase
Wealth of shareholders
Before Debt
Issue
(1)
$200,000
0
$200,000
0
$200,000
10,000
$20.00
After Debt Issue,
But Before
Repurchase
(2)
$222,222
88,889
$311,111
88,889
$222,222
10,000
$22.22
After
Repurchase
(3)
$222,222
0
$222,222
88,889
$133,333
$6,000.00
$22.22
$200,000
$222,222
$133,333
0
$200,000
0
$222,222
88,889
$222,222
80
Strasburg after Recapitalization
Key Points



Short Term investments used to
repurchase stock
Stock price is unchanged
Value of stock falls to $133,333


Firm no longer owns the short-term
investments
Wealth of shareholders remains at
$222,222
81
Shortcuts



The corporate valuation approach will
always give the correct answer
There are some shortcuts for finding
S, P, and n
Shortcuts on next slides
82
Calculating S, the Value of
Equity after the Recap

S = (1 – wd) Vop

At wd = 40%:
(15-13)

SPrior = S + (D – D0)

S = (1 – 0.40) $222,222

S = $133,333

SPrior = $133,333 + (88,889 – 0)

SPrior = $222,222
(15-14)
83
Calculating P, the Stock Price
after the Recap
P = [S + (D – D0)]/n0
(15-15)
P = $133,333 + ($88,889 – 0)
10,000
P = $22.22 per share
84
Number of Shares after a
Repurchase, n






# Repurchased = (D - D0) / P
n = n0 - (D - D0) / P
# Rep. = ($88,889 – 0) / $22.22
# Rep. = 4,000
n = 10,000 – 4,000
n = 6,000
85
TABLE 15.5
Strasburg’s Stock Price & EPS
86
Analyzing the Recap
Percent
financed
with debt, wd
(1)
0%
10%
20%
30%
40%
50%
60%
Value of
operations,
Vop
(2)
$200,000
206,186
212,540
217,984
222,222
216,216
200,000
Market
value
of debt, D
(3)
$0
20,619
42,508
65,395
88,889
108,108
120,000
Market
value
of equity, S
(4)
$200,000
185,567
170,032
152,589
133,333
108,108
80,000
Stock
price, P
(5)
$20.00
$20.62
$21.25
$21.80
$22.22
$21.62
$20.00
Number of
shares after
repurchase, n
(6)
$10,000
9,000
8,000
7,000
6,000
5,000
4,000
Net income,
NI
(7)
$24,000
23,010
21,934
20,665
19,200
16,865
13,920
Earnings
per share,
EPS
(8)
$2.40
$2.56
$2.74
$2.95
$3.20
$3.37
$3.48
Table 15-5
87
FIGURE 15.5
Effects of Capital Structure on Firm Value, Price and EPS
88
Effects of Capital Structure on
Price and EPS
Stock Price
EPS
$25
$6
Price
$20
$4
$15
EPS
$10
$2
$5
$0
0%
10%
20%
30%
40%
50%
$0
60%
Percent Financed with Debt
89
Optimal Capital Structure

wd = 40% gives:
Highest corporate value
 Lowest WACC
 Highest stock price per share
 Does NOT maximize EPS

90