FIN_3000 problem 9
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Sure, I'd be happy to help. Please go ahead and provide the example, and I'll focus on understanding the methodology used. Then, you can provide the next set of instructions with different values for the question.
Marpor Industries has no debt and expects to generate free cash flows of $ 20 million each year. Marpor believes that if it permanently increases its level of debt to $ 42 million, the risk of financial distress may cause it to lose some customers and receive less favorable terms from its suppliers. As a result, Marpor's expected free cash flows with debt will be only $ 19 million per year. Suppose Marpor's tax rate is 21 %, the risk-free rate is 7 %, the expected return of the market is 13.5 %, and the
beta of Marpor's free cash flows is 1.25 (with or without leverage).
a. Estimate Marpor's value without leverage.
b. Estimate Marpor's value with the new leverage.
Question content area bottom
Part 1
a. Estimate Marpor's value without leverage.
To calculate the expected return, use the following formula:
Upper E left bracket Upper R right bracket equals r Subscript f Baseline plus beta times left parenthesis r Subscript m Baseline minus r Subscript f right parenthesis
Therefore,
Upper E left bracket Upper R right bracket equals 0.07 plus 1.25 times left parenthesis 0.135 minus 0.07 right parenthesis equals 0.151 equals 15.1 %
The expected return is 15.1%.
Part 2
To compute the Marpor's value without leverage, use the following formula:
Upper V Superscript Upper U equals StartFraction FCF Over Upper E left bracket Upper R right bracket EndFraction
Therefore,
Upper V Superscript Upper U equals StartFraction $ 20 million Over 0.151 EndFraction equals $ 132 million
Marpor's value without leverage is $132 million. Part 3
b. Estimate Marpor's value with the new leverage.
To compute Marpor's value with leverage, we compute the value of its free cash flows less expected distress costs, and then add the value of the interest tax shield using the following formula:
Upper V Superscript Upper L equals StartFraction FCF Over Upper E left bracket Upper R right bracket EndFraction plus tau Subscript c Baseline times Upper D
Therefore,
Upper V Superscript Upper L equals StartFraction $ 19 million Over 0.151 EndFraction plus 0.21 times $ 42 million equals $ 134.65 million
Marpor's value with the new leverage is $134.65 million. Part 4
Marpor's value without leverage is $132 million. However, Marpor's value with leverage is $134.65 million because of the effects of the tax shield.
The methodology used in the example is as follows:
Calculate the expected return: This is done using the Capital Asset Pricing Model (CAPM) formula, which is
�[�]=��+�×(��−��)
E
[
R
]=
r
f
+
β
×(
r
m
−
r
f
)
, where
��
r
f
is the risk-free rate,
��
r
m
is the expected return of the market, and
�
β
is the beta of the company's cash flows. In this case, the risk-free rate (
��
r
f
) is 7%, the expected return of the market (
��
r
m
) is 13.5%, and the beta (
�
β
) of Marpor's cash flows is 1.25. So, the expected return (
[
]
� �
E
[
R
]
) is calculated to be 15.1%.
Estimate Marpor's value without leverage: Marpor's value without leverage (
��
V
U
) is calculated using the formula
=
[
]
�� ���� �
V
U
=
E
[
R
]
FCF
, where
���
FCF
is the free cash flows generated by Marpor. In this case, the free cash flows (
���
FCF
) are $20 million, and the expected return (
[
]
� �
E
[
R
]
) calculated earlier is 15.1%. So, the value without leverage (
��
V
U
) is $132 million.
Estimate Marpor's value with the new leverage: Marpor's value with the new leverage (
��
V
L
) is calculated by adding the present value of tax shield to the unleveraged value. The formula used is
=
[
]+
×
�� ���� �
�� �
V
L
=
E
[
R
]
FCF
+
τ
c
×
D
, where
��
τ
c
is the corporate tax rate and
�
D
is the amount of debt. In this case, the free cash flows (
���
FCF
) are $19 million, the expected return (
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[
]
� �
E
[
R
]
) calculated earlier is 15.1%, the corporate tax rate (
��
τ
c
) is 21%, and the amount of debt (
�
D
) is $42 million. So, the value with leverage (
��
V
L
) is $134.65 million.
