Capital structure and the cost of capital
Risk, Return, and Capital Budgeting (Chapter 12)
1. estimating beta



market model – regression Ri =  +  Rm + 
industry beta
time variation
2. Business risk and financial risk
Income statement
10% increase in sales revenue
Sales Revenue
FC
VC (20% of sales)
Depreciation
EBIT (Operating income)
1000
500
200
100
200
1100
500
220
100
280
OPERTING LEVERAGE
40% INCREASE IN EBIT
Interest
EBT
Tax (40%)
EAT
EPS (100 Shares)
100
100
40
60
.6
100
180
72
108
1.08
FINANCIAL LEVERAGE
80% INCREASE IN EPS
3. weighted average – pure arithmetic
Assume constant Rb, Ra, and Rb<Ra
A=B+S
Ra = (B/A) Rb + (S/A) Rs
As B/A , will Rs  or  or remain constant?
Assume Ra and Rb constant.
1
Capital structure and the cost of capital (Chapter 15,16,17)
1. Value of a firm = value of equity + value of interest bearing debt
2. Principle of additivity (Divide and conquer or all court press)
PV(A+B) = PV(A) + PV(b)
A, B: two cash flow streams
i.e. discounting combined CF by appropriate risk-adjusted discount rate (WACC)
is equivalent to
discounting each CF by its appropriate risk-adjusted discount rate and add them.
e.g.
A has payoff $100 in one year and a =1
B has payoff $150 in one year and b=2
Market risk premium =8%
Rf=6%
Using CAPM,
PV(A) = 100/1.14 = 87.72, where 14% = 6 + 1 x 8
PV(B) = 150/1.22 = 122.95
p = 1 x 87.72/210.67 + 2 x 122.95/210.67 = 1.58
PV(A+B) = 250/1.1864 = 210.72
2
Big Picture (Forest or tree) or Summary

Assumptions of the Modigliani-Miller (MM) Model
Homogeneous Expectations
Homogeneous Business Risk Classes
Perpetual Cash Flows
Perfect Capital Markets:
- Perfect competition
- Firms and investors can borrow/lend at the same rate
- Equal access to all relevant information
- No transaction costs
- No taxes

MM'S PROPOSITION I (Debt Policy doesn’t matter)
When there are no taxes and capital markets function well, it makes no difference
whether the firm borrows or individual shareholders borrow. Therefore, the market value
of a company does not depend on its capital structure.
Capital structure does not affect cash flows
- No taxes
- No bankruptcy costs
- No effect on management incentives
AN EVERYDAY ANALOGY
It should cost no more to buy pieces of a chicken (or pizza) than to buy one whole.

The MM Propositions I & II (No Taxes)
Proposition I
Firm value is not affected by leverage
VL = VU
V is independent of the debt ratio.
Proposition II
Leverage increases the risk and return to stockholders
rs = r0 + (B / SL) (r0 - rB)
rB is the interest rate (cost of debt)
rs is the return on (levered) equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity
3

The MM Propositions I & II (with Corporate Taxes)
Proposition I (with Corporate Taxes)
Firm value increases with leverage
VL = VU + Tc B
Proposition II (with Corporate Taxes)
Some of the increase in equity risk and return is offset by interest tax shield
rs = r0 + (B/ SL ) (1- Tc ) (r0 - rB )
rB is the interest rate (cost of debt)
rs is the return on equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity

