Transcript Document

Review of Domestic Capital
Budgeting
1. Identify the SIZE and TIMING of all relevant cash
flows on a time line.
2. Identify the RISKINESS of the cash flows to
determine the appropriate discount rate.
3. Find NPV by discounting the cash flows at the
appropriate discount rate.
4. Compare the value of competing cash flow
streams at the same point in time.
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Measuring Cash Flows
• The guiding principle is to measure incremental cash flows. That is,
how much the project really adds to the cash flow of the parent
• But this is often easier said than done. They are often real problems
in measuring incremental cash flows such as
• Cross Relationship Between Parent and Subsidiary
– Cannibalization
– Cross Fertilization
• Accounting for cash flows
– Transfer pricing (especially when market prices aren’t available)
– Fees royalties and other charges for overhead
• Intangibles
– Good will
– Experience
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Review of Domestic Capital
Budgeting
The basic net present value equation is
T
CFt
TVT
NPV  

 C0
t
T
(1  K )
t 1 (1  K )
Where:
CFt = expected incremental after-tax cash flow in year t,
TVT = expected after tax cash flow in year T, including return
of net working capital,
C0 = initial investment at inception,
K = weighted average cost of capital.
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T = economic life of the project in years.
Review of Domestic Capital
Budgeting
The NPV rule is to accept a project if NPV  0
T
CFt
TVT
NPV  

 C0  0
t
T
(1  K )
t 1 (1  K )
and to reject a project if NPV  0
T
CFt
TVT
NPV  

 C0  0.
t
T
(1  K )
t 1 (1  K )
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Review of Domestic Capital
Budgeting
For our purposes it is necessary to expand
the NPV equation.
CFt  ( Rt  OCt  Dt  I t )(1  τ )  Dt  I t (1  τ )
Rt is incremental revenue
It is incremental interest expense
Ct is incremental operating  is the marginal tax rate
cash flow
Dt is incremental depreciation
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Review of Domestic Capital
Budgeting
For our purposes it is necessary to expand
the NPV equation.
CFt  ( Rt  OCt  Dt  I t )(1  τ )  Dt  I t (1  τ )
 NI t  Dt  I t (1  τ )
 ( Rt  OCt  Dτ )(1  τ )  Dt
 NOIt (1  τ )  Dt
 ( Rt  OCt )(1  τ )  τDt
 OCFt (1  τ )  τDt
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Review of Domestic Capital
Budgeting
We can use
CFt  OCFt (1  τ )  τDt
to restate the NPV equation
T
as:
CFt
TVT
NPV  

 C0
t
T
(1  K )
t 1 (1  K )
OCFt (1  τ )  τ Dt
TVT
NPV  

 C0
t
T
(1  K )
(1  K )
t 1
T
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The Adjusted Present Value
Model
OCFt (1  τ )
τ Dt
TVT
NPV  


 C0
t
t
T
(1  K )
(1  K ) (1  K )
t 1
Can be converted to adjusted present value
(APV)
T
OCFt (1  τ )
τ Dt
τ It
TVT
APV  



 C0
t
t
t
T
(1  Ku )
(1  i) (1  i) (1  Ku )
t 1
T
By appealing to Modigliani and Miller’s results.
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The Adjusted Present Value
Model
OCFt (1  τ )
τ Dt
τ It
TVT
APV  



 C0
t
t
t
T
(1  Ku )
(1  i) (1  i) (1  Ku )
t 1
The APV model is a value additivity approach
to capital budgeting. Each cash flow that is
a source of value to the firm is considered
individually.
T
Note that with the APV model, each cash flow
is discounted at a rate that is appropriate to
the riskiness of the cash flow.
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Capital Budgeting from the
Parent Firm’s Perspective
• Donald Lessard developed an APV model for
a MNC analyzing a foreign capital
expenditure. The model recognizes many of
the particulars peculiar to foreign direct
investment.
T
T
St OCFt (1  τ ) T St τ Dt
St τ It
APV  


t
t
t
(
1

K
)
(
1

i
)
(
1

i
)
t 1
t 1
t 1
ud
d
d
T
St LPt
ST TVT

 S 0C0  S 0 RF0  S 0CL0  
T
t
(1  K ud )
(
1

i
)
t 1
d
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Capital Budgeting from the
Parent Firm’s Perspective
T
St OCFt (1  τ ) T St τ Dt
St τ It
APV  


t
t
t
(
1

K
)
(
1

i
)
(
1

i
)
t 1
t 1
t 1
ud
d
d
T
T
St LPt
ST TVT

 S 0C0  S 0 RF0  S 0CL0  
T
t
(1  K ud )
(
1

i
)
t 1
d
The operating cash flows
must be translated back
into the parent firm’s
currency at the spot rate
expected to prevail in
each period.
The operating cash flows
must be discounted at the
unlevered domestic rate
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Capital Budgeting from the
Parent Firm’s Perspective
T
St OCFt (1  τ ) T St τ Dt
St τ It
APV  


