Tutorial 1
chapter 14:1, 3, 13, 10, 19 chapter in problem 1
chapter 15: 3,5 a. E/cashflow:/2. / 141.494 + 182. 105)=161.799,50
16 1.799,55 /CF
NPV 1,20 =
-100.360 34.464,92 =
NPV =
1 r
+
-
cost
16 1.799,50 /F
b. equity value PV/cashflow:1,20
=
134.132,92
=
equity 1
-
+
c. debt payments 180.360
=
equity receives S 141.494 -100.360. 1,05 36. 107,60 =
%=5010,40
5 & 182. 105-100.368. 1,05 76.71d, 60
=
Initial value by MM is 134.032,94 -100.368 34.464,94 =
141.494
102.105
+
2
Chapter 14, problem 3 161.799,5
a. Elvalue in one
year:0.0.1501 +0.2.1201 44
=
/C
= 4e mizion
=
Equity=value of CF 1
= Fr
b. D 5
=
19,040
=
Therefore, =40-19.840:20,952m debt value =
1 s
c. without
leverage.
= -1 10
=
erve an i
/CF 0.8 150-201
=
+ 0.20.120-201 24
=
erv -5952
=
-1 0.1433
=
14,33%
=
co west F
a. without
average, =
-1 50%
=
without v=
equity
with
leverage,
-22 -1 =
-
100%
cowest CF-FVrdebt,
with r=
equity
chapter 14, problem 13
at debt of 6% 15%
of
cost industry
=
a
D/V DIE
re ru
=
+
rru-vo D 15
=
~= 0,092
=
+10092-06 -
=0.097647
=>
9,76%
Chapter 14, problem 10
any leverage raises the equity of
cost capital. In fact, risk free
leverage raises it the most d oes not share
because it any
of
. the risk
lets differentiate between the rwacc and equity cost
of capital
leverage increases the risk equity,
of also raising the equity cost of
capital
ve vn
=
(ru
+
-
vp
any leverage raises the equity cost of capital
lets check the WACC
D
reacc. D re + E D +
Vo
debt is less risky than equity, so it has a lowest of capital. So an increase in
average decreases WACC,
if
we assume equity cost of capital is constant. However, it
is not ...
Drerck, the benefit of
debt's of
lower cost capital is asset
by the higher equity cost of capital.
, chapter 14, problem 19
Indell increases its net
debt by 40.96 million /35,90 million in new debt +13 minion in cash
paid out.
Therefore, the value of its equity decreases to 170 -
40,96=121,04
=ul+)-*+ -Bu
E
Be E debt, and EV is enterprise
Where D is net value. The only changes in the
equation is the value ofequity.
↑herefore,
pe De, 1.000 2,525
=
-
-
= 2.53
*
Chapter 15, problem 3
a. income 2500. /1-0,401 1506
net =
=
income:EBIT
het -
interest exp. taxes
Thus equity holders 600 per year with
receive dividends es no risk.
63 het
income
E =
0.04
=
37.500 equity/perpetuity):visk free rate
interest
b. income 12500-loo.1-0.4): 540
net =
t. :13500 debtrperpetuity/ exP
free rate
o f1600 per
debt holders receive interest year
D =40,00
=
c. With 13.500 40.000 53. 500
= =
total value equity
=
debt
leverage
+ +
average 37.500
without =
difference:53.500-37.500 16.000
16.000 gerence
d. 5000 0,4 40%
= =
corporate taxate
=
Rate =
rate
the difference is
see that equal to the present
value of the interest
tax shield
chapter 15, problem 5
I 2 3 4 -
I
year 3
debt 130 75 50 25 I 0
interest 10 7,5 5 2,5 O
tax shield 2,5 1,08 1,25 3,63 I
DV 5, 19 It
requires that
can use the value of interest tax shield eauction the debt is
you present only if
permanent.
the firm never the debt.
repay the principal on
here debt is decreasing, so we need to consider every year separately.