Cost of Financial distress, information asymmetry
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3. Money machine
Suppose
M&M world (Um um sweet M&M ..)
Proceeds from short sales are fully obtained.
Two firms are in the exactly same business with possible EBIT with equal probability as
follows:
Recession
Normal
Boom
EBIT
400
1200
2000
Firm U has 400 shares with the price of $20 per share
Firm L has 200 shares with the price of $22 per share and debt of $4,000.
In this perfect market, P/E multiple remains constant for both firms, and equals to 10.
Interest rate for both unlimited borrowing and lending by an individual as well as firms is
10%. Can you create money machine with zero cost today, and how?
Answer
Unlevered
EPS 1
3
Short sell 1L
Borrow
Buy 2U
CF
0
Levered
4
8
R
0
-19.8
+20
0.2
N
-40
-19.8
+60
B
-80
-19.8
+100
R
N
+40
-60
+22.2
B
+80
-100
+22.2
5
+22
+18
-40
0
If levered price is $18,
Buy 1L
Sell 2U
Lend
CF
-18
+40
-22
0
+0
-20
+22.2
2.2
Q: Show EBIT-EPS relationship?
5
4. Whoops!
M&M world without any taxes, again
EBIT=100
All-equity (unlevered) firm: Ro=20%
a. Vu = 100/0.2=500
b. VL =?
Sell bond $250 to repurchase stock at Rb=10%
EBIT
I
EBT
Tax
EAT
=100
= 25
= 75
=0
=75
S
B
VL
= 75/0.2 = 375
= 250
= S + B = 625 (?)
Q: Is this the correct value of VL?
c. In M&M world, what is the value of a firm of unlevered and levered firm by theory?
(graph)
d. What is Rs and WACC of levered firm?
Correct procedure
1)
2)
3)
4)
First, find VL
500
S by VL –B
250
Rs = EAT/S
75/250 = 30%
Check if WACC of both firms are the same
OR
In M&M, Ro remains the same
WACC (Ro) = B/V rb + S/V rs
Rs = Ro + (B/S) ( ro – rb)
Ro = ½ Rb + ½ Rs = 20
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5. M&M irrelevance - Law of conservation of value
Sure, the value of a pie is NOT independent of how it is sliced, if slicer is also a nibbler.
a. Maximizing firm value = minimizing cost of capital, if operating income is fixed.
b. Comment on the following: Shareholders demand – and deserve – higher expected
rates of return than bondholders do. Therefore, debt is cheaper capital source. We can
reduce the WACC by borrowing more.
c. A perfect capital market in which M&M theory holds. – Financial manager’s job is to
find market imperfection and utilize it.
e.g. Czar of junk bond, Michael Milken
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6. Effect of taxes on levered firm (Death and Taxes, Oh no!, it is Debt and Taxes)
Two equivalent approaches
a. VL = after-corporate tax UCF / (1+WACC)
b. VL = after-corporate tax UCF / (1 + Ro) + PV of net interest tax shields
– APV approach
Ro = Cost of unlevered equity
e.g.
Tc
= 35%
EBIT = $100
Plan U – No debt, Ro =20%
Plan L - $400 permanent debt with Rb =10%
What are the VL and WACC?
Vu
VL
EBIT
100
100
Interest
0
40
EBT
100
60
Taxes
35
21
tax savings = 14
EAT
65
39
Note: Quirk in tax on interest income and interest expense
a) After-tax cost of interest to a firm(?):
rb(1-tc)
= 6.5%
b) return to bondholder(?):
rb
= 10%
TS is tax savings or tax shield, not tax refund from IRS.
 TS is tax reduction from overall tax bills, and requires positive taxable income
(earnings) for some time.
 IRS total tax bill is reduced
c) Norwegian quirk on person loan
Tax on interest income (lender) – tax deduction on all personal loans (borrower)
 IRS total tax billl remains the same
1) Vu = 65 / 0.2 =325
2) VL =?
APV approach
VL = Vu + PVTS = 325 +140 = 465
PVTS = 14 /0.10 =140 OR 0.35*400=140
Note:
a) Vu is discounted by unlevered (all-equity) discount rate
b) TS is discounted by interest rate. What is the risk of TS cash flow?
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3) B = 400, S = 65, B/S identity
4) Rs = 39/65=60%
5) WACC
PV(B+S) =PV(B) +PV(S)
After-tax UCF from Asset + TS
= after-tax CF to bondholders + after-tax CF to stockholders
After-tax CF to bondholders = 40
After-tax CF to stockholders = 39
B/S
-------------------------Vu=325
B=400
PVTS=140 S=65
-------------------------Total 465
CF
-------------------------------------UCF 65
CF to bond
40
TS
14
CF to stock 39
---------------------------------------Total 79
Why not WACC = 79/465 = 16.99%
a) Do UCF and TS have the same risk?
UCF/ro + TS/rb = rb B/ rb + rsS/rs
b) Do bondholders care about financial risk? Who bears financial risk? What risk do
bondholders care?
c) What risks do stockholders bear?
business risk + financial risks
Note: WACC is the discount rate for CF from assets (UCF)!
Ro = only business risks
Risk – only beta risk can be averaged by using weights of each part. (!)
Value additivity applies only when risk can be combined linearly or only when return and
risk are linearly related as in CAPM.
WACC =UCF / VL, where UCF =EBIT(1-tc)
WACC = 65 /465 =13.98%
Note that WACC is smaller than Ro of unlevered firm? Is that what you have expected?
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6) Verify with WACC formula
WACC = rs S/V + rb ( 1-tc) B/V, V=S+B
WACC = rs S/V + rb (1-tc) B/V
= 60*(65/465)+10*(1-0.35) *(400/465) = 13.98%
rs = 60 = 20 +(400/65)*(1-.35)*(20-10)
WACC = rb (1-tc) B/V / 1 + rs S/V
7) MM II
B/S
-------------------------Vu
B
TcB
S
--------------------------
CF
-------------------------------------Vu ro
CF to bond
B rb
TcB rb
CF to stock S rs
----------------------------------------
from this identity of B/S and CF statement
rs= ro + (B/S) (1-tc) (r0-rb)
(graph)
8) Will stockholders accept the bond issue when total equity value declines?
Suppose 100 shares for unlevered firm, and issue bond and repruchase stocks.
A
Unlevered
325
S
Stock price = 3.25
325
A
465
Levered
B
400
S
65
?
Answer:
A stock price of levered firm = 4.65
Number of shares repurchased = 400/4.65 = 86.02 shares
Px =65 and (100-x) P =400
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7. Miller’s personal taxes
a. tax advantages of debt – tax deductibility of debt interest at the corporate level
b. tax disadvantage of debt
– personal tax levied on interest income > personal tax on income derived from equity
for each dollar paid by a firm, the payoff net of all taxes to
a. shareholders:
b. debt holders:
(1-tc) (1-ts)
(1-tb)
Relative tax advantage of paying a dollar to the debtholders instead of paying to the
shareholders
RA 
Net after - all - taxes income from equity
(1 - tc)(1 - ts)

