International Capital
Budgeting
INTERNATIONAL
FINANCIAL
MANAGEMENT
Fourth Edition
Chapter Objective:
This chapter discusses the methodology that a
multinational firm can use to analyze the
Fourth Edition
investment of capital in a foreign country.
EUN / RESNICK
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
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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
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-1
Chapter Outline
l
Chapter
Eighteen
INTERNATIONAL
FINANCIAL
MANAGEMENT
EUN / RESNICK
18-0
18
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.
18-2
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Review of Domestic Capital
Budgeting
The basic net present value equation is
T
CFt
TVT
NPV = ∑
+
− C0
t
(1 + K )T
t =1 (1 + K )
Where:
CF t = expected incremental after-tax cash flow in year t,
TVT = expected after tax terminal value 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.
18-4
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-3
Review of Domestic Capital
Budgeting
The NPV rule is to accept a project if NPV ≥ 0
T
NPV = ∑
t =1
CFt
TVT
+
− C0 ≥ 0
t
T
(1 + K ) (1+ K )
and to reject a project if NPV ≤ 0
T
NPV = ∑
t =1
18-5
CFt
TVT
+
− C 0 ≤ 0.
t
T
(1 + K ) (1+ K )
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
1
Review of Domestic Capital
Budgeting
For our purposes it is necessary to expand the NPV
equation.
CFt = (Rt – OCt – D t – I t)(1 – τ) + Dt + It (1 – τ)
Rt is incremental revenue
I t is incremental interest
expense
OCt is incremental operating
cash flow
τ is the marginal tax rate
Dt is incremental depreciation
CFt = (Rt – OCt – D t – I t)(1 – τ) + Dt + It (1 – τ)
CFt = (NI t + D t + I t (1 – τ)
CFt = (Rt – OCt – D t(1 – τ) + Dt
CFt = (NOI t)(1 – τ) + Dt
CFt = (Rt – OCt)(1 – τ) + τ Dt
CFt = (OCFt)(1 – τ) + τ Dt
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-6
Alternative Formulations CFt
Review of Domestic Capital
Budgeting
We can use CF t = (OCF t)(1 – τ) + τ D t
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-7
The Adjusted Present Value Model
T
NPV =
T
Σ
CF t
TVT
+
– C0
t = 1 (1 + K) t
(1 + K) T
as:
T
Σ
(OCF t)(1 – τ) + τ Dt
(1
t=1
+ K) t
+
TVT
– C0
(1 + K) T
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-8
T
Σ
APV =
T
Σ
t=1
(OCF t)(1 – τ)
(1 + Ku
)t
+
τ Dt
τ It
TVT
+
+
– C0
(1 + i) t (1 + i) t (1 + Ku ) 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.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
t
t=1
(OCF t)(1 – τ)
(1 + Ku ) t
t
+
TVT
– C0
(1 + K) T
+
τ Dt
τ It
TVT
+
+
– C0
(1 + i) t (1 + i) t (1 + Ku ) T
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-9
Domestic APV Example
Consider this project, the timing and size of the incremental
after-tax cash flows for an all-equity firm are:
-$1,000
$125
$250
$375
$500
0
1
2
3
4
CF0
CF1
The unlevered cost of equity is r0 = 10%:
= –$1000
The project would be rejected by
an all-equity firm:
= $125
CF2 = $250
CF3 = $500
18-10
Σ (1τ+DK)
By appealing to Modigliani and Miller’s results.
The Adjusted Present Value Model
APV =
(1 + K) t
T
+
Can be converted to adjusted present value (APV)
t=1
NPV =
(OCF t)(1 – τ)
t=1
to restate the NPV equation
NPV =
Σ
18-11
I
= 10
NPV = –$56.50
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
2
Domestic APV Example (continued)
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Now, imagine that the firm finances the project
with $600 of debt at r = 8%.
The tax rate is 40%, so they have an interest tax
shield worth τ×I = .40×$600×.08 = $19.20 each
year.