interest:butstanding debt intrate
interest tax shield:interest, tax rate
purits E, Tri
=
2. 2 1 14 +
+
+
, Tutorial 2
chapter 15:16,20,24,25chapter 15, problem 16
chapter 16: 10,20,24,26 a free cash flow happening every, year:
ErCF
~perpetuity):coc y
= $33.33
=
min
b. apply the trade offtheory to find value of the levered firm:
v v4
=
5c. D
+
v 33.34 =
21%.. 19.85
+
v 37.33
=
min
chapter 15, problem 20
a. debt holders' payoff:
debt holders:interest. (1-5i)=11.11 -0.3311 $6.69 =
min
b. here we are asked to find how much net
income will be reduced after corporate taxes.
dividend cut interest. 11-5c=10./1-0.351:$ 6.5
=
min
c. equity holders' payoff:
income dividend cut.11
q. holders after tax -Jel 6.5.11-0.3) $4.55
min
=
=
per gear
=
e
d. government's payoff:
more tax on interest interest. 5:
-
10.0.331
=
$3.31
=
min
less corp. tax:10.5c 10.0.35 =$3.5 =
min
tax 6.5. Je 6.5.0.3=$ 1.95
min
=
Less dir
=
change 3.11-3.5 =
-1.95 =
-
2.14 min
e. effective tax advantage of the debt:
↑1-cr./1-5e /1 -
0.35 11
-
0.31
** 1
=
-
1 -
5i =1
-
11 -
0.3311 32%
=
chapter 15, problem 24
Thus, there is a tax
advantage of debt as long as the marginal
corporate tax rate, Jc, is above 27.0%
. chapter is, problem as
first, find the taxable income:
income
net 4. I
5.696
=
taxable income (1-5c) (1-0.21
=
min
in the limit, all taxable income can be gone for interest expense. Therefore, imp, can increase its interest expense
by $5.696 min, which corresponds to debt of:
:$71.2
income
add.debt=
taxable min
chapter 14:1, 3, 13, 10, 19 chapter in problem 1
chapter 15: 3,5 a. E/cashflow:/2. / 141.494 + 182. 105)=161.799,50
16 1.799,55 /CF
NPV 1,20 =
-100.360 34.464,92 =
NPV =
1 r
+
-
cost
16 1.799,50 /F
b. equity value PV/cashflow:1,20
=
134.132,92
=
equity 1
-
+
c. debt payments 180.360
=
equity receives S 141.494 -100.360. 1,05 36. 107,60 =
%=5010,40
5 & 182. 105-100.368. 1,05 76.71d, 60
=
Initial value by MM is 134.032,94 -100.368 34.464,94 =
141.494
102.105
+
2
Chapter 14, problem 3 161.799,5
a. Elvalue in one
year:0.0.1501 +0.2.1201 44
=
/C
= 4e mizion
=
Equity=value of CF 1
= Fr
b. D 5
=
19,040
=
Therefore, =40-19.840:20,952m debt value =
1 s
c. without
leverage.
= -1 10
=
erve an i
/CF 0.8 150-201
=
+ 0.20.120-201 24
=
erv -5952
=
-1 0.1433
=
14,33%
=
co west F
a. without
average, =
-1 50%
=
without v=
equity
with
leverage,
-22 -1 =
-
100%
cowest CF-FVrdebt,
with r=
equity
chapter 14, problem 13
at debt of 6% 15%
of
cost industry
=
a
D/V DIE
re ru
=
+
rru-vo D 15
=
~= 0,092
=
+10092-06 -
=0.097647
=>
9,76%
Chapter 14, problem 10
any leverage raises the equity of
cost capital. In fact, risk free
leverage raises it the most d oes not share
because it any
of
. the risk
lets differentiate between the rwacc and equity cost
of capital
leverage increases the risk equity,
of also raising the equity cost of
capital
ve vn
=
(ru
+
-
vp
any leverage raises the equity cost of capital
lets check the WACC
D
reacc. D re + E D +
Vo
debt is less risky than equity, so it has a lowest of capital. So an increase in
average decreases WACC,
if
we assume equity cost of capital is constant. However, it
is not ...
