17-1
Chapter 17
Capital Structure
Determination
17-2
Capital Structure
Determination
? A Conceptual Look
? The Total-Value Principle
? Presence of Market Imperfections and
Incentive Issues
? The Effect of Taxes
? Taxes and Market Imperfections
Combined
? Financial Signaling
17-3
Capital Structure
? Concerned with the effect of capital market
decisions on security prices.
? Assume,(1) investment and asset
management decisions are held constant and
(2) consider only debt-versus-equity financing.
Capital Structure -- The mix (or proportion) of
a firm’s permanent long-term financing
represented by debt,preferred stock,and
common stock equity.
17-4
A Conceptual Look --
Relevant Rates of Return
ki = the yield on the company’s debt
Annual interest on debt
Market value of debt
I
B ==ki
Assumptions:
? Interest paid each and every year
? Bond life is infinite
? Results in the valuation of a perpetual bond
? No taxes (Note,allows us to focus on just
capital structure issues.)
17-5
E
S
A Conceptual Look --
Relevant Rates of Return
==
ke = the expected return on the company’s equity
Earnings available to
common shareholders
Market value of common
stock outstanding
ke
Assumptions:
? Earnings are not expected to grow
? 100% dividend payout
? Results in the valuation of a perpetuity
? Appropriate in this case for illustrating the
theory of the firm
17-6
O
V
A Conceptual Look --
Relevant Rates of Return
==
ko = an overall capitalization rate for the firm
Net operating income
Total market value of the firmko
Assumptions:
? V = B + S = total market value of the firm
? O = I + E = net operating income = interest
paid plus earnings available to common
shareholders
17-7
Capitalization Rate
Capitalization rate,ko,-- the discount rate
used to determine the present value of a
stream of expected cash flows.
ko keki BB + S SB + S= +
What happens to ki,ke,and ko
when leverage,B/S,increases?
17-8
Net Operating
Income Approach
Assume:
? Net operating income equals $1,350
? Market value of debt is $1,800 at 10% interest
? Overall capitalization rate is 15%
Net Operating Income Approach -- A theory of
capital structure in which the weighted average
cost of capital and the total value of the firm
remain constant as financial leverage is changed.
17-9
Required Rate of
Return on Equity
Total firm value = O / ko = $1,350 /,15
= $9,000
Market value = V - B = $9,000 - $1,800
of equity = $7,200
Required return = E / S
on equity* = ($1,350 - $180) / $7,200
= 16.25%
Calculating the required rate of return on equity
* B / S = $1,800 / $7,200 =,25
Interest payments
= $1,800 * 10%
17-10
Total firm value = O / ko = $1,350 /,15
= $9,000
Market value = V - B = $9,000 - $3,000
of equity = $6,000
Required return = E / S
on equity* = ($1,350 - $300) / $6,000
= 17.50%
Required Rate of
Return on Equity
What is the rate of return on equity if B=$3,000?
* B / S = $3,000 / $6,000 =,50
Interest payments
= $3,000 * 10%
17-11
B / S ki ke ko
0.00 --- 15.00% 15%
0.25 10% 16.25% 15%
0.50 10% 17.50% 15%
1.00 10% 20.00% 15%
2.00 10% 25.00% 15%
Required Rate of
Return on Equity
Examine a variety of different debt-to-equity
ratios and the resulting required rate of
return on equity.
Calculated in slides 9 and 10
17-12
Required Rate of
Return on Equity
Capital costs and the NOI approach in a
graphical representation.
0,25,50,75 1.0 1.25 1.50 1.75 2.0
Financial Leverage (B / S)
.25
.20
.15
.10
.05
0
Ca
pi
tal
C
os
ts
(%
)
ke = 16.25% and
17.5% respectively
ki (Yield on debt)
ko (Capitalization rate)
ke (Required return on equity)
17-13
Summary of NOI Approach
?Critical assumption is ko remains constant.
?An increase in cheaper debt funds is
exactly offset by an increase in the
required rate of return on equity.
?As long as ki is constant,ke is a linear
function of the debt-to-equity ratio.
?Thus,there is no one optimal capital
structure.
17-14
Traditional Approach
Optimal Capital Structure -- The capital structure
that minimizes the firm’s cost of capital and
thereby maximizes the value of the firm,
Traditional Approach -- A theory of capital
structure in which their exists an optimal capital
structure and where management can increase
the total value of the firm through the judicious
use of financial leverage.