-$1,000
$125
$250
$375
$500
0
1
2
3
4
The APV of the project under leverage is:
T
Σ
APV =
(OCF t)(1 – τ)
t=1
APV =
(1 + Ku ) t
+
τ Dt
τ It
TVT
+
+
– C0
(1 + i) t (1 + i) t (1 + Ku ) T
$125
$250
$375
$500
+
+
+
1.10 (1.10)2 (1.10)3 (1.10)4
$19.20 $19.20 $19.20
$19.20
+
+
+
+
– $1,000
1.08
(1.08)2 (1.08)3
(1.08)4
APV = $7.09 The firm should accept the project if it finances with debt.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-12
Capital Budgeting from the Parent
Firm’s Perspective
T
Σ
APV =
(OCF t)(1 – τ)
t=1
l
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(1 + Ku ) t
+
τ Dt
τ It
TVT
+
+
– C0
(1 + i) t (1 + i) t (1 + Ku ) T
The APV model is useful for a domestic firm
analyzing a domestic capital expenditure or for a
foreign subsidiary of a MNC analyzing a proposed
capital expenditure from the subsidiary’s
viewpoint.
The APV model is NOT useful for a MNC in
analyzing a foreign capital expenditure from the
parent firm’s perspective.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-14
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-13
Capital Budgeting from the Parent
Firm’s Perspective
l
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 − t ) T S t t Dt
S tI
+∑
+∑ t t t
t
t
(1 + K ud )
t= 1
t =1 (1 + id )
t = 1 (1+ id )
T
APV = ∑
+
T
STTVT
S LP
− S0 C0 + S0 RF0 + S 0CL0 + ∑ t t t
T
(1 + K ud )
t =1 (1+ id )
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-15
Capital Budgeting from the Parent
Firm’s Perspective
T
APV =
T
T
(1 – τ)
SτD
SτI
+Σ
+Σ
Σ S(1OCF
+K )
(1 + i )
(1 + i )
t
t=1
+
t
t
ud
t
t=1
t
d
t
t
t=1
T
t
d
t
APV =
t
t=1
Σ
T
S tTVT
S tLPt
– S 0 C0 + S0 RF0 + S0 CL0 +
(1 + Kud) T
t = 1(1 + id ) t
T
T
(1 – τ)
SτD
SτI
+Σ
+Σ
Σ S(1OCF
+K )
(1 + i )
(1 + i )
+
t
t
ud
t
t=1
t
d
t
t
t=1
t
d
t
Σ
T
S tTVT
S tLPt
– S 0 C0 + S0 RF0 + S0 CL0 +
(1 + Kud) T
t = 1(1 + id ) t
The operating cash flows must The operating cash flows
be translated back into the
must be discounted at the
parent firm’s currency at the
unlevered domestic rate
spot rate expected to prevail
in each period.
18-16
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-17
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
3
Capital Budgeting from the Parent
Firm’s Perspective
T
APV =
T
T
(1 – τ)
SτD
SτI
+Σ
+Σ
Σ S(1OCF
+K )
(1 + i )
(1 + i )
t
t
t=1
+
t
ud
t
Capital Budgeting from the Parent
Firm’s Perspective
t
t=1
d
t
t
T
t
t=1
d
APV =
t
Σ
The marginal corporate tax
rate, τ, is the larger of the
parent’s or foreign
subsidiary’s.
+
Use PPP, IRP et cetera for the predictions.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-20
Capital Budgeting from the Parent
Firm’s Perspective: Example
l
We can use a simplified APV:
T
APV =
T
t
+
t
t
ud
t
t=1
t
d
t
t
t=1
18-22
d
t
t
t=1
t
d
t
Σ
T
S tTVT
S tLPt
– S 0 C0 + S0 RF0 + S0 CL0 +
T
(1 + Kud)
t = 1(1 + id ) t
Denotes the present value
(in the parent’s currency) of
any concessionary loans,
CL0 , and loan payments,
LPt , discounted at id .
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
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A U.S.-based MNC is considering a European
opportunity.
It’s a simple example
n
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There is no incremental debt
There is no incremental depreciation
There are no concessionary loans
There are no restricted funds
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-21
Capital Budgeting from the Parent
Firm’s Perspective: Example
t
d
t
Σ
T
S tTVT
S tLPt
– S 0 C0 + S0 RF0 + S0 CL0 +
T
(1 + Kud)
t = 1 (1 + id ) t
T
APV =
t=1
A U.S. MNC is considering a European opportunity.
