1

Chapter 15

Capital Structure Decisions:

Part I

2

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

3

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

4

Capital Structure and Firm Value

V = ∑∞

t=1

FCFt

(1 + WACC)t

WACC= wd (1-T) rd + wcers

(15-1)

(15-2)

5

Capital Structure Effects Preview

The impact of capital structure on value depends upon the effect of debt on: WACC FCF

6

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

The Effect of Debt on WACC

7

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

8

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

9

The Effect of Additional Debt

Impact of indirect costs Sales & Productivity

Customers choose other sources Workers worry about their jobs

NOWC Suppliers tighten credit

NOPAT FCF

10

The Effect of Additional Debt on Managerial Behavior

Reduces agency costs: Debt reduces free cash flow

waste Increases agency costs:

Underinvestment potential

11

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

12

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

13

Business risk: Uncertainty about future pre-tax operating income (EBIT).

Probability

EBITE(EBIT)0

Low risk

High risk

Note: Business risk focuses on operating income, ignoring financing effects.

14

Factors That Influence Business Risk

1. Demand variability (uncertainty unit sales)

2. Sales price variability3. Input cost variability4. Ability to adjust output prices for

changes input costs5. Ability to develop new products6. Foreign risk exposure7. Degree of operating leverage (DOL)

15

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.

16

Figure 15.1Illustration of Operating Leverage

17

Higher operating leverage leads to more business risk: small sales decline causes a larger EBIT decline.

Sales

$ Rev.TC

F

QBE

EBIT}$

Rev.

TC

F

QBESales

18

Strasburg Electronics Company

Input Data Plan A Plan BLow FC High FC

Price $2.00 $2.00Variable costs $1.50 $1.00Fixed costs $20,000 $60,000Capital $200,000 $200,000Tax Rate 40% 40%

19

Strasburg Expected Sales

Operating Performance

Units Dollar

Demand Probability Sold Sales

Terrible 0.05 0 $0Poor 0.2 40,000 $80,000Average 0.5 100,000 $200,000Good 0.2 160,000 $320,000Wonderful 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

Data Applicable to Both Plans

20

Strasburg Plan A

Pre-tax Net Op Profit Return onUnits Operating Operating After Taxes InvestedSold Costs Profit (EBIT) (NOPAT) Capital

0 $20,000 ($20,000) ($12,000) -6.0%40,000 $80,000 $0 $0 0.0%

100,000 $170,000 $30,000 $18,000 9.0%160,000 $260,000 $60,000 $36,000 18.0%200,000 $320,000 $80,000 $48,000 24.0%

Exp. Values: $170,000 $30,000 $18,000 9.0%Std. Dev.: $24,698 7.4%Coef. of Var.: 0.82 0.82

Plan A: Low Fixed, High Variable Costs

Figure 15-1 Lower Panel

21

Strasburg Plan B

Pre-tax Net Op Profit Return on

Units Operating Operating After Taxes InvestedSold Costs Profit (EBIT) (NOPAT) Capital

0 $60,000 ($60,000) ($36,000) -18.0%40,000 $100,000 ($20,000) ($12,000) -6.0%100,000 $160,000 $40,000 $24,000 12.0%160,000 $220,000 $100,000 $60,000 30.0%200,000 $260,000 $140,000 $84,000 42.0%

Exp. Values: $160,000 $40,000 $24,000 12.0%

Std. Dev.: 49,396 14.8%

Coef. of Var.: 1.23 1.23

Plan B: High Fixed, Low Variable Costs

Figure 15-1 Lower Panel

22

Strasburg: Plans A & B

Plan A: Low Fixed Costs, Low Operating Leverage

$0

$50,000

$100,000

$150,000

$200,000

0 50000 100000

Sales (units)

Rev

enue

s an

d co

sts

Revenues

VC

FC

Plan B: High Fixed Costs, High Operating Leverage

$0

$50,000

$100,000

$150,000

$200,000

0 50000 100000

Sales (units)

Rev

enue

s an

d co

sts Revenues

VC

FC

Figure 15-1 Upper Panel

23

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

24

Strasburg Breakeven

units000,6000.1$00.2$

000,60$Q

units000,4050.1$00.2$

000,20$Q

BBE

ABE

25

Strasburg: Plans A & B

Plan A: Low Fixed Costs, Low Operating Leverage

$0

$50,000

$100,000

$150,000

$200,000

0 50000 100000

Sales (units)

Rev

enue

s an

d co

sts

Revenues

VC

FC

Plan B: High Fixed Costs, High Operating Leverage

$0

$50,000

$100,000

$150,000

$200,000

0 50000 100000

Sales (units)

Rev

enue

s an

d co

sts Revenues

VC

FC

26

Probability

EBITL

Low operating leverage

High operating leverage

EBITH

Higher operating leverage leads to higher expected EBIT and higher risk.

