Home > Capital structure and the cost of capital
Capital structure and the
cost of capital
Risk, Return, and Capital Budgeting
(Chapter 12)
Income statement
10% increase in sales revenue
Sales Revenue 1000 1100
FC 500 500 OPERTING LEVERAGE
VC (20% of sales) 200 220
Depreciation 100 100
EBIT (Operating income) 200 280
40% INCREASE IN EBIT
Interest 100 100 FINANCIAL LEVERAGE
EBT 100 180
Tax (40%) 40 72
EAT 60 108
EPS (100 Shares) . 6 1.08
80% INCREASE IN EPS
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.
Capital structure and the cost of capital (Chapter 15,16,17)
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
Big Picture (Forest or tree)
or Summary
Homogeneous Expectations
Homogeneous Business Risk Classes
Perpetual Cash Flows
Perfect Capital Markets:
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
AN EVERYDAY ANALOGY
It should cost
no more to buy pieces of a chicken (or pizza) than to buy one whole.
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
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
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 Levered
EPS 1 3 5 0 4 8
R N B
Short sell 1L +22 0 -40 -80
Borrow +18 -19.8 -19.8 -19.8
Buy 2U -40 +20 +60 +100
CF 0 0.2
If levered price is $18,
R N B
Buy 1L -18 +0 +40 +80
Sell 2U +40 -20 -60 -100
Lend -22 +22.2 +22.2 +22.2
CF 0 2.2
Q: Show EBIT-EPS relationship?
M&M world without any taxes, again
EBIT=100
All-equity (unlevered) firm:
Ro=20%
Sell bond $250 to repurchase
stock at Rb=10%
EBIT =100
I = 25
EBT = 75
Tax = 0
EAT =75
S = 75/0.2 = 375
B = 250
VL = S + B = 625 (?)
Q: Is this the correct value
of VL?
(graph)
Correct procedure
OR
In
M&M, Ro remains the same
WACC (Ro) = B/V rb + S/V rs
Rs = Ro + (B/S) ( ro – rb)
Ro = � Rb + � Rs = 20
Sure, the value of a pie is
NOT independent of how it is sliced, if slicer is also a nibbler.
e.g. Czar of junk bond, Michael Milken
Two equivalent approaches
–
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
EBT 100 60
Taxes 35 21 tax savings = 14
EAT 65 39
Note: Quirk in tax on interest income and interest expense
TS is tax savings or tax shield, not tax refund from IRS.
Tax on interest income (lender) – tax deduction on all personal loans (borrower)
IRS total tax billl remains the same
APV approach
VL = Vu + PVTS = 325 +140 = 465
PVTS = 14 /0.10 =140 OR 0.35*400=140
Note:
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 CF
-------------------------- --------------------------------------
Vu=325 B=400 UCF 65 CF to bond 40
PVTS=140 S=65 TS 14 CF to stock 39
-------------------------- ----------------------------------------
Total 465 Total 79
Why not WACC = 79/465 = 16.99%
UCF/ro +
TS/rb = rb B/ rb + rsS/rs
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?
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
B/S CF
-------------------------- --------------------------------------
Vu B Vu ro CF to bond B rb
TcB S 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)
Suppose 100 shares for
unlevered firm, and issue bond and repruchase stocks.
Unlevered Levered
A 325 S 325 A 465 B 400
S 65
Stock price = 3.25 ?
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
– 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
Relative tax advantage of paying
a dollar to the debtholders instead of paying to the shareholders
If RA>1, net-of-all taxes,
return to shareholders > return to bondholders
PV of net tax advantage of
one dollar of perpetual debt
Classic M&M with corporate taxes | Miller equilibrium
with corporate and personal taxes |
Corporate
income is taxed at tc
No taxes on personal income |
Corporate income
is taxed at tc
Personal tax rate on equity income: ts Personal tax rate on debt income : tb |
Debt adds value by reducing corporate tax payments | Trade-off:
Net after-all taxes equity income: (1-tc)(1-ts) Net after-all taxes debt income: (1-tb) |
Capitalized tax advantage of one $1 of debt: tc | |
VL = Vu +Btc | VL = Vu +BT |
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
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
where,
Note: discount rate
is after-personal tax rerurn, (1-tb) rb
In equilibrium, (1-tc)(1-ts) = (1-tb) or T=0
(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%
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)
=
(20.75+12*(1-.4)*2/3)/(1+(1-.4)*2/3)
=18.25%
(unlevered cost of equity)
apply the
formula again with
rs= 18.25
+ (1/3) *0.60* (18.25-12) = 19.5%
� *12 *0.6
+ � *19.5 = 16.425%
asset
= weighted average beta of bond and stock
(graph of CAPM)
graph of CAPM
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%
then asset
= 1.5*0.6 =0.9
ro using
SML = 8+0.9*8.5= 15.65%, approximately
asset
= 0.47*(1-.4)*(2/5)+1.5*(3/5)=1.0128
Ro = 8+1.0128*8.5=16.61%
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.
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
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
e.g.
cash =10 bond = 9
equity = 1
Why does
the equity have any value ?
Will stockholdes take this
project?
If stockholders takes the project
do nothing Win Lose
B = 10 20 0
S = 0 100 0
bond due = 20
cash = 10
cost of project = 15
safe project with NPV = 5
Will stockholdes take this
project?
do nothing issue stock ($5) and take project
B=10 15
S =0 0
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?
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.
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.
APV = NPV + NPVF
NPV: NPV of unlevered firm
NPVF: NPV of financing side effects
WACC has to be adjusted
to incorporate side effects
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?
Financial Asset
Distress restructuring
Financial Private workout
restructuring
Legal bankruptcy Reorganization (Chapter11)
* prepackaged bankruptcy
Liquidation
(Chapter 7)
Note: Absolute priority rules
(APR) is sometimes violated
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