The size and timing of the after-tax cash flows are:
T
(1 – τ)
SτD
SτI
+Σ
+Σ
Σ S(1OCF
+K )
(1 + i )
(1 + i )
t=1
t
t
Capital Budgeting from the Parent
Firm’s Perspective: Example
n
3. Calculate NPV using the home currency cost
of capital.
T
t
ud
18-19
Capital Budgeting from the Parent
Firm’s Perspective
One recipe for international decision makers:
1. Estimate future cash flows in foreign
currency.
2. Convert to the home currency at the predicted
exchange rate.
t
S 0RF0 represents the value of
accumulated restricted funds
(in the amount of RF0) that
are freed up by the project.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-18
t
t=1
T
S tTVT
S tLPt
– S 0 C0 + S0 RF0 + S0 CL0 +
T
(1 + Kud)
t = 1(1 + id ) t
OCF t represents only the
portion of operating cash
flows available for remittance
that can be legally remitted to
the parent firm.
T
(1 – τ)
SτD
SτI
+Σ
+Σ
Σ S(1OCF
+K )
(1 + i )
(1 + i )
S tOCF t(1 – τ) – S C
0 0
t = 1 (1 + K ) t
ud
Σ
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
–€600
€200
€500
€300
0
1
2
3
The inflation rate in the euro zone is π€ = 3%, the inflation
rate in dollars is π$ = 6%, and the business risk of the
investment would lead an unlevered U.S. based firm to
demand a return of Kud = i$ = 15%.
18-23
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
4
Capital Budgeting from the Parent
Firm’s Perspective: Example
–€600
€200
€500
€300
0
1
2
3
The current exchange rate is S 0($/€) =
Capital Budgeting from the Parent
Firm’s Perspective: Example
$257.28
€200
0
€200
€500
€300
0
1
2
3
CF 0 = (€600)× S 0($/€) =(€600)× $1.25 = $750
€
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
–$750
–€600
–$750
–€600
$1.25
€
Is this a good investment from the perspective of the
U.S. shareholders?
To address that question, let’s convert all of the cash
flows to dollars and then find the NPV at i$ = 15%.
18-24
Capital Budgeting from the Parent
Firm’s Perspective: Example
Finding the dollar value of the initial cash
$1.25
flow is easy; convert at the spot rate: S 0($/€) =
€
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-25
Capital Budgeting from the Parent
Firm’s Perspective: Example
€500
€300
–$750
–€600
$257.28
€200
$661.94
€500
€300
2
3
0
1
2
3
1
The exchange rate expected to prevail in the first year, S1 ($/€),
can be found with PPP:
1 +π
1.06 $1.25
S 1($/€) = 1 + π$ × S0 ($/€) =
×
= $1.2864/€
€
1.03
€
1.06
CF 2 =
1.03
×
1.06
1.03
×
$1.25
€
× €500 = $661.94
CF 1 = €200 × S 1 ($/€) = €200 × $1.2864/€ = $257.28
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-26
Capital Budgeting from the Parent
Firm’s Perspective: Example
–$750
–€600
$257.28
€200
$661.94
€500
0
1
2
CF 3 =
1.06
1.03
×
1.06
1.03
×
1.06
1.03
×
$408.73
€300
3
$1.25
€
× €300 = $408.73
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-27
Capital Budgeting from the Parent
Firm’s Perspective: Example
–$750
$257.28
$661.94
0
1
2
Find the NPV using the cash flow menu of your financial
calculator and and interest rate i$ = 15%:
CF1 = $257.28
CF3 = $408.73
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
3
CF0 = –$750
CF2 = $661.94
18-28
$408.73
18-29
I
= 15
NPV = $242.99
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
5
Capital Budgeting from the Parent
Firm’s Perspective: Example
–$750
$257.28
$661.94
0
1
2
$408.73
3
Without a financial calculator, the NPV can be found as:
NPV = –$750 +
$257.28 $661.94
$408.73
= $242.99
+
+
1.15
(1.15)2
(1.15)3
Capital Budgeting from the Parent
Firm’s Perspective: Alternative
Another recipe for international decision makers:
1. Estimate future cash flows in foreign
currency.