27

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

28

Strasburg - Extended

To date – no debt Two financing choices:

Remain at 0 debt Move to $100,000 debt and

$100,000 book equity

29

Table 15.1Strasburg Electronics – Effects of Financial Leverage

30

Strasburg with No DebtDebt $0Book equity $200,000Interest rate n.a.

Demand for Pre-tax Taxes Netproduct Probability EBIT Interest income (40%) income ROE

(1) (2) (3) (4) (5) (6) (7) (8)Terrible 0.05 ($60,000) $0 ($60,000) ($24,000) ($36,000) -18.0%Poor 0.2 (20,000) 0 (20,000) (8,000) (12,000) -6.0%Normal 0.5 40,000 0 40,000 16,000 24,000 12.0%Good 0.2 100,000 0 100,000 40,000 60,000 30.0%Wonderful 0.05 140,000 0 140,000 56,000 84,000 42.0%Expected value: $40,000 $0 $40,000 $16,000 $24,000 12.0%Standard deviation: 14.8%Coefficient of variation: 1.23

Table 15-1 Section I

ROE = Net Income/Book Equity

Expected ROE = ROE under each demand X Probability

31

Strasburg with 50% Debt

Debt $100,000Book equity $100,000Interest rate 10%

Demand for Pre-tax Taxes Netproduct Probability EBIT Interest income (40%) income ROE

(1) (2) (3) (4) (5) (6) (7) (8)Terrible 0.05 ($60,000) $10,000 ($70,000) ($28,000) ($42,000) -42.0%Poor 0.2 (20,000) 10,000 (30,000) (12,000) (18,000) -18.0%Normal 0.5 40,000 10,000 30,000 12,000 18,000 18.0%Good 0.2 100,000 10,000 90,000 36,000 54,000 54.0%Wonderful 0.05 140,000 10,000 130,000 52,000 78,000 78.0%Expected value: $40,000 $10,000 $30,000 $12,000 $18,000 18.0%Standard deviation: 29.6%Coefficient of variation: 1.65

Table 15-1 Section II

32

Section I. Zero DebtDebtBook equityInterest rate

Demand for Netproduct Probability income ROE

(1) (2) (7) (8)Terrible 0.05 ($36,000) -18.0%Poor 0.2 (12,000) -6.0%Normal 0.5 24,000 12.0%Good 0.2 60,000 30.0%Wonderful 0.05 84,000 42.0%Expected value: $24,000 12.0%Standard deviation: 14.8%Coefficient of variation: 1.23

Section II. $100,000 of DebtDebtBook equityInterest rate

Demand for Netproduct Probability income ROE

(1) (2) (7) (8)Terrible 0.05 ($42,000) -42.0%Poor 0.2 (18,000) -18.0%Normal 0.5 18,000 18.0%Good 0.2 54,000 54.0%Wonderful 0.05 78,000 78.0%Expected value: $18,000 18.0%Standard deviation: 29.6%Coefficient of variation: 1.65

Strasburg w/ Zero Debt

Strasburg w/ 50% Debt

Higher ROE

Higher Risk

33

Leveraging Increases ROE

More EBIT goes to investors: Total dollars paid to investors:

I: NI = $24,000 II: NI + Int = $18,000 + $10,000 = $28,000

Taxes paid: I: $16,000; II: $12,000

Equity $ proportionally lower than NI

34

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%

35

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

36

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

37

MM (1958) Assumptions

1. No brokerage costs2. No taxes3. No bankruptcy costs4. Investors can borrow and lend at the

same rate as corporations5. All investors have the same

information6. EBIT is not affected by the use of debt

38

MM Theory: Zero TaxesFirm U Firm L

EBIT $3,000 $3,000Interest

0 1,200

NI $3,000 $1,800

CF to shareholder

$3,000 $1,800

CF to debt holder

0 $1,200

Total CF $3,000 $3,000

Notice that the total CF are identical.

39

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

40

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

41

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

42

Value of Firm, V

0Debt

VL

VU

Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.

