2. The value of a firm is defined to be the sum
of the value of the firm’s debt and the
firm’s equity.
V=B+S
• If the goal of the firm’s
management is to make the S B
firm as valuable as possible,
then the firm should pick the
debt-equity ratio that makes
the pie as big as possible.
Value of the Firm
16-3
There are two important questions:
1.Why should the stockholders care about
maximizing firm value? Perhaps they should
be interested in strategies that maximize
shareholder value.
2.What is the ratio of debt-to-equity that
maximizes the shareholder’s value?
As it turns out, changes in capital structure
benefit the stockholders if and only if the value
of the firm increases.
16-4
Consider an all-equity firm that is contemplating going into
debt. (Maybe some of the original shareholders want to cash
out.)
Current Proposed
Assets $20,000 $20,000
Debt $0
Equity $20,000 $8,000
Debt/Equity ratio 0.00 $12,000
Interest rate n/a 2/3
Shares outstanding400 8%
Share price $50 240
$50 16-5
2
3. Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
Net income $1,000 $2,000 $3,000
EPS $2.50 $5.00 $7.50
ROA 5% 10% 15%
ROE 5% 10% 15%
Current Shares Outstanding = 400 shares
16-6
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 1.8% 6.8% 11.8%
ROE 3.0% 11.3% 19.7%
Proposed Shares Outstanding = 240 shares
16-7
12.00
10.00 Debt
8.00 No Debt
6.00 Break-even Advantage
EPS
point to debt
4.00
2.00
0.00
1,000 2,000 3,000
(2.00) Disadvantage EBIT in dollars, no taxes
to debt 16-8
3
4. 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
16-9
Recession Expected Expansion
EPS of Unlevered Firm $2.50 $5.00 $7.50
Earnings for 40 shares $100 $200 $300
Less interest on $800 (8%) $64 $64 $64
Net Profits $36 $136 $236
ROE (Net Profits / $1,200) 3.0% 11.3% 19.7%
We are buying 40 shares of a $50 stock, using $800 in margin.
We get the same ROE as if we bought into a levered firm.
B $800 2
Our personal debt-equity ratio is:
S $1,200 3 16-10
RecessionExpected Expansion
EPS of Levered Firm $1.50 $5.67 $9.83
Earnings for 24 shares$36 $136 $236
Plus interest on $800 (8%)$64$64 $64
Net Profits $100 $200 $300
ROE (Net Profits / $2,000) 5% 10% 15%
Buying 24 shares of an otherwise identical levered
firm along with some of the firm’s debt gets us to the
ROE of the unlevered firm.
This is the fundamental insight of M&M
16-11
4
5. We can create a levered or unlevered position
by adjusting the trading in our own account.
This homemade leverage suggests that
capital structure is irrelevant in determining
the value of the firm:
VL = VU
16-12
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
16-13
The derivation is straightforward:
B S
RW ACC RB RS Then set RWACC R0
B S B S
B S B S
RB RS R0 multiply both sides by
B S B S S
B S B B S S B S
RB RS R0
S B S S B S S
B B S
RB RS R0
S S
B B B
RB RS R0 R0 RS R0 ( R0 RB )
S S S
16-14
5
6. Cost of capital: R (%)
B
RS R0 ( R0 RB )
SL
B S
R0 RW ACC RB RS
B S B S
RB RB
Debt-to-equity Ratio B
S
16-15
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 the interest tax shield
RS = R0 + (B/S) (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
S is the value of levered equity
16-16
The total cash flow to all stakeholde rs is
( EBIT RB B) (1 TC ) RB B
The present value of this stream of cash flows is VL
Clearly ( EBIT RB B) (1 TC ) RB B
EBIT (1 TC ) RB B (1 TC ) RB B
EBIT (1 TC ) RB B RB BTC RB B
The present value of the first term is VU
The present value of the second term is TCB
VL VU TC B 16-17
6
7. Start with M&M Proposition I with taxes: VL VU TC B
Since VL S B S B VU TC B
VU S B(1 TC )
The cash flows from each side of the balance sheet must equal:
SRS BRB VU R0 TC BRB
SRS BRB [S B(1 TC )]R0 TC RB B
Divide both sides by S
B B B
RS RB [1 (1 TC )]R0 TC RB
S S S
B
Which quickly reduces to RS R0 (1 TC ) ( R0 RB )
S 16-18
Cost of capital: R B
(%)
RS R0 ( R0 RB )
SL
B
RS R0 (1 TC ) ( R0 RB )
SL
R0
B SL
RW ACC RB (1 TC ) RS
B SL B SL
RB
Debt-to-equity
ratio (B/S) 16-19
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
All Equity
EBT $1,000 $2,000 $3,000
Taxes (Tc = 35%) $350 $700 $1,050
Total Cash Flow to S/H $650 $1,300 $1,950
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest ($800 @ 8% ) 640 640 640
EBT $360 $1,360 $2,360
Levered
Taxes (Tc = 35%) $126 $476 $826
Total Cash Flow $234+640 $884+$640 $1,534+$640
(to both S/H & B/H): $874 $1,524 $2,174
EBIT(1-Tc)+TCRBB $650+$224 $1,300+$224 $1,950+$224
$874 $1,524 $2,174
16-20
7
8. All-equity firm Levered firm
S G S G
B
The levered firm pays less in taxes than does the all-equity firm.
Thus, the sum of the debt plus the equity of the levered firm is
greater than the equity of the unlevered firm.
This is how cutting the pie differently can make the pie “larger.”
-the government takes a smaller slice of the pie!
16-21
In a world of no taxes, the value of the firm is
unaffected by capital structure.
This is M&M Proposition I:
V L = VU
Proposition I holds because shareholders can achieve
any pattern of payouts they desire with homemade
leverage.
In a world of no taxes, M&M Proposition II states that
leverage increases the risk and return to stockholders.
B
RS R0 ( R0 RB )
SL
16-22
In a world of taxes, but no bankruptcy costs, the value
of the firm increases with leverage.
This is M&M Proposition I:
VL = V U + T C B
Proposition I holds because shareholders can achieve
any pattern of payouts they desire with homemade
leverage.
In a world of taxes, M&M Proposition II states that
leverage increases the risk and return to stockholders.
B
RS R0 (1 TC ) ( R0 RB )
SL
16-23
8
9. Why should stockholders care about
maximizing firm value rather than just the
value of the equity?
How does financial leverage affect firm value
without taxes? With taxes?
What is homemade leverage?
16-24
9
