MBAC 6060
Chapter 16
Capital Structure
(How Much Debt?)
1
Chapter Overview
• We looked a the return required by a company’s
investors
• It is the same as the company’s cost
• It is the required return on the company’s investments
WACC = WERE + WDRD(1 - T)
• WE and WD are the Percentages of Equity and Debt
• RE and RD are the Costs of Equity and Debt
2
Chapter Overview
• We also looked (in the context of the CAPM) at the
effects of debt on Equity Risk
βEquity = βAssets (1 + D/E)
• For a given risk of the firms assets (βAssets)
– A function of cyclicality and operating leverage
• How does the choice of debt level (D/E) change the risk
of equity (βEquity)
So the Question is:
• How much Debt should a firm have?
• What should be the firm’s Capital Structure?
– Capital Structure is defined by WE and WD
– Sometimes D/E
3
Aside: Compare WD = D/V to D/E
• If WD = D/V = 20% then calculate D/E:
– E/V = 1 - D/V = 80%
– D/E = (D/V)/(E/V) = 0.20/0.80 = 0.25
• If WD = D/V = 50% then calculate D/E:
– E/V = 1 - D/V = 50%
– D/E = (D/V)/(E/V) = 0.50/0.50 = 1.00
• If WD = D/V = 60% then calculate D/E:
– E/V = 1 - D/V = 40%
– D/E = (D/V)/(E/V) = 0.60/0.40 = 1.50
4
Chapter Overview
• WACC is the discount rate for all the firm’s
projects
– The lower the rate, the higher the value of the
projects
– A firm is the sum of its projects
– So the higher the value of the firm
• So how does WACC (and therefore firm value)
change as WE and WD (or D/E) change?
5
Chapter Overview
Definition: Adding Financial Leverage
– Issue bonds to finance an expansion
– Issue bonds and use the proceeds to buy back stock
• Examine the effects of adding leverage:
1. The Value of the company
• Value Unlevered (VU) versus the Value Levered (VL)
2. The Required Return on the Assets (RA)
3. The Required Return on the Equity (RE)
• First assume no taxes
• Second look at the effects of taxes
6
Notation:
In this chapter, the text book uses both:
D = Debt or B = Bond
and
E = Equity or S = Stock
and
A = Assets or 0 = An All Stock firm
7
But First: Corporate Dividend Policy
• Covered in Chapter 19
Main Results:
• The price of a stock decreases by the amount of
a cash dividend
• But, if instead of paying a dividend
• Cash is used to repurchase shares
• Then the share price increases by the amount
that would have been paid
8
Example:
•
•
•
•
Company has Earnings (NI) = $500,000
Number of Shares = 100,000
EPS = $5.00
Assume PE Ratio = 20x
– PE accounts for current earnings, risk of earnings and NPVGO
• Share Price given EPS = $5.00 x 20 = $100
• Company also has $100,000 in Excess Cash
• Excess Cash per Share = $100,000/100,000 = $1
• Total Share Value = $100 + $1 = $101
• Two Choices to pay Excess Cash to Shareholders:
1. Pay $1.00 per share dividend
2. Repurchase $100,000/$101 = 990 Shares
9
Pay $1.00 per share dividend
• Share Value before Dividend = $101
–
–
–
–
–
EPS = $5.00
PE Ratio = 20x
Share Price given Earnings = $5 x 20 = $100
Excess Cash per Share = $100,000/100,000 = $1
Share price = $101
• After Dividend
– Still have same current and expected earnings ($500,000)
– Same number of Shares so EPS = $500,000/100,000 = $5
– Same PE Ratio = 20
• Paying excess cash does not change NPVGO
– Share Value = $5 x 20 = $100
– Plus $1 in cash
All Shareholders have = $100 share + $1 cash
10
Repurchase $100,000/$101 = 990 Shares
• Share Value before Repurchase = $101
–
–
–
–
–
EPS = $5.00
PE Ratio = 20x
Share Price given Earnings = $5 x 20 = $100
Excess Cash per Share = $100,000/100,000 = $1
Share price = $101
• After Repurchase
–
–
–
–
Still have same current and expected earnings ($500,000)
Fewer Shares: 100,000 – 990 = 99,010 shares
So higher EPS = $500,000/99,010 = $5.05
Same PE Ratio = 20
• Paying out Excess Cash does not change NPVGO
– Share Value = $5.05 x 20 = $101
990 Shareholders have $101 in cash
99,010 Shareholders have $101 share
11
Price Drop from Cash Dividend – MSFT
On November 15, 2004, MSFT paid a $3.08 dividend
12
Dividends vs. Repurchases
(Figure 19.5 Page 582)
13
Now to Capital Structure
• What does adding Leverage do to:
1. The Required Return on the Equity (RE)
2. The Required Return on the Assets (RA)
3. The Value of the Company
– Value Unlevered (VU) versus the Value
Levered (VL)
14
Modigliani & Miller
• These theories, formulas and propositions were developed by
Franco Modigliani and Merton Miller
MM I (without Taxes)
•
•
“Changing how the pie is sliced does not make it any bigger.”
