3. Uncertainty about future operating income
(EBIT), i.e., how well can we predict operating
income?
Probability Low risk
High risk
0 E(EBIT) EBIT
Note that business risk does not include effect
of financial leverage.
4. Uncertainty about demand (sales).
Uncertainty about output prices.
Uncertainty about costs.
Product, other types of liability.
Competition.
Operating leverage.
5. Operating Leverage is defined as
(%change in EBIT)/(%change in sales).
Operating leverage is high if the
production requires higher fixed costs
and low variable costs.
High fixed cost can leverage small
increase in sales into high increase in
EBIT.
6. More operating leverage leads to more
business risk, for then a small sales
decline causes a big profit decline.
$ Rev. $ Rev.
TC } Profit
TC
FC
FC
QBE Sales QBE Sales
7. Low operating leverage
Probability
High operating leverage
EBITL EBITH
Typical situation: Can use operating
leverage to get higher E(EBIT), but risk also
increases.
8. Business risk:
◦ Uncertainty in future EBIT. It is measured by the
CV of EBIT or by the CV of ROE of a firm that
does not use debt (or PS) financing.
Financial risk:
◦ Additional risk placed on common stockholders
when financial leverage is used. It is measured
by the increase in the CV of ROE.
◦ Financial risk depends on the amount of debt (or
preferred stock) financing the firm uses.
8
9. Two firms with the same operating leverage,
business risk, and probability distribution of EBIT.
Only differ with respect to their use of debt (capital
structure).
Firm U Firm L
No debt $5,000 of 8% debt
$20,000 in assets $20,000 in assets
40% tax rate 40% tax rate
10. Economic State Probability EBIT
Bad 0.20 $500
Average 0.50 $600
Good 0.30 $700
11. E(EBIT) = Σ EBITi . Pi
n 2
EBIT i
E ( EBIT ) Pi
i 1
CV = σ / E(EBIT)
11
13. Total risk is the risk born by the
stockholders. It is measured by the volatility
of ROE.
Total Risk = Business Risk + Financial Risk
Only firms that use financial leverage (e.g.,
debt or PS) would have financial risk.
Firms that use no financial leverage would
have only business risk. These firms’ total
risk is equal to their business risk, i.e., the
volatility of their ROE would be the same as
the volatility of their EBIT.
13
16. Firm U has only business risk and
no financial risk
E (ROE) = (0.20)(6%) + (0.50)(9%) +
(0.30)(12%) = 9.3%
ROE = (6-9.3)2 (0.20) + (9-9.3)2 (0.50)
(12-9.3)2 (0.30)
= 2.1%
CVROE = 2.1% / 9.3%
= 0.226 (Total Risk )
16
17. Firm L has financial risk
in addition to business risk
E (ROE) = (0.20)(6%) + (0.50)(12%) + (0.30)(18%)
= 12.6%
ROE = (6-12.6)2 (0.20) + (12-12.6)2(0.50)
(18-12.6)2 (0.30)
= 4.2%
CVROE = 4.2% / 12.6% = 0.333 (Total Risk)
Fin. Risk = Total Risk (0.333) - Bus. Risk (0.115)
=0.218
17
18. CV(U)=0.226
CV(L)=0.333
Probability
Firm U
Firm L
6% 9% 12% 12% 18% ROE
Firm L has a higher expected ROE but it also has more
risk because in addition to business risk it also has
financial risk.
18
19. MM theory
◦ Zero taxes
◦ Corporate taxes
Trade-off theory
Signaling theory
Pecking order
19
20. MM assume: (1) no transactions costs; (2)
individuals can borrow at the same rate
as corporations.
MM prove that there would be no
difference between firms using leverage
or investors borrowing and investing
(home made leverage). The total values of
Firm U and Firm L should be equal:
VL = VU
Therefore, capital structure is irrelevant.
20
22. Corporate tax laws allow interest to be
deducted, which reduces taxes paid by
levered firms.
MM show that the total CF to Firm L’s
investors is equal to the total CF to Firm U’s
investor plus an additional amount due to
interest deductibility:
VL = VU + TD
If T=40%, then every dollar of debt adds 40
cents of extra value to firm.
22
23. Value of Firm
VL = VU + TD
TD
VU
0 Financial Leverage
Under MM with corporate taxes, the firm’s value
increases continuously as more and more debt is
used.
24. MM theory ignores bankruptcy (financial
distress) costs, which increase as more
leverage is used.
At low leverage levels, tax benefits
outweigh bankruptcy costs.
At high levels, bankruptcy costs outweigh
tax benefits.
An optimal capital structure exists that
balances these costs and benefits.
24
25. Tax Shield
Value of Firm
Maximum Firm Value
VU
VL
0 Financial Leverage
Optimal Capital Structure
Distress Costs
26. Choosing the Optimal Capital
Structure: A Numerical Example
• Currently, the firm is all-equity financed.
• Expected EBIT = $200,000.
• The firm expects zero growth.
• Currently the firm’s rs = 10%; b = 1.0;
T = 40%; rRF = 4%; RPM = 6%.
26
29. Beta changes with leverage.
bU is the beta of a firm when it has no
debt (the unlevered beta). bL is the beta
of a firm when it uses debt financing
(leverage).
Hamada’s Equation showing the
relationship between bL and bU
bL = bU [1 + (1 - T)(D/S)]
29
40. wd WACC Corp. Value
0% 10.00% $1,200,000
20% 9.56% $1,255,230
30% 9.52% $1,260,504
Minimum Maximum
40% 9.84% WACC $1,219,512 Value
50% 10.55% $1,137,441
The corporation’s value is maximized
when WACC is minimized. 40
41. wd = 30% gives:
◦ Lowest WACC
◦ Highest corporate value
But wd = 20% is close. Optimal range is
pretty flat between 20% and 30%.
41
42. Optimal Capital Structure
13.6%
rs
Cost of 12.4%
Capital 11.54%
10.90%
WACC
10% 10.55%
9.56% 9.84%
9.52%
rd(1-T)
7.5%
4.2% 4.8% 6%
x
0% 20% 30% 40% 50% Debt/Assets
Optimal 42
43. MM assumed that investors and
managers have the same information.
But, managers often have better
information. Thus, they would:
◦ Sell stock if stock is overvalued.
◦ Sell bonds if stock is undervalued.
Investors understand this, so view new
stock sales as a negative signal.
Implications for managers?
43
44. Firms use internally generated funds first,
because there are no flotation costs or
negative signals.
If more funds are needed, firms then
issue debt because it has lower flotation
costs than equity and not negative
signals.
If more funds are needed, firms then
issue equity.
44