Net after - all - taxes income from debt
(1 - tb)
If RA>1, net-of-all taxes, return to shareholders > return to bondholders
PV of net tax advantage of one dollar of perpetual debt
 T  1  RA 
(1 - tc)(1 - ts)
(1 - tb)
Classic M&M with corporate taxes
Corporate income is taxed at tc
No taxes on personal income
Debt adds value by reducing corporate tax
payments
Capitalized tax advantage of one $1 of
debt: tc
VL = Vu +Btc
Miller equilibrium
with corporate and personal taxes
Corporate income is taxed at tc
Personal tax rate on equity income: ts
Personal tax rate on debt income : tb
Trade-off:
Net after-all taxes equity income: (1-tc)(1-ts)
Net after-all taxes debt income: (1-tb)
(1 - tc)(1 - ts)
(1 - tb)
VL = Vu +BT
T  1
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Why should shareholders care about personal taxes that are paid by debt holders?
 Relative taxation of debt and equity income affects the relative price (and required
return) of bonds and stock.
e.g.
Assume riskless bond and riskless stock.
after-tax risk-free return: 6%
tb=40%
ts=20%
For investors,
Before-tax return on bond =10%
- gross-up from before-tax return of 6% = 6/(1-.4)
Before-tax return on stock =7.5% (= 6/(1-.2)
A manager of a firm (tc=34%) faces
a. After-corporate tax cost of debt = 6.6% =10 x (1-.34)
b. Cost of equity =7.5%
and switches to debt
net advantage of redirection of $1 from equity holders to bondholders
(1-tb) - (1-tc)(1-ts)
e.g. (1-.4)-(1-.34)(1-.2) = .6-.528=.072 or 7.2%
PV of net advantage of perpetual debt

[(1 - tb) - (1 - tc)(1 - ts)] interest
(1 - tb) rb
where, T  1

[(1 - tb) - (1 - tc)(1 - ts)] rbB
(1 - tb) rb
 TB
(1 - tc)(1 - ts)
(1 - tb)
Note: discount rate is after-personal tax rerurn, (1-tb) rb
In equilibrium, (1-tc)(1-ts) = (1-tb) or T=0
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8. Unlevered cost of capital and equity
(graph of modified MM II)
e.g.
assume current leverage is 40% debt and 60% equity.
equity beta
= 1.5
market risk premium =8.5%
risk-free rate = 8%
Rb=12%
Tc =40%
1) cost of equity and WACC with current leverage?
Rs =20.75% for a firm with 40% debt and 60% equity. (CAPM)
WACC with 40% debt = (2/5)*12*(1-.4) + (3/5)*20.75 = 15.33%
(graph)
2) all equity (unlevered) cost of capital?
ro 
rs  rd (1 - tc) B/S
1  (1 - tc) B/S
= (20.75+12*(1-.4)*2/3)/(1+(1-.4)*2/3)
=18.25% (unlevered cost of equity)
3) cost of equity with 25% of B and 75% of S?
apply the formula again with
rs= 18.25 + (1/3) *0.60* (18.25-12) = 19.5%
4) WACC with 25% of B and 75% of S?
¼ *12 *0.6 + ¾ *19.5 = 16.425%
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9.  and Leverage
asset = weighted average beta of bond and stock
(graph of CAPM)
S
 B