17-15
Optimal Capital Structure,
Traditional Approach
Traditional Approach
Financial Leverage (B / S)
.25
.20
.15
.10
.05
0
Ca
pi
tal
C
os
ts
(%
) ki
ko
ke
Optimal Capital Structure
17-16
Summary of the
Traditional Approach
? The cost of capital is dependent on the capital
structure of the firm.
?Initially,low-cost debt is not rising and replaces
more expensive equity financing and ko declines.
?Then,increasing financial leverage and the
associated increase in ke and ki more than offsets
the benefits of lower cost debt financing.
? Thus,there is one optimal capital structure
where ko is at its lowest point.
? This is also the point where the firm’s total
value will be the largest (discounting at ko).
17-17
Total Value Principle,
Modigliani and Miller (M&M)
? Advocate that the relationship between
financial leverage and the cost of capital is
explained by the NOI approach.
? Provide behavioral justification for a constant
ko over the entire range of financial leverage
possibilities.
? Total risk for all security holders of the firm is
not altered by the capital structure.
? Therefore,the total value of the firm is not
altered by the firm’s financing mix.
17-18
Market value
of debt ($65M)
Market value
of equity ($35M)
Total firm market
value ($100M)
Total Value Principle,
Modigliani and Miller
? M&M assume an absence of taxes and market
imperfections.
? Investors can substitute personal for corporate
financial leverage.
Market value
of debt ($35M)
Market value
of equity ($65M)
Total firm market
value ($100M)
? Total market value is not altered by the capital
structure (the total size of the pies are the same).
17-19
Arbitrage and Total
Market Value of the Firm
Arbitrage -- Finding two assets that are
essentially the same and buying the
cheaper and selling the more expensive.
Two firms that are alike in every respect
EXCEPT capital structure,MUST have
the same market value.
Otherwise,arbitrage is possible.
17-20
Arbitrage Example
Consider two firms that are identical
in every respect EXCEPT,
? Company NL -- no financial leverage
? Company L -- $30,000 of 12% debt
? Market value of debt for Company L equals its
par value
? Required return on equity
-- Company L is 15%
-- Company L is 16%
? NOI for each firm is $10,000
17-21
Earnings available to = E = O - I
common shareholders = $10,000 - $0
= $10,000
Market value = E / ke
of equity = $10,000 /
.15 =
$66,667
Total market value = $66,667 + $0
= $66,667
Overall capitalization rate = 15%
Debt-to-equity ratio = 0
Arbitrage Example,
Company NL
Valuation of Company NL
17-22
Arbitrage Example,
Company L
Earnings available to = E = O - I
common shareholders = $10,000 - $3,600
= $6,400
Market value = E / ke
of equity = $6,400 /,16
= $40,000
Total market value = $40,000 + $30,000
= $70,000
Overall capitalization rate = 14.3%
Debt-to-equity ratio =,75
Valuation of Company L
17-23
Completing an
Arbitrage Transaction
Assume you own 1% of the stock of
Company L (equity value = $400).
You should:
1,Sell the stock in Company L for $400.
2,Borrow $300 at 12% interest (equals 1% of debt
for Company L).
3,Buy 1% of the stock in Company NL for
$666.67,This leaves you with $33.33 for other
investments ($400 + $300 - $666.67).
17-24
Completing an
Arbitrage Transaction
Original return on investment in Company L
$400 x 16% = $64
Return on investment after the transaction
?$666.67 x 16% = $100 return on Company NL
?$300 x 12% = $36 interest paid
?$64 net return ($100 - $36) AND $33.33 left over.
This reduces the required net investment to
$366.67 to earn $64.
17-25
Summary of the
Arbitrage Transaction
? The equity share price in Company NL rises
based on increased share demand.
? The equity share price in Company L falls
based on selling pressures.
? Arbitrage continues until total firm values are
identical for companies NL and L.
? Therefore,all capital structures are equally as
acceptable.
? The investor uses personal rather than
corporate financial leverage.
17-26
Market Imperfections
and Incentive Issues
?Agency costs (Slide 28)
?Debt and the incentive to
manage efficiently
?Institutional restrictions
?Transaction costs
?Bankruptcy costs (Slide 27)
17-27
Required Rate of Return
on Equity with Bankruptcy
Financial Leverage (B / S)
RfReq
ui
re
d R
ate
o
f R
etu
rn
on
Eq
ui
ty
(k e
) ke with no leverage
ke without bankruptcy costs
ke with bankruptcy costs
Premium
for financial
risk
Premium
for business
risk
Risk-free
rate
17-28
Agency Costs
? Monitoring includes bonding of agents,auditing
financial statements,and explicitly restricting
management decisions or actions.