t
t
t
(
1

K
)
(
1

i
)
(
1

i
)
t 1
t 1
t 1
ud
d
d
T
T
St LPt
ST TVT

 S 0C0  S 0 RF0  S 0CL0  
T
t
(1  K ud )
(
1

i
)
t 1
d
OCFt represents only the
portion of operating cash
flows available for
remittance that can be
legally remitted to the
parent firm.
The marginal corporate tax
rate, , is the larger of the
parent’s or foreign
subsidiary’s.
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Capital Budgeting from the
Parent Firm’s Perspective
T
St OCFt (1  τ ) T St τ Dt
St τ It
APV  


t
t
t
(
1

K
)
(
1

i
)
(
1

i
)
t 1
t 1
t 1
ud
d
d
T
T
St LPt
ST TVT

 S 0C0  S 0 RF0  S 0CL0  
T
t
(1  K ud )
(
1

i
)
t 1
d
S0RF0 represents the value Denotes the present value
of accumulated restricted
(in the parent’s currency) of
any concessionary loans,
funds (in the amount of
CL0, and loan payments,
RF0) that are freed up by
LPt , discounted at id .
the project.
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Which Currency?
Time Period
Free Cash Flow
0
-£56.00
1
£10.40
2
£8.90
3
£9.70
4
£9.90
5
£10.40
Terminal Value (Period 5)
£78.00
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Assume Subsidiary WACC=15%
Time Period
Free Cash Flow
pv (15%)
0
-£56.00
-£56.00
1
£10.40
£9.04
2
£8.90
£6.73
3
£9.70
£6.38
4
£9.80
£5.60
5
£10.40
£5.17
5
£78.00
£38.78
Pound NPV
$ NPV (S=1.7)
£15.70
$26.70
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Suppose R($)=6% R(pound)=10%
• Then Irp means S1=S0(1.06)/1.10
Time Period
Free Cash
Flow
0
-£56.00
1
£10.40
2
S
FCF ($)
1.7
-$95.20
1.638
$17.04
£8.90
1.579
$14.05
3
£9.70
1.521
$14.76
4
£9.80
1.466
$14.37
5
£10.40
1.413
$14.69
5
£78.00
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1.413
$110.18
Estimating the Future Expected
Exchange Rates
We can appeal to PPP:
(1  π d )t
St  S 0
(1  π f )t
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Suppose (1+WACC($))/(1+WACC(U.K))=(1+r($))/(1+r(U.K))
• WACC($)=(1.15)*(1.06)/(1.1)=10.8%
Time
Period
Free Cash
Flow
S
0
FCF ($)
PV
-£56.00
1.7
-$95.20
-$95.20
1
£10.40
1.638
$17.04
$15.37
2
£8.90
1.579
$14.05
$11.44
3
£9.70
1.521
$14.76
$10.84
4
£9.80
1.466
$14.37
$9.53
5
£10.40
1.413
$14.69
$8.79
5
£78.00
1.413
$110.18
$65.93
NPV
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$26.70
Moral
• If the assumptions are met, it doesn’t seen
to matter what currency is used to evaluate
the project
• But
– What if IRP doesn’t hold
– What if the Wacc’s are inconsistent with the
risk free rates
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International Capital Budgeting
A recipe for international decision makers:
1. Estimate future cash flows in foreign currency.
2. Convert to U.S. dollars at the predicted
exchange rate.
3. Calculate APV using the U.S. cost of capital.
Example
– 600
200
500
300
0
1 year
2 years
3 years
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International Capital Budgeting
– 600
0
200
1 year
500
2 years
300
3 years
Facts
i$  15%
π$  6%
 = 3%
S0($/ ) = $.55265
Is this a good
investment from the
perspective of the
U.S. shareholders?
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Solution
CF0 = ( 600) S0($/ ) =( 600)($.5526/ ) = $331.6
CF1 = ( 200)E[St($/ )]
E[St($/ )] can be found by appealing to the interest rate
differential:
E[S1($/ )] = [(1.06/1.03)S0($/ )]
= [(1.06/1.03)($.5526/ ) ] = $.5687/
so CF1 = ( 200)($.5687/ ) = $113.7
Similarly,
CF2 = [(1.06)2/(1.03)2 ] S0($/ )( 500) = $292.6
CF3 = [(1.06)3/(1.03)3 ] S0($/ )( 300) = $180.7
APV = -$331.60 + $113.7/(1.15) + $292.6/(1.15)2 + $180.7/(1.15)3
= $107.3 > 0 so accept.
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Risk Adjustment in the Capital
Budgeting Process
• Clearly risk and return are correlated.
• Political risk may exist along side of
business risk, necessitating an adjustment
in the discount rate.
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Sensitivity Analysis
• In the APV model, each cash flow has a
probability distribution associated with it.
• Hence, the realized value may be different
from what was expected.
• In sensitivity analysis, different estimates
are used for expected inflation rates, cost
and pricing estimates, and other inputs for
the APV to give the manager a more
complete picture of the planned capital
investment.
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Real Options
• The application of options pricing theory to
the evaluation of investment options in real
projects is known as real options.
– A timing option is an option on when to make
the investment.
– A growth option is an option to increase the
scale of the investment.
– A suspension option is an option to temporarily
cease production.
– An abandonment option is an option to quit the
investment early.
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