Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Explain in a few sentences what each example means. This is strictly qualitative.
![2
38
F2
W
ed
3
Pretax versus After-Tax Free Cash Flows
Will the same valuation arise if the analyst discounts pretax-free cash flows at a pretax cost
of capital and after-tax free cash flows at an after-tax cost of capital? The answer is no if
costs of debt and equity capital receive different tax treatments. For tax purposes, firms can
typically deduct the costs of debt capital but cannot deduct the costs of equity capital.
Example 8: Tax Effects on Free Cash Flows
Suppose the firm faces the following costs of capital:
Debt
Equity
Pretax:
-After-tax:
80
E
Proportion
in Capital
Structure
F3
0.33
0.67
1.00
$
4
Assume that this firm expects to generate $90 million of pretax-free cash flows and $54 mil-
lion of after-tax free cash flows [= (10.40) X $90 million] one year from today. This firm
would be valued using pretax and after-tax amounts (assuming a one-year horizon) as follows:
888
F4
Pretax
Cost
R
10%
18%
%
These values are not equivalent because cash inflows from assets are taxed at 40 percent
and cash outflows to service debt give rise to a tax savings of 40 percent. However, the cost
of equity capital does not provide a tax benefit. The appropriate valuation in this case is
$47.37 million. Thus, the analyst should use after-tax free cash flows and the after-tax cost
of capital.
5
Selecting a Forecast Horizon
The analyst will need to project periodic free cash flows over the remaining expected life of
the resource to be valued. This life is a finite number of years for a resource with a finite
physical life, such as a machine or a building, or a financial instrument with a finite stated
maturity such as a bond a mortgage or a lonce Pu
Tax After-Tax
Effect
Cost
0.40
F5
T
6%
18%
^
6
F6
MacBook Air
Y
Weighted Average
Cost of Capital
Pretax
$90 million X 1/1.1533 = $78.04 million
$54 million X 1/1.14 = $47.37 million
&
3.33%
12.00%
15.33%
7
Page < 4
Ja
F7
U
* 00
After-Tax
2.00%
12.00%
14.00%
8
DII
F8
1
(
9
DD
F9
>
)
0
0
of 5 -
F10
I'
P](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a44212c-b8b1-4ff0-bde6-3e570916b708%2Fed3b7c49-c987-4d72-943e-d192594a4b65%2Fv26ewza_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2
38
F2
W
ed
3
Pretax versus After-Tax Free Cash Flows
Will the same valuation arise if the analyst discounts pretax-free cash flows at a pretax cost
of capital and after-tax free cash flows at an after-tax cost of capital? The answer is no if
costs of debt and equity capital receive different tax treatments. For tax purposes, firms can
typically deduct the costs of debt capital but cannot deduct the costs of equity capital.
Example 8: Tax Effects on Free Cash Flows
Suppose the firm faces the following costs of capital:
Debt
Equity
Pretax:
-After-tax:
80
E
Proportion
in Capital
Structure
F3
0.33
0.67
1.00
$
4
Assume that this firm expects to generate $90 million of pretax-free cash flows and $54 mil-
lion of after-tax free cash flows [= (10.40) X $90 million] one year from today. This firm
would be valued using pretax and after-tax amounts (assuming a one-year horizon) as follows:
888
F4
Pretax
Cost
R
10%
18%
%
These values are not equivalent because cash inflows from assets are taxed at 40 percent
and cash outflows to service debt give rise to a tax savings of 40 percent. However, the cost
of equity capital does not provide a tax benefit. The appropriate valuation in this case is
$47.37 million. Thus, the analyst should use after-tax free cash flows and the after-tax cost
of capital.
