# Mini Case Debt for Equity

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```					                      FMDS 441 Chapter 15 & 16 Handout
a1    The riskiness of the firm's assets if it uses no debt. It can be measured by the uncertainty inherent in a firm's
future operating income. Business risk can be influenced by numerous factors including:
n Demand variability
n Sales price variability
n Input cost variability
n Ability to adjust output prices for changes in input costs
n Ability to develop new products in a timely, cost-effective manner (The faster a firm's products become
obsolete, the greater a firm's business risk).
n The extent to which costs are fixed; operating leverage
a2    The use of fixed operating costs to lever the company's return on equity. Firms with high operating leverage will
experience higher ROE during good times, and lower ROE in bad times than firms with low operating leverage.
b1.   Financial risk is the additional risk placed on the common stockholders are a result of the decision to finance with
debt and/or preferred stock. If a company uses both debt and equity, basically all the business risk is passed onto
stockholders because the debt holders are "guaranteed" fixed interest payments. However, the use of financial
leverage may increase expected ROE to existing stockholders, because debt is relatively cheap (until a certain
point is reached).
b2    Business risk will exists regardless of whether a firm uses all equity or some portion of debt and equity. It
depends on a number of factors (as discussed in part a). On the other hand, financial risk depends only on the
amount of debt financing.
c.    A firm's total risk is:
Total risk = Business risk + Financial Risk
Total risk = σROE
Financial risk for a leveraged firm = σROE - σROE(Unlevered)
Hamada combined the CAPM and the MM with-corporate-taxes model to obtain this expression for KSL:
 D
k Slevered = krf + (kM - krf ) bUnlevered + (kM - krf ) bUnlevered (1 - T) 
 S
or

kS
L
= k
su
+    (
k s - k d 1
u         )         - T 
  Debt 

  Equity 
Leverage also affects beta. A company's unlevered beta is determined solely by business risk, but as leverage
increases, so does beta. In a market framework, business risk is measured by an unlevered beta, whereas
financial risk is measured by the change in beta; and total risk is measured by the leveraged beta.
 D
bLevered = bUnlevered + bUnlevered (1 - T) 
 S
= Unlevered beta, which      +   Increased volatility of

reflects the riskiness        the returns to equity due

of the firm' s assets          to the use of debt         This represents
or                                                                                                  how much your
Business risk = bU                                                beta will increase
Financial risk = bL - bU = bU (1 - T)                           financial leverage.
 S
Total market risk = bL
d1 & d2
U                                    L
EBIT             2000             3000     \$4,000       \$2,000      \$3,000        \$4,000
Interest           \$0                \$0        \$0       \$1,200      \$1,200        \$1,200
EBT            \$2,000          \$3,000      \$4,000        \$800       \$1,800        \$2,800
Taxes           (\$800)         (\$1,200)   (\$1,600)       (\$320)      (\$720)      (\$1,120)
NI             \$1,200           \$1,800     \$2,400         \$480      \$1,080        \$1,680

Total Assets              \$20,000       \$20,000        \$20,000      \$20,000     \$20,000       \$20,000
Total Equity              \$20,000       \$20,000        \$20,000      \$10,000     \$10,000       \$10,000
U                                    L
EBIT/Total Assets           10.00%          15.00%      20.00%       10.00%       15.00%       20.00%
Return on Investment         6.00%            9.00%     12.00%        8.40%       11.40%       14.40%
Return on Equity             6.00%            9.00%     12.00%        4.80%       10.80%       16.80%
Times Interest Earned     #DIV/0!       #DIV/0!        #DIV/0!          1.67           2.50      3.33
d3        n   The firm's basic earning power (BEP) as measured by EBIT/Total Assets is the same for both companies.
Thus, the use of debt does not affect BEP.
n   Due to the tax savings effect, Firm L has a higher ROI (if ROI is calculated as [(NI+Interest)/Total Assets].
The expected ROI (given the probabilities stated in Question d) is:
E(ROIU) = 0.25(6.0%) + 0. 5(9. 0%) + 0.25(12. 0%) = 9. 0%
E(ROIL ) = 0.25(8.4%) + 0. 5(11.4%) + 0.25(14. 4%) = 11. 4%
n   The Leveraged Firm has the higher expected ROE
E(ROEU) = 0.25(6. 0%) + 0. 50(9. 0%) + 0.25(12. 0%) = 9. 0%
E(ROEL ) = 0.25(4. 8%) + 0. 50(10.8%) + 0.25(16. 8%) = 10.8%
n   Thus, the use of financial leverage has increased the expected profitability to shareholders. The higher ROE
results partly from the tax savings, partly because a fewer number of shareholders have to foot all the
n   Firm L has a wider range of ROEs and, thus a higher standard deviation.
σROE( Unlevered) = 2.12%, and CV = 0.24
σROE( Levered) = 4.24%, and CV = 0. 39
n   Thus, in a total risk sense, L is twice as risky (4.24/2.12 = 2) as Firm U. Firm L's business risk is 2.12%, but
its total risk is 4.24%, so its financial risk is 4.24% - 2.12% = 2.12%.
n   When EBIT = \$2,000, the unlevered firm has a higher ROE and leverage has a negative impact on
profitability. However, the expected level of EBIT is \$3,000 at which point leverage does benefit equity
holders.
n   The use of debt will increase a levered firm's ROE only if E(ROIU) is greater than Kd(1-tax rate).