  s      b (1 - tc) 
V
 V

A  
a) Why b is adjusted by (1-tc)?
graph of CAPM
b) In practice, it is simplified by assuming that the beta of bond is zero.
asset = (S/V) s
e.g.
assume current leverage is 40% debt and 60% equity.
equity beta
= 1.5
risk-free rate = 8%
Tc =40%
a) assume beta of debt = 0
then asset = 1.5*0.6 =0.9
ro using SML = 8+0.9*8.5= 15.65%, approximately
b) if debt = 0.47
asset = 0.47*(1-.4)*(2/5)+1.5*(3/5)=1.0128
Ro = 8+1.0128*8.5=16.61%
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10. Conflicts of interest and Agency problem (Digression)
It is important to understand the agency problem in the context of "conflicts of interest".
Bigger issue in financial economics is the conflicts of interest among participants.
Agency problem deals with the conflicts of interest between principal and agent.
1. between manager and stockholder
Fractional ownership of owner cum manager
Shirking
Firms run by the founder or by professional managers
Stock options
Perquisites
M&A
Control of the firm
Corporate governance issues e.g. board of directors, proxy fight
Dual class common stock
Free cash flow
Good to have financial slack (Myers & Majluf)
Bad when manager have opportunity to waste or take negative NPV project
Debt reduces FCF
Dividends
M&A
Certification
Is bank loan or credit line beneficial to stockholders?
Underwriting of new stock issues
2. between stockholder and bondholder
In near bankruptcy, a firm has an incentive to take risky project, to not take positive NPV
project, and to milk the firm.
Bond covenants
3. Describe conflicts of interest in a firm where the fraction of ownership by
government is significant.
4. What are participants in the resource allocation process in Japan Inc. and what
conflicts of interest might occur?
15
11. Costs of financial distress
a. direct costs of financial distress
- legal and administrative costs
b. Costs of Financial Distress - Costs arising from bankruptcy or distorted business
decisions before bankruptcy.
1) impaired ability to conduct business (e.g. lost sales, no supplies, etc.)
2) risk shifting
e.g.
 A firm holds cash of 10 and bond of 20 due next period
B/S in market value
cash
=10 bond = 9
equity = 1
Why does the equity have any value ?

New project
- initial investment = 10
- CF $120 with 10% probability
- CF $0 with 90 % probability

NPV
= -2
Will stockholdes take this project?
do nothing
B = 10
S=0
If stockholders takes the project
Win
Lose
20
0
100
0
16
3) refusing to contribute equity capital
bond due
= 20
cash
= 10
cost of project = 15
safe project with NPV = 5
Will stockholdes take this project?
do nothing
B=10
S =0
issue stock ($5) and take project
15
0
4) cash in and run, leaving empty shell