5
Selecting a Forecast Horizon
The analyst will need to project periodic free cash flows over the remaining expected life of
the resource to be valued. This life is a finite number of years for a resource with a finite
physical life, such as a machine or a building, or a financial instrument with a finite stated
maturity such as a bond a mortgage or a lonce Pu
Tax After-Tax
Effect
Cost
0.40
F5
T
6%
18%
^
6
F6
MacBook Air
Y
Weighted Average
Cost of Capital
Pretax
$90 million X 1/1.1533 = $78.04 million
$54 million X 1/1.14 = $47.37 million
&
3.33%
12.00%
15.33%
7
Page < 4
Ja
F7
U
* 00
After-Tax
2.00%
12.00%
14.00%
8
DII
F8
1
(
9
DD
F9
>
)
0
0
of 5 -
F10
I'
P
![3
80
Page <
3
the effects of general price changes, the discount rate should be a real rate of return, exclud-
ing the inflation component.
F3
Example 7: Nominal versus Real Free Cash Flows
A firm owns an asset that it expects to sell one year from today for $115.5 million. The firm
expects the general price level to increase 10 percent during this period. The real interest
rate is 5 percent. The nominal discount rate should be 15.5 percent to measure the com-
pound effects of the real rate of interest and inflation [0.155= (1.10 X 1.05)-1].
Discounting nominal or real free cash flows, the present value of the asset to the firm is
$100 million, as shown:
Nominal Free Cash Flows
$115.5 million
Real Free Cash Flows
$115.5 million/1.10
Scanned by CamScanner
$
4
888
F4
%
5
X
F5
X
X
X
In both computations, we derived the value of the equity of the firm by computing the
present value of the free cash flows to common equity shareholders. As a practical matter,
analysts usually find it more straightforward to discount nominal free cash flows using
nominal discount rates than to adjust nominal free cash flows to real free cash flows and
then discount real free cash flows using real interest rates. Discount rates derived from the
CAPM are nominal because the risk-free rate component incorporates expected inflation.
Further, stated and effective interest rates on long-term debt also are nominal because they
incorporate expected inflation rates. Thus, readily available or easily estimable discount
A
Discount Rate Including
Expected Inflation
1/(1.05 X 1.10)
6
Discount Rate Excluding
Expected Inflation
1/1.05
MacBook Air
F6
&
7
AA
F7
=
* 00
=
8
ate liahilities, revenues, and expenses. These
Value
$100 million
DII
FB
Value
$100 million
(
DD
F9
)
> of 5
0
T
F10
(1
F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a44212c-b8b1-4ff0-bde6-3e570916b708%2Fed3b7c49-c987-4d72-943e-d192594a4b65%2Fnlewfbf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3
80
Page <
3
the effects of general price changes, the discount rate should be a real rate of return, exclud-
ing the inflation component.
F3
Example 7: Nominal versus Real Free Cash Flows
A firm owns an asset that it expects to sell one year from today for $115.5 million. The firm
expects the general price level to increase 10 percent during this period. The real interest
rate is 5 percent. The nominal discount rate should be 15.5 percent to measure the com-
pound effects of the real rate of interest and inflation [0.155= (1.10 X 1.05)-1].
Discounting nominal or real free cash flows, the present value of the asset to the firm is
$100 million, as shown:
Nominal Free Cash Flows
$115.5 million
Real Free Cash Flows
$115.5 million/1.10
Scanned by CamScanner
$
4
888
F4
%
5
X
F5
X
X
X
In both computations, we derived the value of the equity of the firm by computing the
present value of the free cash flows to common equity shareholders. As a practical matter,
analysts usually find it more straightforward to discount nominal free cash flows using
nominal discount rates than to adjust nominal free cash flows to real free cash flows and
then discount real free cash flows using real interest rates. Discount rates derived from the
CAPM are nominal because the risk-free rate component incorporates expected inflation.
Further, stated and effective interest rates on long-term debt also are nominal because they
incorporate expected inflation rates. Thus, readily available or easily estimable discount
A
Discount Rate Including
Expected Inflation
1/(1.05 X 1.10)
6
Discount Rate Excluding
Expected Inflation
1/1.05
MacBook Air
F6
&
7
AA
F7
=
* 00
=
8
ate liahilities, revenues, and expenses. These
Value
$100 million
DII
FB
Value
$100 million
(
DD
F9
)
> of 5
0
T
F10
(1
F
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