e         Assumptions:
1. Business risk can be measured by the SD of EBIT (or ROE) and firms with same degree of risk can be grouped
2. All investors have the same expectation about a firm's future earnings
3. No transaction costs to anyone
4. All debt is risk-free, everyone can borrow and lend at the risk-free rate (Yikes!)
5. All cash flows are perpetuities--debt is perpetual
6. All earnings are paid in the form of dividends--hence, no growth, thus expected EBIT is constant over time
but can have yearly variations in reality
7. The 1958 paper (Proposition I) assumed no taxes (either corporate or personal)
f1                 FORMULAS                           Firm U                                          Firm L
EBIT=\$500,000                                     EBIT=\$500,000
EBIT              500,000/.14 = \$3,571,429                                  VU=VL
VU =
KSU                                                                      \$3,571,429
D+S=VL                                                                           SL=VL - D
= \$3,571,429 - \$1,000,000 = \$2,571,429

(         D
)
.14                   .14 + (.14 - .08)(1000000/2571429)= 16.33%
k sL = k su + k su - k d  
 S

WACC=wdkd +weke                     WACCu= .14                   WACCL = .72 x .1633 + .28 x .08 = .14 or 14%
f2a

WACC under M&M Proposition I

1.0000
0.9000
0.8000
0.7000
0.6000
0.5000
K

0.4000
0.3000
0.2000
0.1000
0.0000

19.8333
0.0000

0.0593

0.1261

0.2019

0.2887

0.3889

0.5060

0.6447

0.8116

1.0161

1.2727

1.6042

2.0488

2.6765

3.6296

5.2500

8.6154
Debt/Equity

Kequity                                                             Kdebt                                                           WACC

f2b

Value of the Firm (M&M Proposition I)

4,000,000
3,500,000
3,000,000
Value of firm

2,500,000
Value of levered firm = Value of unlevered firm
2,000,000
1,500,000
1,000,000
500,000
0
0

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

2,200,000

2,400,000

2,600,000

2,800,000

3,000,000

3,200,000

3,400,000
200,000

400,000

600,000

800,000

Amount of debt financing

g                                       FORMULAS                                                                                                     Firm U                                                                                                                    Firm L
EBIT=\$500,000                                                                                                                  EBIT=\$500,000
EBIT (1 - tax rate)                                                                 500,000(1-.4)/.14 =                                                                                                        VL=VU + (tax rate)(Debt)
VU =                                                                                                                              \$2,142,857                                                                                       =\$2,142,857 + 400,000
ksu
= \$2,542,857
D+S=VL                                                                                                                                                                                                                        SL=VL - D
= \$2,542,857 - \$1,000,000 = \$1,542,857

(                            )
.14                                                         .14 + (.14 - .08)(1-.4)(1000000/1,542,857)=
k sL = k s u + k su - k d (1 - tax rate                                                                                                                                                                                     16.33%1

WACC=wdkd(1-tc) +weke                                                                                        WACCu= .14                                                                        WACCL = .6067 x .1633 + ..3933 x .08 x (1-
.4) = .118 or 11.8%