nature of business
- low debt for intangible assets
- growth opportunity (Internet firms) or stable revenue stream
benefit of low debt
- unused debt capacity and financial slack
- control of managerial agency costs
opportunity cost of low debt (or benefit of high debt)
- tax deduction
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12. Asymmetric information
To the outside world Smith & Co. and Jones, Inc. are identical. Each runs a successful
business with good growth opportunities. The two businesses are risky, however, and
investors have learned from experience that current expectations are frequently bettered
or disappointed. Current stock prices each firm is $100 per share, but true values can be
higher at $120 or lower at $80.
Both firms need to raise new money to fund capital investment. They can do this
either by issuing bonds or by issuing new stocks.
One manages (lets’ call her A) reason as follows:
Sell stock for $100 per share? Ridiculous! It’s worth at least $120. A stock issue
would hand a free gift to new investors. I just wish those stupid, skeptical shareholders
would appreciate the true value of this company. Our new factories will make us the
world’s lowest-cost producer. We’ve painted a rosy picture for the press and security
analyst’, but it just doesn’t seem to be working. Oh, well, the decision is obvious: we’ll
issue debt, not underpriced equity. A debt issue will save underwriting fees too.
The other manager (let’s call him B) is in a different mood:
Beefalo burgers were a hit for a while, but it looks like the fad is a fad. Our
company gotta find some good new product or it’s all downhill from here. Fortunately
the stock price has held up pretty well and we had some good short-run news for the
press and security analysts. Now’s the time to issue stock. We have major investments
under way, and why add increased debt service to my other worries?
Q. Why can’t the optimistic financial manager simply educate investors?
Suppose there are two press releases.
Jones, Inc, announced plans to issue $120 million of five-year senior notes.
Smith & Co announced plans to issue 1.2 million new shares to raise $120 million.
Q. As a rational investor, what would you learn from this press release?
1) Who is likely to be the manager of Smith & Co and Jones, Inc., i.e. A or B?
2) What is likely to happen to the stock price as a result of the press release?
A1. Jones is optimistic.
A2. Smith cannot sell stock at $100 per share.
Q. Under what circumstances, does it make sense to issue equity?
Answer.
- Too much leverage already
- High-tech firms
- Pecking order follows.
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13. Financial choices (I am dead tired now.)
Trade-off Theory - Theory that capital structure is based on a trade-off between tax
savings and distress costs and benefits of debt.
Pecking Order Theory - Theory stating that firms prefer to issue debt rather than
equity if internal finance is insufficient.
Consider the following story:
The announcement of a stock issue drives down the stock price because investors
believe managers are more likely to issue when shares are overpriced.
Therefore firms prefer internal finance since funds can be raised without sending
adverse signals.
If external finance is required, firms issue debt first and equity as a last resort.
The most profitable firms borrow less not because they have lower target debt ratios
but because they don't need external finance.
Some Implications:
 Internal equity may be better than external equity.
- Financial slack is valuable.
- If external capital is required, debt is better. (There is less room for difference
in opinions about how much debt is worth).
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14. Value of a firm with financial leverage (Hue! At last.)
A) The Adjusted-Present-Value (APV) Approach
APV = NPV + NPVF
NPV: NPV of unlevered firm
- NPV = PVUCF - Initial investment for entire project
- PVUCF: PV of Unlevered Cash Flows (UCF)
- UCF=CF from operations - Capital Spending - Added NWC
- Discount rate: r0
NPVF: NPV of financing side effects
- PV of Tax Subsidy to Debt
- Costs of Issuing New Securities
- The Costs of Financial Distress
- Subsidies to Debt Financing
B) WACC approach
- UCF discounted by WACC
WACC has to be adjusted to incorporate side effects
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15. Estimating discount rate
1) Calculate the firm’s cost of capital and not the cost of equity
2) Be consistent in your treatment of inflation - Use industry data to estimate the cost of
capital for the firm, not just the firm’s own data. The cost of capital cannot be
calculated, but only be estimated.
16. Quiz:
A manager Q of so-so company is campaigning for a pet project knows WACC formula.
And think. Aha! My firm has good credit rating. It could borrow, say, 90 percent of the
projects’ cost if it likes. That means B/V = .9 and S/V =.1. My firm’s borrowing rate is 8
percent, and the required return on equity is 15 percent. Therefore the WACC is
.08 *(1-.35)(.9) +.15(.1)=.062 or 6.2 percent. When I discount at that rate, my project
looks great.
What are logical errors?
1. debt ratio of 90%
2. project’s overall contribution to the firm’s borrowing capacity
3. both rs and rb 
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17. Financial Distress
Financial
Distress
Asset
restructuring
Financial
Private workout
restructuring
Legal bankruptcy
Reorganization (Chapter11)
* prepackaged bankruptcy
Liquidation (Chapter 7)
Responses to Financial Distress
Asset Restructuring
Merging with another firm
Selling major assets
Reducing capital spending and R&D spending
Financial Restructuring
Issuing new securities
Negotiating with banks and other creditors
Exchanging debt for equity
Filing for bankruptcy
Bankruptcy versus Private Workout
Advantages
- Available new credit - "debtor in possession" or "DIP" debt
- Discontinued accrual of interest on pre-bankruptcy unsecured debt
- An automatic stay provision
- Tax advantages
- Requires only approval by 1/2 of creditors owning 2/3 of outstanding debt
Disadvantages
-
A long and expensive process
Judges are required to approve major business decisions
Distraction to management
’Hold out' by stockholders
Note: Absolute priority rules (APR) is sometimes violated
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