2. Estimate the foreign currency discount rate.
3. Calculate the foreign currency NPV using the
foreign cost of capital.
4. Translate the foreign currency NPV into
dollars using the spot exchange rate
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-30
18-31
Foreign Currency Cost of Capital
Method
– €600
€200
€500
€300
Foreign Currency Cost of Capital
Method
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0
π€ = 3%
1
2
3
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Before we find i€ let’s use our intuition.
Since the euro-zone inflation rate is 3% lower than the
dollar inflation rate, our euro denominated discount rate
should be lower than our dollar denominated discount rate.
Let ’s find i€ and use that on the euro
cash flows to find the NPV in euros.
i$ = 15%
Then translate the NPV into dollars at
the spot rate.
$1.25
The current exchange rate is S 0($/€) = €
π$ = 6%
18-32
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Finding the Foreign Currency Cost of
Capital: i€
Recall that the Fisher Effect holds that
inflation
rate
(1 + e) =
nominal
rate
18-34
(1 + π$)
1.15
e=
Finding the Foreign Currency Cost of
Capital: i€
(1 + e$) =
So for example the real rate in the U.S. must be 8.49%
(1 + i$)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
If Fisher Effect holds here and abroad then
(1 + e) × (1 + π$) = (1 + i$)
real
rate
18-33
– 1 = 0.0849
(1 + π$)
and
(1 + e€) =
(1 + i€)
(1 + π€)
If the real rates are the same in dollars and euros (e€ = e$ )
we have a very useful parity condition:
(1 + i$)
(1 + π$)
1.06
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
(1 + i$)
18-35
=
(1 + i€)
(1 + π€)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
6
International Capital Budgeting:
Example
Finding the Foreign Currency Cost of
Capital: i€
If we have any three of these variables, we can find the
fourth:
(1 + i$)
(1 + i€)
=
(1 + π$)
(1 + π€)
i€ =
(1.06)
–1
18-37
– €600
€200
€500
€300
0
1
2
3
€200
€500
€300
+
+
= €194.39
1.1175 (1.1175) 2 (1.1175) 3
l
$1.25 = $242.99
€
€194.39 ×
n
l
APV =
t
+
t
t
ud
t
f
t=1
€194.39 ×
$1.25 = $242.99
€
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
l
Change the foreign cash flows into dollars at the
exchange rates expected to prevail. Find the $NPV
using the dollar cost of capital.
Find the foreign currency NPV using the foreign
currency cost of capital. Translate that into dollars at
the spot exchange rate.
18-39
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
l
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Clearly risk and return are correlated.
Political risk may exist along side of business risk,
necessitating an adjustment in the discount rate.
T
(1 – τ)
SτD
SτI
+Σ
+Σ
Σ S(1OCF
+K )
(1 + i )
(1 + i )
t=1
S0
18-40
S0
T
= 11.75
Risk Adjustment in the Capital
Budgeting Process
Using the intuition just developed, we can modify
Lessard’s APV model as shown above, if we find
it convenient.
S0
I
NPV = €194.39
If you watch your rounding, you will get exactly
the same answer either way.
Which method you prefer is your choice.
Back to the full APV
T
3
You have two equally valid approaches:
n
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
S0
2
International Capital Budgeting
Without a financial calculator, the NPV can be found as:
l
1
CF3 = €300
Capital Budgeting from the Parent
Firm’s Perspective: Example
18-38
0
CF2 = €500
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
NPV = –€600 +
€300
CF1 = €200
(1.15) × (1.03)
i€ = 0.1175
18-36
€500
CF0 = –€600
(1 + i$) × (1 + π€ )
(1 + π$)
€200
Find the NPV using the cash flow menu and i€ = 11.75%:
In our example, we want to find i€
(1 + i€) =
– €600
t
d
t
t
f
t=1
t
d
t
f
T
S tTVT
– S 0 C0 + S0 RF0 + S0 CL0 + S tLPt
(1 + Kud) T
t = 1(1 + id ) t
f
f
S
0
Copyright © 2007 by The McGraw-Hill Companies,
Inc. All rights reserved.