TD

MM relationship between value and debt when corporate taxes are considered.

43

Cost of Capital (%)

0 20 40 60 80 100Debt/Value Ratio (%)

rs

WACCrd(1 - T)

MM relationship between capital costs and leverage when corporate taxes are considered

44

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

45

Miller’s Model with Corporate and Personal Taxes

VL = VU + 1− D (15-8)

Tc = corporate tax rate.Td = personal tax rate on debt income.Ts = personal tax rate on stock income.

(1 - Tc)(1 - Ts)

(1 - Td)

46

Tc = 40%, Td = 30%, and Ts = 12%

VL = VU + 1− D

= VU + (1 - 0.75)D

= VU + 0.25D

Value rises with debt; each $1 increase in debt raises Levered firm’s value by $0.25.

(1 - 0.40)(1 - 0.12)(1 - 0.30)

47

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.

48

Figure 15.2 Effect of Leverage on Value

49

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.

50

Pecking Order Theory Firms use internally generated funds

first (1): No flotation costs No negative signals

If more funds are needed, firms then issue debt (2) Lower flotation costs than equity No negative signals

If more funds are still needed, firms then issue equity (3)

51

Pecking Order Theory

INTERNAL EXTERNAL

DEBT 2

EQUITY 1 3

52

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

53

Agency problem #2: “Underinvestment” Debt increases risk of financial

distress Managers may avoid risky

projects even if they have positive NPVs

Debt Financing & Agency Costs

54

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

55

Windows of Opportunity

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

Managers try to “time the market” when issuing securities.

56

Empirical Evidence Tax benefits are important

$1 debt adds $0.10 to value Supports Miller model with personal taxes

Bankruptcies are costly 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

57

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

58

Implications for Managers

Take advantage of tax benefits by issuing debt, especially if the firm has: High tax rate Stable sales Less operating leverage

59

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)

60

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

61

The Optimal Capital Structure

Maximizes shareholder wealth Maximizes firm value Maximizes stock price Minimizes WACC Does NOT maximize EPS

62

Estimating the Optimal Capital Structure: 5 Steps

1. Estimate the interest rate the firm will pay (cost of debt)

2. Estimate the cost of equity3. Estimate the WACC4. Estimate the free cash flows and

their present value (value of the firm)

5. Deduct the value of debt to find Shareholder Wealth Maximize

63

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%

64

TABLE 15.2

Step 1:Estimates of Cost of Debt

65

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 debtS = Market value of firm’s

equityT = Firm’s corporate tax rate

66

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%

67

TABLE 15.3Strasburg’s optimal Capital Structure

68

Step 3: Strasburg’s WACC & Optimal Capital Structure

Note: The Capital Structure that MAXIMIZES firm value is the one that MINIMIZES WACC

Table 15-3 Strasburg's Optimal Capital Structure

Percent Market After-tax Value offinanced Debt/Equity, cost of debt, Estimated Cost of operations,

with debt, wd D/S (1-T) rd beta, b equity, rs WACC Vop

(1) (2) (3) (4) (5) (6) (7)0% 0.00% 4.80% 1.00 12.0% 12.00% $200,000

10% 11.11% 4.80% 1.07 12.4% 11.64% $206,18620% 25.00% 4.86% 1.15 12.9% 11.29% $212,54030% 42.86% 5.10% 1.26 13.5% 11.01% $217,98440% 66.67% 5.40% 1.40 14.4% 10.80% $222,22250% 100.00% 6.60% 1.60 15.6% 11.10% $216,21660% 150.00% 8.40% 1.90 17.4% 12.00% $200,000

69

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.

FCF = NOPAT + Investment in capital = EBIT(1-T) + 0= $40,000 (1-0.4) = $24,000.

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:

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).

70

Figure 15.3Strasburg’s Required Rate of Return on Equity

71

Figure 15-4: Effects of Capital Structure on Cost of Capital

0%

5%

10%

15%

20%

0% 10% 20% 30% 40% 50% 60%

Percent Financed with Debt

Cost of Equity

WACC

After-Tax Cost of Debt

72

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

73

Step 4: Strasburg’s Firm Value

Table 15-3 Strasburg's Optimal Capital Structure

Percent Market After-tax Value offinanced Debt/Equity, cost of debt, Estimated Cost of operations,

with debt, wd D/S (1-T) rd beta, b equity, rs WACC Vop

(1) (2) (3) (4) (5) (6) (7)0% 0.00% 4.80% 1.00 12.0% 12.00% $200,000

10% 11.11% 4.80% 1.07 12.4% 11.64% $206,18620% 25.00% 4.86% 1.15 12.9% 11.29% $212,54030% 42.86% 5.10% 1.26 13.5% 11.01% $217,98440% 66.67% 5.40% 1.40 14.4% 10.80% $222,22250% 100.00% 6.60% 1.60 15.6% 11.10% $216,21660% 150.00% 8.40% 1.90 17.4% 12.00% $200,000

