Chapter 2- Capital
Structure
Determination
After studying this chapter, you
should be able to:
•
Define “capital structure.”
•
Explain the net operating income (NOI) approach to capital structure
and valuation of a firm; and, calculate a firm's value using this approach.
•
Explain the traditional approach to capital structure and the valuation of
a firm.
Capital Structure
Capital Structure -- The mix (or proportion) of a firm’s
permanent long-term financing represented by debt,
preferred stock, and common stock equity.
– 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 debtversus-equity financing.
A Conceptual Look --Relevant
Rates of Return
ki = the yield on the company’s debt
ki
=
I
B
=
Annual interest on debt
Market value of debt
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.)
A Conceptual Look --Relevant
Rates of Return
ke = the expected return on the company’s equity
Earnings available to
EE
common shareholders
ke = S =
Market value of common
S
stock outstanding
Assumptions:
• Earnings are not expected to grow
• 100% dividend payout
• Results in the valuation of a perpetuity
A Conceptual Look --Relevant
Rates of Return
ko = an overall capitalization rate for the firm
ko =
OO
VV
=
Net operating income
Total market value of the firm
Assumptions:
• V = B + S = total market value of the firm
• O = I + E = net operating income = interest paid
plus earnings available to common shareholders
Capitalization Rate
Capitalization Rate, ko -- The discount rate used to
determine the present value of a stream of expected
cash flows.
ko = ki
B
B+S
+
ke
S
B+S
What happens to ki, ke, and ko
when leverage, B/S, increases?
Net Operating Income
Approach
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.
Assume:
– Net operating income equals $1,350
– Market value of debt is $1,800 at 10% interest
– Overall capitalization rate is 15%
Required Rate of Return on
Equity
Calculating the 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
Interest payments
equity
= $7,200
= $1,800 x 10%
Required return = E / S
on equity*
= ($1,350 - $180) / $7,200
= 16.25%
* B / S = $1,800 / $7,200 = .25
Required Rate of Return on
Equity
What is the rate of return on equity if B=$3,000?
Total firm value
= O / ko
= $1,350 / .15
= $9,000
Market value
=V-B
= $9,000 - $3,000 of
Interest payments
equity
= $6,000
= $3,000 x 10%
Required return = E / S
on equity*
= ($1,350 - $300) / $6,000
= 17.50%
* B / S = $3,000 / $6,000 = .50
Required Rate of Return on
Equity
Examine a variety of different debt-to-equity ratios
and the resulting required rate of return on equity.
B/S
0.00
0.25
0.50
1.00
2.00
ki
--10%
10%
10%
10%
ke
15.00%
16.25%
17.50%
20.00%
25.00%
Calculated in slides 9 and 10
ko
15%
15%
15%
15%
15%
Required Rate of Return on
Equity
Capital costs and the NOI approach in a graphical
representation.
.25
Capital Costs (%)
.20
ke = 16.25% and
17.5% respectively
ke (Required return on equity)
.15
ko (Capitalization rate)
.10
ki (Yield on debt)
.05
0
0
.25
.50
.75
1.0 1.25 1.50
Financial Leverage (B / S)
1.75
2.0
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.
Traditional Approach
Traditional Approach -- A theory of capital structure in
which there exists an optimal capital structure and where
management can increase the total value of the firm
through the judicious use of financial leverage.
Optimal Capital Structure -- The capital structure that
minimizes the firm’s cost of capital and thereby
maximizes the value of the firm.
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).
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.
Total Value Principle:
Modigliani and Miller
Market value
of debt ($35M)
Market value
of debt ($65M)
Market value
of equity ($65M)
Market value
of equity ($35M)
Total firm market
value ($100M)
Total firm market
value ($100M)

Total market value is not altered by the capital structure (the
total size of the pies are the same).
•
•
M&M assume an absence of taxes and market imperfections.
Investors can substitute personal for corporate financial
leverage.
Arbitrage and Total Market
Value of the Firm
Two firms that are alike in every respect
EXCEPT capital structure MUST have the same
market value.
Otherwise, arbitrage is possible.
Arbitrage -- Finding two assets that are
essentially the same and buying the cheaper
and selling the more expensive.