Chapter 17
International
Capital Budgeting
Chapter Outline
Review of Domestic Capital Budgeting
The Adjusted Present Value Model
Capital Budgeting from the Parent Firm’s
Perspective
Risk Adjustment in the Capital Budgeting Process
Sensitivity Analysis
Real Options
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.
International Capital Budgeting
One 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 NPV using the U.S. cost of capital.
International Capital Budgeting
Example
– 600€
200€
500€
300€
0
1
2
3
€ = 3%
i$ = 15%
$ = 6%
$.55265
S0($/€) =
€
Is this a good
investment from the
perspective of the
U.S. shareholders?
International Capital Budgeting:
Example
$331.60
– 600€
0
200€
1 year
500€
2 years
300€
3 years
CF0 = (€600)× S0($/€) =(€600)× $.55265 = $331.60
€
International Capital Budgeting:
Example
$331.60
– 600€
0
$113.70
200€
1 year
500€
2 years
300€
3 years
CF1 = (€200)×E[ S1($/€)] =
E[ S1($/€)] can be found by appealing to the interest rate
differential:
E[S€(1)] = 1.06  S0($/€) = 1.06  $.55265 = $.5687/€
1.03
1.03
€
so CF1 = (€200)×($.5687/€) = $113.7
International Capital Budgeting:
Example
$331.60
– 600€
0
Similarly,
$113.70
$292.60
200€
500€
1 year
2 years
CF2 = 1.06 × 1.06 × S0($/€) (€500) = $292.6
1.03 1.03
300€
3 years
International Capital Budgeting:
Example
$331.60
– 600€
0
$113.70
$292.60
$180.70
200€
500€
300€
1 year
2 years
3 years
(1.06)3
CF3 =
× S0($/€) (€300) = $180.7
3
(1.03)
$113.70 $292.60 $180.70
NPV  $336.60 


 $107.30
2
3
(1.15)
(1.15)
(1.15)
International Capital Budgeting
Another recipe for international decision makers:
1. Estimate future cash flows in foreign currency.
2. Estimate the foreign currency discount rate.
3. Calculate the foreign currency NPV using the
foreign cost of capital.
4. Translate the foreign currency NPV into
dollars using the spot exchange rate
Foreign Currency Cost of Capital
Method
– €600
€200
0
1
€ = 3%
i$ = 15%
$ = 6%
$.55265
S0($/€) =
€
€500
€300
3
2
Let’s find i€ and use that on
the euro cash flows to find
the NPV in euros.
Then translate the NPV into
dollars at the spot rate.
Finding the Foreign Currency Cost of
Capital: i€
Recall that if Fisher Effect holds here and abroad…
(1 + e)×(1 + $) = (1 + i$)
(1 + e) =
(1 + i$)
(1 + $)
(1 + i€) = (1 + e) × (1 + €)
and if the real rates are the same, then
(1 + i€) =
(1 + i$)×(1 + €)
(1 + $)
International Capital Budgeting
Example
– €600
€200
€500
€300
0
1
2
3
(1 + i€) =
(1 + i$)×(1 + €)
(1 + $)
=
(1.06)
= 11.75%
NPV 11.75% = € 194.39
€ = 3%
i$ = 15%
$ = 6%
(1.15)×(1.03)
S0($/€) =
$.55265
€
$.55265
€ 194.39×
€
= $107.43
International Capital Budgeting
You have two equally valid approaches:
– Change the foreign cash flows into dollars at the exchange
rates expected to prevail. Find the $NPV using the dollar cost
of capital.
– Find the foreign currency NPV using the foreign currency cost
of capital. Translate that into dollars at the spot exchange rate.
If you watch your rounding, you will get exactly the same
answer either way.
Which method you prefer is your choice.
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.
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 )
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
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 )
 ( NIt  Dt  I t (1  τ )
 ( Rt  OCt  Dτ )(1  τ )  Dt
 NOI t (1  τ )  Dt
 ( Rt  OCt )(1  τ )  τDt
 OCFt (1  τ )  τDt
Review of Domestic Capital
Budgeting
CFt  OCFt (1  τ )  τDt
We can use
to restate the NPV equation
T
as:
CFt
TVT
NPV  

 C0
t
T
(1  K )
t 1 (1  K )
OCFt (1  τ )  τDt
TVT
NPV  

 C0
t
T
(1  K )
(1  K )
t 1
T
The Adjusted Present Value Model
OCFt (1  τ )
τDt
TVT
NPV  


 C0
t
t
T
(1  K )
(1  K ) (1  K )
t 1
T
Can be converted to adjusted present value (APV)
T
OCFt (1  τ )
τDt
τI t
TVT
APV  



 C0
t
t
t
T
(1  i) (1  i) (1  Ku )
t 1 (1  K u )
By appealing to Modigliani and Miller’s results.
The Adjusted Present Value Model
OCFt (1  τ )
τDt
τI t
TVT
APV  



 C0
t
t
t
T
(1  i) (1  i) (1  Ku )
t 1 (1  K u )
T
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.
Note that with the APV model, each cash flow is
discounted at a rate that is appropriate to the
riskiness of the cash flow.
Domestic APV Example
Consider a project of the Pearson Company, the timing and size of the
incremental after-tax cash flows for an all-equity firm are:
-$1,000
$125
$250
0
1
2
The unlevered cost of equity is r0 = 10%:
NPV10%  $1,000 
$375
$500
3
4
$125
$250
$375
$500



(1.10) (1.10) 2 (1.10) 3 (1.10) 4
NPV10%  $56.50
The project would be rejected by an all-equity firm: NPV < 0.
Domestic APV Example (continued)
Now, imagine that the firm finances the project with $600 of debt
at r = 8%.
Pearson’s tax rate is 40%, so they have an interest tax shield
worth ×I = .40×$600×.08 = $19.20 each year.
 The net present value of the project under leverage is:
APV  NPV  NPVF
4
$19.20
APV  $56.50  
t
(
1
.
08
)
t 1
APV  $56.50  63.59  $7.09
Note that with the
APV model, each cash
flow is discounted at a
rate that is appropriate
to the riskiness of the
cash flow.
 So, Pearson should accept the project with debt.
Domestic APV Example (continued)
Note that there are two ways to calculate the NPV of the loan.
Previously, we calculated the PV of the interest tax shields.
Now, let’s calculate the actual NPV of the loan:
$600  .08  (1  .4) $600
NPVloan  $600  

t
4
(
1
.
08
)
(
1
.
08
)
t 1
NPVloan  $63.59
APV  NPV  NPVloan
4
APV  $56.50  63.59  $7.09
Which is the same answer as before.
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
St OCFt (1  τ ) T St τDt
St τI t
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
Capital Budgeting from the Parent
Firm’s Perspective
T
St OCFt (1  τ ) T St τDt
St τI t
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
Capital Budgeting from the Parent
Firm’s Perspective
T
St OCFt (1  τ ) T St τDt
St τI t
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.
Capital Budgeting from the Parent
Firm’s Perspective
T
St OCFt (1  τ ) T St τDt
St τI t
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 of
accumulated restricted funds (in
the amount of RF0) that are freed
up by the project.
Denotes the present value
(in the parent’s currency) of
any concessionary loans,
CL0, and loan payments,
LPt , discounted at id .
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.
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.
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.