A firm’s total value is not affected by its capital structure:
VL = VU
MM II (without Taxes)
•
Changing capital structure does increase equity risk and equity return but
does not change the WACC
RE = RA + (RA – RD)D/E
MM I (with Taxes):
•
With taxes, adding debt does increase firm value. Firm value does depend
on its capital structure:
VL = VU + TC x D
MM II (with Taxes):
•
With taxes Leverage increases equity risk and equity return and does
decrease WACC.
RE = RA + (RA – RD)(1 – TC)D/E
15
First Results (no Taxes):
ValueLevered = ValueUnlevered
VL = VU
• The value of the firm does not increase with the addition
of leverage
• Changing the way the pie is sliced does not increase the
slice of the pie
• People can borrow just as easily as the company
Result:
• A company can’t create value just by replicating what
people can do on their own
• This result is know as MM I
16
MM I without Taxes: Levering Does Not Create Value
• A company can’t create value just by replicating what
people can do on their own
Show this by comparing a persons returns from
1. Owning a levered firm
2. Increasing ownership in an Unlevered firm by borrowing
– Called “homemade leverage”
This is shown in Example 16.1
17
Example 16.1
Unlevered Firm
Assets
Debt
Equity
Borrow Rate
Price/Share
Shares
$8,000
$8,000
Levered Firm
$8,000
$0
$0
$0
$8,000 $8,000 $8,000
$8,000 $8,000
$8,000
$4,000 $4,000 $4,000
$4,000 $4,000 $4,000
10%
10%
10%
$20
$20
$20
$20
$20
$20
400
400
400
200
200
200
100
$1,000
300
$3,000
500
$5,000
100
300
$1,000 $3,000
500
$5,000
Costs
$600
$1,800
$3,000
$600 $1,800
$3,000
EBIT
Int Exp
$400
$1,200
$2,000
$400 $1,200
$2,000
$0
$0
$0
$400 $400
$400
EBT
Tax Exp
NI
$400
$0
$400
$1,200
$0
$1,200
$2,000
$0
$2,000
$0
$0
$0
$800
$0
$800
$1,600
$0
$1,600
$1
$3
$5
$0
$4
$8
Units Sold
Sales
EPS
Shares Owned
Cost
Borrow
Out of Pocket
Borrow Rate
Shares x EPS
Int Exp
Net Payoff
Return
Own the Unlevered Firm
200
200
200
$4,000 $4,000 $4,000
$2,000 $2,000 $2,000
$2,000 $2,000 $2,000
Own the Levered Firm
100 100
100
$2,000 $2,000 $2,000
$0
$0
$0
$2,000 $2,000 $2,000
10%
$200
$200
$0
10%
$600
$200
$400
10%
$1,000
$200
$800
10%
$0
$0
$0
10%
$400
$0
$400
10%
$800
$0
$800
0%
20%
40%
0%
20%
40%
• The Unlevered Firm has $0 debt
• A share price of $20
• And EPS of $1, $3 or $5
• The Levered Firm has $4,000 debt
• A share price of $20
• And EPS of $0, $4 or $8
• Putting up $2,000 to buy 100 share
of the Levered Firm produces
returns of
• $0/$2,000 = 0%
• $400/$2,000 = 20%
• $800/$2,000 = 40%
• Putting up $2,000 and Borrowing
$2,000 to buy 200 share of the
Unlevered Firm produces returns of
0%, 20% or 40%
• Since the returns available to an
owner of the Levered Firm are
easily replicated by an individual
borrowing and buying shares of the
Unlevered Firm, firms create no
value by levering
Second Result (still no Taxes):
RE = RA + (RA – RD)D/E
• RA is the required return on the firm’s assets
– RA is function of cyclicality and operating leverage
• RD is the required return on the firm’s debt
– RD is a function of the risk of the assets and the amount of debt
– We cover this later
• D/E is the measure of leverage
• RE is the required return on the firm’s equity
Result:
• RE increases as leverage increases
• This result is know as MM II
19
Derivation:
WACC = WERE + WDRD
RA = WERE + WDRD
RA = (E/V) RE + (D/V) RD
RA = E/(D + E)RE + D/(D + E) RD
• Do a bunch of Algebra.