Note: The Capital Structure that MAXIMIZES firm value is the one that MINIMIZES WACC

74

Implications for Strasburg

Firm should recapitalize (“recap”)

Issue debt Use funds to repurchase equity Optimal debt = 40%

WACC = 10.80% Maximizes Firm Value

75

Anatomy of Strasburg’s Recap: Before Issuing Debt

$200,000

0

$200,000

0

Value of equity (S) $200,000

Number of shares 10,000 $20.00

Value of stock $200,000

0Wealth of shareholders $200,000

Stock Price per Share

Value of Operations

+ Short Term investments

Total Value of the Firm

− Market Value of Debt

+ Cash distributed in repurchase

76

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

77

Anatomy of a Recap: After Debt, but Before Repurchase

Before Debt Issue

After Debt Issue, But Before Repurchase

(1) (2)$200,000 $222,222

0 88,889

$200,000 $311,111

0 88,889

Value of equity (S) $200,000 $222,222

Number of shares 10,000 10,000 $20.00 $22.22

Value of stock $200,000 $222,222

0 0Wealth of shareholders $200,000 $222,222

Stock Price per Share

Value of Operations

+ Short Term investments

Total Value of the Firm

− Market Value of Debt

+ Cash distributed in repurchase

Vop $222,222

Debt = $88,889S/T funds = $88,889

Stock Price $22.22

Shareholder wealth $222.222

78

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.

79

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

80

Anatomy of Strasburg’s Recap: After Repurchase

Before Debt Issue

After Debt Issue, But Before Repurchase

After Repurchase

(1) (2) (3)$200,000 $222,222 $222,222

0 88,889 0

$200,000 $311,111 $222,222

0 88,889 88,889

Value of equity (S) $200,000 $222,222 $133,333

Number of shares 10,000 10,000 $6,000.00 $20.00 $22.22 $22.22

Value of stock $200,000 $222,222 $133,333

0 0 88,889Wealth of shareholders $200,000 $222,222 $222,222

Stock Price per Share

Value of Operations

+ Short Term investments

Total Value of the Firm

− Market Value of Debt

+ Cash distributed in repurchase

81

Strasburg after RecapitalizationKey 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

82

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

83

Calculating S, the Value of Equity after the Recap

S = (1 – wd) Vop (15-13)

At wd = 40%: SPrior = S + (D – D0) (15-14)

S = (1 – 0.40) $222,222 S = $133,333 SPrior = $133,333 + (88,889 – 0)

SPrior = $222,222

84

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

85

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

86

TABLE 15.5 Strasburg’s Stock Price & EPS

87

Analyzing the Recap

Percent Value of Market Market Number of Earnings financed operations, value value Stock shares after Net income, per share,

with debt, wd Vop of debt, D of equity, S price, P repurchase, n NI EPS

(1) (2) (3) (4) (5) (6) (7) (8)0% $200,000 $0 $200,000 $20.00 $10,000 $24,000 $2.40

10% 206,186 20,619 185,567 $20.62 9,000 23,010 $2.5620% 212,540 42,508 170,032 $21.25 8,000 21,934 $2.7430% 217,984 65,395 152,589 $21.80 7,000 20,665 $2.9540% 222,222 88,889 133,333 $22.22 6,000 19,200 $3.2050% 216,216 108,108 108,108 $21.62 5,000 16,865 $3.3760% 200,000 120,000 80,000 $20.00 4,000 13,920 $3.48

Table 15-5

88

FIGURE 15.5 Effects of Capital Structure on Firm Value, Price and EPS

89

Effects of Capital Structure on Price and EPS

$0

$5

$10

$15

$20

$25

0% 10% 20% 30% 40% 50% 60%

Percent Financed with Debt

Stock Price

$0

$2

$4

$6

EPS

EPS

Price

90

Optimal Capital Structure

wd = 40% gives: Highest corporate value Lowest WACC Highest stock price per

share Does NOT maximize EPS