Drerck, the benefit of
debt's of
lower cost capital is asset
by the higher equity cost of capital.
, chapter 14, problem 19
Indell increases its net
debt by 40.96 million /35,90 million in new debt +13 minion in cash
paid out.
Therefore, the value of its equity decreases to 170 -
40,96=121,04
=ul+)-*+ -Bu
E
Be E debt, and EV is enterprise
Where D is net value. The only changes in the
equation is the value ofequity.
↑herefore,
pe De, 1.000 2,525
=
-
-
= 2.53
*
Chapter 15, problem 3
a. income 2500. /1-0,401 1506
net =
=
income:EBIT
het -
interest exp. taxes
Thus equity holders 600 per year with
receive dividends es no risk.
63 het
income
E =
0.04
=
37.500 equity/perpetuity):visk free rate
interest
b. income 12500-loo.1-0.4): 540
net =
t. :13500 debtrperpetuity/ exP
free rate
o f1600 per
debt holders receive interest year
D =40,00
=
c. With 13.500 40.000 53. 500
= =
total value equity
=
debt
leverage
+ +
average 37.500
without =
difference:53.500-37.500 16.000
16.000 gerence
d. 5000 0,4 40%
= =
corporate taxate
=
Rate =
rate
the difference is
see that equal to the present
value of the interest
tax shield
chapter 15, problem 5
I 2 3 4 -
I
year 3
debt 130 75 50 25 I 0
interest 10 7,5 5 2,5 O
tax shield 2,5 1,08 1,25 3,63 I
DV 5, 19 It
requires that
can use the value of interest tax shield eauction the debt is
you present only if
permanent.
the firm never the debt.
repay the principal on
here debt is decreasing, so we need to consider every year separately.
interest:butstanding debt intrate
interest tax shield:interest, tax rate
purits E, Tri
=
2. 2 1 14 +
+
+
, Tutorial 2
chapter 15:16,20,24,25chapter 15, problem 16
chapter 16: 10,20,24,26 a free cash flow happening every, year:
ErCF
~perpetuity):coc y
= $33.33
=
min
b. apply the trade offtheory to find value of the levered firm:
v v4
=
5c. D
+
v 33.34 =
21%.. 19.85
+
v 37.33
=
min
chapter 15, problem 20
a. debt holders' payoff:
debt holders:interest. (1-5i)=11.11 -0.3311 $6.69 =
min
b. here we are asked to find how much net
income will be reduced after corporate taxes.
dividend cut interest. 11-5c=10./1-0.351:$ 6.5
=
min
c. equity holders' payoff:
income dividend cut.11
q. holders after tax -Jel 6.5.11-0.3) $4.55
min
=
=
per gear
=
e
d. government's payoff:
more tax on interest interest. 5:
-
10.0.331
=
$3.31
=
min
less corp. tax:10.5c 10.0.35 =$3.5 =
min
tax 6.5. Je 6.5.0.3=$ 1.95
min
=
Less dir
=
change 3.11-3.5 =
-1.95 =
-
2.14 min
e. effective tax advantage of the debt:
↑1-cr./1-5e /1 -
0.35 11
-
0.31
** 1
=
-
1 -
5i =1
-
11 -
0.3311 32%
=
chapter 15, problem 24
Thus, there is a tax
advantage of debt as long as the marginal
corporate tax rate, Jc, is above 27.0%
. chapter is, problem as
first, find the taxable income:
income
net 4. I
5.696
=
taxable income (1-5c) (1-0.21
=
min
in the limit, all taxable income can be gone for interest expense. Therefore, imp, can increase its interest expense
by $5.696 min, which corresponds to debt of:
:$71.2
income
add.debt=
taxable min