• See footnote 8,page 497
RE = RA + (RA – RD)D/E
20
Example:
An Unlevered Firm earns $100 per year forever
• Unlevered means D/E = 0
• No Interest Expense and No Taxes
 EBIT = EBT = NI = $100
• The firm has 100 shares of stock
• EPS = $100/100 = $1
• Price per share = $10
• RE = $1/$10 = 10%
• RE = RA + (RA – RD)D/E
 10% = RA + 0  RA = 10%
• Firm Value = 100 x $10 = $100/0.10 = $1,000
If the firm issues $200 of 5% debt and repurchases $200 of stock
• What does this do to the firm’s cost of equity (RE)?
• What does this do the firm’s WACC?
• What does this do to the firm’s value (VL versus VU)?
21
What does this do to the firm’s cost of equity (RE)?
If the firm issues $200 of 5% debt and repurchases $200 of stock:
• EBIT = $100
– Assets, AT and PM did not change
• Interest Expense = $200 x 5% = $10
• EBT = NI = EBIT – Interest Expense = $100 - $10 = $90
– $90 per year forever
• New Shares = 100 - $200/$10 = 100 – 20 = 80
• New EPS = NI/Shares = $90/80 = $1.125
• New RE = $1.125/$10 = 11.25%
OR
• RE = RA + (RA – RD)D/E
• D/E = $200/$800 = 0.25
• RA = 10%
– The firm’s assets did not change
• RE = 10% + (10% – 5%)0.25 = 11.25%
Leverage increases the Equity’s risk so RE Increases!
22
What does this do to the firm’s WACC?
Before the Leverage:
• RE = 10.00%
• WE = 1.00
• No Taxes (yet)
• WACC = WERE + WDRD(1 - T)
• WACC = 1.00(10.00%) + 0 = 10.00%
If the firm issues $200 of 5% debt and repurchases $200 of stock:
• RE = 11.25%
• WE = $800/$1,000 = 0.80
• RD = 5.00%
• WD = $200/$1,000 = 0.20
• Still No Taxes (yet)
• WACC = WERE + WDRD(1 - T)
• WACC = 0.80(11.25%) + 0.20(5.00%) = 10.00%
WACC does not change!
23
What does this do to the firm’s Value?
• Firm Value is the NPV of all the firm’s projects
• The WACC does not change so the discount rate does not change
• If the discount rate does not change, then the NPVs do not change
Firm Value Does Not Change!
Recap:
MM I without Taxes: VL = VU
MM II without Taxes: RE = RA + (RA – RD)D/E
The Point:
• Financing decisions do not create value
• Operating decisions create value!
24
Now Included Taxes:
• First consider the Value of a Levered Firm
• Since Interest payments are tax deductable
Example:
• A firm’s EBIT = $100
• Tax Rate = 35%
• With no Debt and therefore no Interest Expense:
• EBIT = EBT = $100
• Tax Expense = $100 x 0.35 = $35
• NI = $100 - $35 =$65
OR
• NI = EBIT(1 – T) = $100(1 – 0.35) = $65
• So $65 per year to give to investors
25
Now Assume $200 of 5% Debt:
• RD = 5%
• EBIT = $100
• Interest Expense = 0.05 x $200 = $10
• EBT = $100 - $10 = $90
• Tax Expense = $90 x 0.35 = $31.50
• NI = EBT – Tax Exp = $90 - $31.50 = $58.50
OR
• NI = (EBIT – RDD) - (EBIT – RDD)T
• NI = (EBIT – RDD)(1 –T)
• NI = ($100 – 0.05 x $200)(1 – 0.35) = $58.50
• NI = ($90)(0.65) = 58.50
• $58.50 to Equity holders and $10 to Debt holders
• $58.50 + $10 = $68.50
• Total CFs No Debt = NI = $65
• Total CFs debt = NI + Interest Expense = $58.50 + $10 = $68.50
With Taxes, Debt Increases Money Available to Stakeholders
26
Debt Creates a Tax Shield
• D = $200 RD = 5% T = 35%
• CF to Equity holders = NI
– NI = (EBIT – RDD)(1 –T)
– NI = EBIT(1 – T) – RDD(1 –T)
– NI = EBIT(1 – T) – RDD + TRDD
• CF to Debt holders = Interest Expense
– Interest Expense = RDD
• Total CFs to Equity and Debt holders
– Total CFs = EBIT(1 – T) – RDD + TRDD + RDD
– Total CFs = EBIT(1 – T) + TRDD
•
•
•
•
•
•
Unlevered: Total CFs = EBIT(1 – T)
Levered: Total CFs = EBIT(1 – T) + TRDD
TRDD is the increase in CFs from adding debt.