Σ
18-41
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
7
Sensitivity Analysis
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Real Options
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.
l
n
n
n
n
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-42
Value of the Option to Delay: Example
A French firm is considering a one-year investment
in the United Kingdom with a pound-denominated
rate of return of 15%.
The firm’s local cost of capital is i€ = 10%
–£1,000
£1,150
0
1
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.
18-43
Value of the Option to Delay: Example
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Suppose that the bank of England is considering
either tightening or loosening its monetary policy.
It is widely believed that in one year there are only
two possibilities:
n
n
The cash flows are
l
The current exchange rate is S0(€|£) = €2.00
£
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-44
S1 (€|£) = €2.20 per £
S1 (€|£) = €1.80 per £
Following revaluation, the exchange rate is
expected to remain steady for at least another
year.
18-45
Option to Delay: Example
l
If S1(€|£) = €1.80 per £
the project will have
turned out to be a loser
for the French firm:
l
If S1(€|£) = €2.20 per £
the project will have
turned out to be a winner
for the French firm:
€2,070
–€2,000
€2,530
0
1
0
1
18-46
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option to Delay: Example
–€2,000
IRR = 3.50%
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
IRR = 26.50%
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
l
An important thing to notice is that there is an
important source of risk (exchange rate risk) that
isn’t incorporated into the French firm’s local cost
of capital of i€ = 10%.
l
Even with that, we can see that taking the project on
today entails a “ win big—lose big” gamble on exchange
rates.
Analogous to buying an at -the-money call option on
British pounds with a maturity of one year.
n
l
That’ s why there are no NPV estimates on the last slide.
18-47
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
8
Option to Delay: Example
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Option to Delay: Example
The remaining slides assume a knowledge of the
material contained in chapter 7.
Especially the notion of a replicating portfolio.
But also basic things like a call options gives the
holder the right to buy a specific asset at a specific
price for a specific amount of time.
l
S1 (€|£)
l
= €2,530
€1.80/£
€2,070 = €2,070 + €0
= €2,070
18-49
l
l
l
€2,070
1+ i€
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-50
Suppose that our option dealer quotes an option premium
of €0.05 per pound and our banker quotes the euro-zone
risk-free rate at i€ = 6%.
The NPV of the project at time zero to the French firm is
NPV0 = –€2,000 + €115 + €2,070 = €67.83
1.06
Before we accept a positive NPV project, we should make
sure that we are not bypassing alternative projects with
higher NPVs.
§ Waiting a year to start the same project is an alternative.
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Option to Delay: Example
l
l
l
If S1(€|£) = €2.20 per £
–€1,800
€2,070
–€2,200
€2,530
0
1
0
1
IRR = 15%
NPV1 = €81.82 = –€1,800 + €2,070
1.10
18-52
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Do The Right Thing
If the firm can wait a year to start the project the
cash flows look like
If S1(€|£) = €1.80 per £
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option to Delay: Example
So the present value of the project at time zero can
be found by getting a quote from an option dealer
on an at-the-money call on £2,300 and adding to
that the present value of €2,070 at the euro-zone
risk-free rate.
The Net Present Value of the project is that sum
less the cost of the project, –€2,000:
NPV = –€2,000 + value of option +
Replicating
= Portfolio
€2,530 = €2,070 + €460
Option to Delay: Example
l
British
Call
Investment = Bond + Option
€2.20/£
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
18-48
The payoff in one year of portfolio consisting of an at -themoney call option written on £2,300 plus a risk-free bond
with a future value of €2,070 equals the payoff of the
British investment:
IRR = 15%
NPV1 = €100
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
l
We have a choice: to invest in the project today or to wait
a year.
If we jump in today, the NPV0 is €67.83 and the FV in one
year is NPV1 = €74.61 = 1.10 × €67.83
Clearly it’s better to wait a year.
n Worst case, NPV1 = €81.82 and there is a chance that
the NPV at time one is €100
n Both of these outcomes beat €74.61
18-53
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
9
End Chapter Eighteen
18-54
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
10