Comparison of values: Marpor's value without leverage is $132 million, whereas Marpor's value with leverage is $134.65 million due to the effects of the tax shield.
This methodology involves calculating the expected return, estimating the value without leverage, considering the impact of leverage on cash flows, and incorporating the tax shield to determine the value with leverage.
Marpor Industries has no debt and expects to generate free cash flows of $ 17 million each year. Marpor believes that if it permanently increases its level of debt to $ 30 million, the risk of financial distress may cause it to lose some customers and receive less favorable terms from its suppliers. As a result, Marpor's expected free cash flows with debt will be only $ 16 million per year. Suppose Marpor's tax rate is 21 %, the risk-free rate is 4 %, the expected return of the market is 14 %, and the beta of Marpor's free cash flows is 1.2 (with or without leverage).
a. Estimate Marpor's value without leverage.
b. Estimate Marpor's value with the new leverage.
Question content area bottom
Part 1
a. Estimate Marpor's value without leverage.
Marpor's value without leverage is $
enter your response here million. (Round to the nearest integer.)
Part 1: Estimate Marpor's value without leverage.
To calculate Marpor's value without leverage, we need to use the formula for the expected return (
[
]
� �
E
[
R
]
) based on the given data:
�[�]=��+�×(��−��)
E
[
R
]=
r
f
+
β
×(
r
m
−
r
f
)
Where:
●
��
●
r
●
f
●
●
is the risk-free rate (4% or 0.04).
●
��
●
r
●
m
●
●
is the expected return of the market (14% or 0.14).
●
�
●
β
is the beta of Marpor's free cash flows (1.2).
Using these values, we can calculate the expected return (
[
]
� �
E
[
R
]
):
�[�]=0.04+1.2×(0.14−0.04)
E
[
R
]=0.04+1.2×(0.14−0.04)
[
]=0.04+1.2×0.1
� �
E
[
R
]=0.04+1.2×0.1
[
]=0.04+0.12
� �
E
[
R
]=0.04+0.12
[
]=0.16
� �
E
[
R
]=0.16
Now, to find Marpor's value without leverage (
��
V
U
), we use the formula:
=
[
]
�� ���� �
V
U
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=
E
[
R
]
FCF
Given that Marpor's free cash flows (
���
FCF
) are $17 million, we can substitute the values:
=170.16
��
V
U
=
0.16
17
=106.25
��
V
U
=106.25
So, Marpor's value without leverage is approximately $106 million. (Rounded to the nearest million.)
b. Estimate Marpor's value with the new leverage.
Marpor's value with the new leverage is $
enter your response here million. (Round to two decimal places.)
To estimate Marpor's value with the new leverage, we need to consider the impact of debt on its free
cash flows and incorporate the tax shield.
First, let's calculate the expected return (
[
]
� �
E
[
R
]
) using the same formula as before:
�[�]=��+�×(��−��)
E
[
R
]=
r
f
+
β
×(
r
m
−
r
f
)
Given:
●
��
●
r
●
f
●
●
= 4% or 0.04
●
��
●
r
●
m
●
●
= 14% or 0.14
●
�
●
β
= 1.2
�[�]=0.04+1.2×(0.14−0.04)
E
[
R
]=0.04+1.2×(0.14−0.04)
[
]=0.04+1.2×0.1
� �
E
[
R
]=0.04+1.2×0.1
[
]=0.04+0.12
� �
E
[
R
]=0.04+0.12
[
]=0.16
� �
E
[
R
]=0.16
Next, let's calculate Marpor's value with the new leverage (
��
V
L
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) using the formula:
=
[
]+
×
�� ���� �
�� �
V
L
=
E
[
R
]
FCF
+
τ
c
×
D
Given:
●
���
●
FCF
(with debt) = $16 million
●
[
]
� �
●
E
[
R
]
= 0.16 (as calculated)
●
��
●
τ
●
c
●
●
= 21% or 0.21 (tax rate)
●
�
●
D
= $30 million (amount of debt)
=160.16+0.21×30
��
V
L
=
0.16
16
+0.21×30
=100+6.3
��
V
L
=100+6.3
=106.3
��
V
L
=106.3
So, Marpor's value with the new leverage is approximately $106.3 million. (Rounded to two decimal places.)
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