It is the annual tax savings or tax shield
So what is it worth?
TRDD = (0.35)(0.05)($200) = $3.50
• Recall: $68.50 - $65 = $3.50
27
Debt Creates a Tax Shield
• Unlevered:
Total CFs = EBIT(1 – T) = $65
• Levered:
Total CFs = EBIT(1 – T) + TRDD = $65 + $3.50 = $68.50
• TRDD is the annual increase in Total CFs from adding debt
Assume T, Debt and RD are constant forever
• Then the Tax Shield is a perpetuity
• At what rate should we discount the perpetuity?
• Assume the tax savings has the same risk as the debt
• So discount the annual Tax Shield at RD
• So if Tax Shield is a perpetuity discounted by RD,
• Then the PV of the Tax Shield is:
• PV of Tax Shield = TRDD/RD = TD
MM I with Taxes: VL = VU + TC x D
With Taxes, Adding Debt Increases Firm Value
28
What Happens to Equity Risk and Return?
Equity Risk:
• Without Taxes: βEquity = βAssets (1 + D/E)
• With Taxes: βEquity = βAssets [1 + (1 - T)D/E]
(See Chapter 13, footnote 6, page 405)
Equity Return:
• Without Taxes: RE = RA + (RA – RD)D/E
• With Taxes: RE = RA + (RA – RD)(1 – T)D/E
29
New Example:
An Unlevered Firm earns $100 per year forever
Calculate the RE and WACC:
• Unlevered means D/E = 0
• No Interest Expense
• So EBIT = EBT = $100
• Taxes = 35%
• NI = EBIT(1 – T) = $100(1 – 0.35) = $65
• The firm has 100 shares of stock
• EPS = $65/100 = $0.65
• Price per share = $6.50
• RE = $0.65/$6.50 = 10%
• WACC = RA = WERE + WDRD(1 - T) = 1.00(10.00%) + 0 = 10.00%
• Value = $6.50 x 100 = $650
The firm issues $200 of 5% debt and repurchases $200 of stock
• What does this do to the firm’s value (VL versus VU)?
• What does this do to the firm’s cost of equity (RE)?
• What does this do the firm’s WACC?
30
What does this do to the firm’s Value?
•
•
•
•
•
•
Unlevered Value (VU) is the PV of the after-tax EBIT
T = 35%
D = $200
RD = 5%
VU = EBIT(1 – T)/WACC = $100(1 – 0.35)/0.10 = $650
VL = VU + PV of Tax Shield
Recall:
• Annual Tax Shield = Tax Rate x Interest Expense = RD x D x T
• PV of Annual Tax Shield = (RD x D x T)/RD = TD
• VL = VU + TD
• VL = $650 + $200 x 0.35 = $650 + $70 = $720
With Taxes, Adding Debt Increases Firm Value
31
What does this do to the firm’s cost of equity (RE)?
Calculate the New RE: for the Levered Firm:
• RE = RA + (RA – RD)(1 – T)D/E
• RA = 10.00%
• RD = 5.00%
• T = 35%
• Value = $720
• D = $200
• E = $720 - $200 = $520
• D/E = 200/520 = 0.3846
RE = RA + (RA – RD)(1 – T)D/E
= 10% + (10% - 5%)(1- 0.35)0.3846 = 11.25%
• Unlevered RE = 10.00%
• Levered RE = 11.25%
Leverage increases the Equity’s risk so RE Increases
32
What does this do to the firm’s WACC?