? Costs are borne by shareholders (Jensen & Meckling).
? Monitoring costs,like bankruptcy costs,tend to rise at
an increasing rate with financial leverage.
Agency Costs -- Costs associated with
monitoring management to ensure that it behaves
in ways consistent with the firm’s contractual
agreements with creditors and shareholders.
17-29
Example of the Effects
of Corporate Taxes
Consider two identical firms EXCEPT,
? Company ND -- no debt,16% required
return
? Company D -- $5,000 of 12% debt
? Corporate tax rate is 40% for each company
? NOI for each firm is $10,000
The judicious use of financial leverage
(i.e.,debt) provides a favorable impact
on a company’s total valuation.
17-30
Earnings available to = E = O - I
common shareholders = $2,000 - $0
= $2,000
Taxe Rate (T) = 40%
Income available to = EACS (1 - T)
common shareholders = $2,000 (1 -,4)
= $1,200
Total income available to = EAT + I
all security holders = $1,200 + 0
= $1,200
Corporate Tax Example,
Company ND
Valuation of Company ND (Note,has no debt)
17-31
Earnings available to = E = O - I
common shareholders = $2,000 - $600
= $1,400
Taxe Rate (T) = 40%
Income available to = EACS (1 - T)
common shareholders = $1,400 (1 -,4)
= $840
Total income available to = EAT + I
all security holders = $840 +
$600 =
$1,440*
Corporate Tax Example,
Company D
Valuation of Company D (Note,has some debt)
* $240 annual tax-shield benefit of debt (i.e.,$1,440 - $1,200)
17-32
Tax-Shield Benefits
Tax Shield -- A tax-deductible expense,The
expense protects (shields) an equivalent dollar
amount of revenue from being taxed by reducing
taxable income.
Present value of
tax-shield benefits
of debt*
= (r) (B) (tc)
r
= (B) (tc)
* Permanent debt,so treated as a perpetuity
** Alternatively,$240 annual tax shield /,12 = $2,000
= ($5,000) (.4) = $2,000*
17-33
Value of the Levered Firm
Value of unlevered firm = $1,200 /,16
(Company ND) = $7,500*
Value of levered firm = $7,500 + $2,000
(Company D) = $9,500
Value of Value of Present value of
levered = firm if + tax-shield benefits
firm unlevered of debt
* Assuming zero growth and 100% dividend payout
17-34
Summary of
Corporate Tax Effects
? The greater the financial leverage,the lower the
cost of capital of the firm.
? The adjusted M&M proposition suggest an optimal
strategy is to take on the maximum amount of
financial leverage.
? This implies a capital structure of almost 100%
debt! Yet,this is not consistent with actual
behavior.
? The greater the amount of debt,the greater the
tax-shield benefits and the greater the value of the
firm.
17-35
Other Tax Issues
?Corporate plus personal taxes
Personal taxes reduce the corporate tax
advantage associated with debt.
Only a small portion of the explanation why
corporate debt usage is not near 100%.
?Uncertainty of tax-shield benefits
Uncertainty increases the possibility of
bankruptcy and liquidation,which reduces
the value of the tax shield.
17-36
Bankruptcy Costs,
Agency Costs,and Taxes
As financial leverage increases,tax-shield
benefits increase as do bankruptcy and
agency costs.
Value of levered firm
= Value of firm if unlevered
+ Present value of tax-shield benefits
of debt
- Present value of bankruptcy and
agency costs
17-37
Bankruptcy Costs,
Agency Costs,and Taxes
Optimal Financial Leverage
Taxes,bankruptcy,and
agency costs combined
Net tax effect
Financial Leverage (B/S)
Co
st
of
Ca
pi
ta
l (%
)
Minimum Cost
of Capital Point
17-38
Financial Signaling
? Theory is based on the idea that insiders
(managers) know something about the firm that
outsiders (security holders) do not.
? Changing the capital structure to include more
debt conveys that the firm’s stock price is
undervalued.
? This is a valid signal because of the possibility
of bankruptcy.
? A manager may use capital structure changes
to convey information about the profitability
and risk of the firm.