1Even though this number is the same as the unlevered firm in part (f), it is at a higher Debt/Equity ratio. The debt/equity ratio in part (f) is 38.89%, whereas the
debt/equity ratio in part (g) is 64.81%. Therefore, the Kslevered is rising, but at a slower rate because of the tax savings on debt. PLEASE NOTE: In class we
discussed this issue at a higher Debt/Asset or Debt/Value ratio. The same principle applies whether we’re using Debt/Value or Debt/Equity as our horizontal
axis.
WACC under Proposition II

1.5000
1.3000
1.1000
0.9000
0.7000
k
0.5000
0.3000
0.1000
-0.1000   0

0.152838

0.336538

0.561497

0.843373

1.206897

1.693548

2.378641

3.414634

5.163934

20.26316
8.75
Debt/Equity ratio

Kequity                                                                                   Kdebt (after-tax)                                                                            WACC

Value of Firm (M&M Proposition II)

4,000,000
3,500,000
3,000,000
Value of Firm

Tax shield of debt
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

2,200,000

2,400,000

2,600,000

2,800,000

3,000,000

3,200,000

3,400,000
200,000

400,000

600,000

800,000
0

\$ Debt

Value (unlevered)                                                                        Value (levered)
h1
               (                                 )(
 1 - tax ratecorporate 1 - tax ratepersonal equity              ) Debt
VL = VU + 1 -                                                                     



                              (
1 - tax ratepersonal debt                      )        

     (1 - .4)(1 - .25)  
= VU + 1 -                     Debt

    
     (1 - .3)    
= VU + .3571 × Debt

An interesting point to note is that the value of the unlevered firm has dropped (compared to Proposition II--when
only corporate taxes were considered). The equity holders still have the same after-tax required rate of return.
Thus, their before-tax return will increase (to 18.67%2), increasing the denominator (K ). However, it is easier
Su
to determine the value of the unlevered firm using the following formula (where KSU is the original 14%):
(                                  )(
EBIT 1 - tax ratecorporate 1 - tax ratepersonal equity         )
VU =
k sU
\$500,000(1 - .4)(1 - .25)
=
.14
= \$1,607,143
h2            The gain to the levered firm under Miller is not quite as large as the gain under Proposition II. Under Proposition
II the value of the levered firm is the unlevered firm value + .4(Debt). Under Miller the value of the levered firm
is the unlevered firm value + .3571(Debt).

According to the Miller model, if:
tax ratepersonal debt increases .............                     Valuelevered decreases
tax ratecorporate increases ..................                    Valuelevered increases
tax ratepersonal equity increases.............                    Valuelevered increases

h3            Adding personal taxes reduces the value of the firm. Corporate tax laws favor debt over equity, and thus provide
an incentive for firms to use debt financing. Personal tax laws favor investment in equity rather than debt (as
equity income is effectively taxed at a lower rate). Thus, individuals require a higher risk-adjusted before-tax
return on debt to be induced to buy debt rather than equity, which reduces the advantage to issuing debt. Miller's
model argues that personal taxes lower (but do not eliminate) the tax advantage of debt.
i             Proposition I: capital structure is irrelevant
Proposition II: Firm should use 100% debt
Miller: Firm should use 100% debt
Miller's argument is the most realistic of the three. However, in reality firms use about 40% debt. Why?
j             As more debt is used, firms face the higher probability of future financial distress. This increases the risk to both
debt holders and stockholders (financial risk). Both the M&M propositions and the Miller model ignored these
costs. Thus, these models underestimated the true required rate of return via the WACC.

When we add financial distress/agency costs (and taxes), the models become:
VL = VU +            X     Debt - PVfinancial distress costs - PVagency costs
144 44  2             3
4
144 24443
Bankruptcy costs
use either the complex
term from the Miller model
or tax ratecorporate

We see that using debt then involves a trade-off in risk vs. return. At some point the PV of the bankruptcy costs
and agency costs will outweigh the debt tax shield.

The equation is reflected graphically on the next page.

2To determine the new unlevered stockholders required rate of return with a personal equity tax of 25%, perform the following manipulation:

.14 = X (1 - .25)
X = .186666667
If I had used this new required rate of return for unlevered stockholders, the formula would be:

(
EBIT 1 - tax ratecorporate          )
VU =
k sU
\$500,000(1 - .4)
=
.1866667
= \$1,607,143.4
Value of
Firm                                         VL
III

PV of debt                         PVbankruptcy costs
tax shield

Actual Value of Firm

Value of firm
with no leverage

Optimal amt of debt

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Description: Mini Case Debt for Equity document sample