Before the Leverage:
• RE = 10.00%
• WE = 1.00
• Taxes = 35%
• WACC = WERE + WDRD(1 - T)
• WACC = 1.00(10.00%) + 0 = 10.00%
If the firm issues $200 of 5% debt and repurchases $200 of stock:
• RE = 11.25%
• WE = $520/$720 = 0.7222
• RD = 5.00%
• WD = $200/$720 = 0.2778
• T = 35%
• WACC = WERE + WDRD(1 - T)
• WACC = 0.7222(11.25%) + 0.2778(5.00%)(1 – 0.35) = 9.03%
Leverage Lowers the Cost of Capital!
33
One More Look at Value – Lowering the WACC
Unlevered WACC was 10%
VU = EBIT(1 – T)/WACC
VU = $100(1 – 0.35)/0.10 = 65/0.10 = $650
Levered WACC is 9.03%
• VL = EBIT(1 – T)/WACC
• VL = $100(1 – 0.35)/0.0903 = 65/0.0903 = $720
With Taxes, Adding Debt Lowers WACC
And this Increases Firm Value
34
One More Look at the Firm’s Cost of Equity (RE)
Consider the CAPM:
• RE = Rf + βEquity[E(RM) – Rf]
For the Market:
• E(RM) – Rf = 8.33%
• Rf = 5.00%
RE for the Unlevered Firm:
• βEquity = 0.60
• RE = Rf + βEquity[E(RM) – Rf] = 5.00% + 0.60[8.33%] = 10.00%
Also:
• βEquity = βAssets [1 + (1 - T)D/E]
• 0.60 = βAssets [1 + (1 - T)0/E]
• βAssets = 0.60
35
One More Look at the Firm’s Cost of Equity (RE)
For the Levered Firm
• D/E = 200/520 = 0.3846
• βAssets = 0.60
• D/E = 200/520 = 0.3846
• βEquity = βAssets [1 + (1 - T)D/E] = 0.60[1 + (0.65)(0.3846)]
• βEquity = 0.60[1 + 0.25] = 0.60(1.25) = 0.75
• RE = Rf + βEquity[E(RM) – Rf] = 5.00% + 0.75[8.33%] = 11.25%
• This is the same RE as we got from MM II:
RE = RA + (RA – RD)(1 – T)D/E
= 10% + (10% - 5%)(1- 0.35)0.3846 = 11.25%
36
Recap: With Taxes:
Leverage Increases Equity Risk (βEquity)
• βEquity = βAssets [1 + (1 - T)D/E]
• βEquity from 0.60 to 0.75
Leverage Increases Equity Return (RE)
• RE = RA + (RA – RD)(1 – T)D/E
• RE from 10.00% to 11.25%
Leverage Decreases WACC
• WACC from 10.00% to 9.03%
Leverage Increases Value
• VL = VU + TD
• Value from $650 to $720
37
So if Increasing Leverage Increases Value
Why not 100% Debt?
• Let’s try 90% debt instead:
Same Company with NI = $65 and VU = $650
• Now issue $854 of 5% Debt (instead of $200)
• VL = VU + TD = $650 + (.35)$854 = $650 + $299 = $949
• E = $949 – $854 = $95
• WE = $95/$949 = 0.10 and WD = 854/949 = 0.90
• D/E = $854/$95 = 9.00
Calculate New RE:
• RE = RA + (RA – RD)(1 – T)D/E = 10% + (10% - 5%)(.65)9 = 39.22%
Calculate New WACC:
• WACC = 0.10(39.22%) + 0.90(5%)(1 – 0.35) = 6.85%
• WACC from 10.00% to 6.85%
• Old Value: $65/0.10 = $650
• New Value: $65/0.0685 = $948
Why does this not work?
38
How Firms Establish Capital Structure
• Most corporations have low Debt-Asset ratios.
• Changes in financial leverage affect firm value.
– Firm value increases with leverage
• This is consistent with M&M with taxes.
– Another interpretation is that firms signal good news
when they lever up
• Differences in capital structure across industries.
• Evidence that firms behave as if they had a
target Debt-Equity ratio
39
Factors in Target D/E Ratio
• Taxes
– Since interest is tax deductible, highly profitable firms
should use more debt (i.e., greater tax benefit).
• Types of Assets
– The costs of financial distress depend on the types of
assets the firm has.
– Airplanes vs. Fixed Assets
• Uncertainty of Operating Income
– Cyclicality and Operating Leverage
– Even without debt, firms with uncertain operating
income have a high probability of experiencing
financial distress
40
Some Debt to Value Ratios
41
Some Others
42