Capital Budgeting
(Chapter 8)
Professor Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
Berlin, 04.01.2006
Fußzeile
1
The Capital Budgeting Decision
Process
The capital budgeting process involves three basic
steps:
• Generating long-term investment proposals;
• Reviewing, analyzing, and selecting from the
proposals that have been granted, and
• Implementing and monitoring the proposals
that have been selected.
Managers should separate investment and
financing decisions.
Berlin, 18th of June, 2007
Fußzeile
2
Capital Budgeting Decision
Techniques
Accounting rate of return (ARR): focuses on
project’s impact on accounting profits
Payback period: most commonly used
Net present value (NPV): best technique
theoretically; difficult to calculate realistically
Internal rate of return (IRR): widely used with
strong intuitive appeal, theoretically inappropriate.
Profitability index (PI): related to NPV
Berlin, 18th of June, 2007
Fußzeile
3
A Capital Budgeting Process Should:
Account for the time value of money;
Account for risk;
Focus on cash flow;
Rank competing projects appropriately, and
Lead to investment decisions that maximize
shareholders’ wealth.
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Fußzeile
4
Accounting Rate Of Return (ARR)
Can be computed from available accounting data
Average profits after taxes
ARR 
Average investm ent
• Need only profits after taxes and depreciation
• Average profits after taxes are estimated by
subtracting average annual depreciation from the
average annual operating cash inflows.
Average profits = Average annual
operating cash inflows
after taxes
Average annual
depreciation
ARR uses accounting numbers, not cash flows; no
time value of money.
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Fußzeile
5
Payback Period
The payback period is the amount of time required
for the firm to recover its initial investment.
• If the project’s payback period is less than the
maximum acceptable payback period, accept
the project.
• If the project’s payback period is greater than
the maximum acceptable payback period,
reject the project.
Management determines maximum acceptable
payback period.
Berlin, 18th of June, 2007
Fußzeile
6
Net Present Value
The present value of a project’s cash inflows and
outflows
Discounting cash flows accounts for the time value of
money.
Choosing the appropriate discount rate accounts for
risk.
CF3
CFN
CF1
CF2
NPV  CF0 


 ... 
2
3
(1  r )
(1  r )
(1  r )
(1  r ) N
Accept projects if NPV > 0.
Berlin, 18th of June, 2007
Fußzeile
7
Global Wireless
 Global Wireless is a worldwide provider of
wireless telephony devices.
 Global Wireless evaluating major expansion of
its wireless network in two different regions:
• Western Europe expansion
• A smaller investment in Southeast U.S. to establish a
toehold
Western Europe ($ millions)
Southeast U.S. ($ millions)
Initial outlay
-$250
Initial outlay
-$50
Year 1 inflow
$35
Year 1 inflow
$18
Year 2 inflow
$80
Year 2 inflow
$22
Year 3 inflow
$130
Year 3 inflow
$25
Year 4 inflow
$160
Year 4 inflow
$30
Year 5 inflow
$175
Year 5 inflow
$32
Berlin, 04.01.2006
Fußzeile
8
Calculating NPVs for
Global Wireless Projects
 Assuming Global Wireless uses 18% discount rate,
NPVs are:
Western Europe project: NPV = $75.3 million
NPVWestern Europe  $75.3  250 
35
80
130
160
175




(1.18) (1.18) 2 (1.18)3 (1.18) 4 (1.18)5
Southeast U.S. project: NPV = $25.7 million
NPVSoutheast U .S .  $25.7  50 
18
22
25
30
32




(1.18) (1.18) 2 (1.18)3 (1.18) 4 (1.18)5
Should Global Wireless invest in one project or
both?
Berlin, 18th of June, 2007
Fußzeile
9
Pros and Cons of Using
NPV as Decision Rule
NPV is the “gold standard” of investment decision
rules.
Key benefits of using NPV as decision rule:
• Focuses on cash flows, not accounting earnings
• Makes appropriate adjustment for time value of money
• Can properly account for risk differences between
projects
Though best measure, NPV has some drawbacks:
• Lacks the intuitive appeal of payback, and
• Doesn’t capture managerial flexibility (option value) well.
Berlin, 18th of June, 2007
Fußzeile
10
Internal Rate of Return
Internal rate of return (IRR) is the discount rate that
results in a zero NPV for the project:
CF3
CFN
CF1
CF2
NPV  0  CF0 


 .... 
2
3
(1  r ) (1  r )
(1  r )
(1  r ) N
• IRR found by computer/calculator or manually by
trial and error.
The IRR decision rule is:
• If IRR is greater than the cost of capital, accept
the project.
• If IRR is less than the cost of capital, reject the
project.
Berlin, 18th of June, 2007
Fußzeile
11
Calculating IRRs for Global
Wireless Projects
Global Wireless will accept all projects with at least
18% IRR.
Western Europe project: IRR (rWE) = 27.8%
0  250 
35
80
130
160
175




(1  rWE ) (1  rWE ) 2 (1  rWE )3 (1  rWE )4 (1  rWE )5
Southeast U.S. project: IRR (rSE) = 36.7%
18
22
25
30
32
0  50 




2
3
4
(1  rSE ) (1  rSE )
(1  rSE ) (1  rSE )
(1  rSE )5
Berlin, 18th of June, 2007
Fußzeile
12
Calculating IRRs for Global
Wireless Projects
r IRR   r1  NPV1 
r2  r1
NPV2  NPV1
 25%  18.6 
30%  25%
 27.91%
 13.4  18.6
3 5 0 ,0
W.Europe
S. U.S.
3 0 0 ,0
2 5 0 ,0
2 0 0 ,0
27.91%
1 5 0 ,0
1 0 0 ,0
5 0 ,0
0 ,0
-5 0 ,0
-1 0 0 ,0
0 ,0 %
Berlin, 18th of June, 2007
5 ,0 %
1 0 ,0 %
1 5 ,0 %
2 0 ,0 %
2 5 ,0 %
Fußzeile
3 0 ,0 %
3 5 ,0 %
4 0 ,0 %
4 5 ,0 %
13
Advantages and
Disadvantages of IRR
Advantages of IRR:
• Properly adjusts for time value of money (???)
• Uses cash flows rather than earnings
• Accounts for all cash flows
• Project IRR is a number with intuitive appeal
Disadvantages of IRR
• “Mathematical problems”: multiple IRRs, no real solutions
• Scale problem
• Timing problem
Berlin, 18th of June, 2007
Fußzeile
14
Multiple IRRs
NPV ($)
IRR
NPV>0
NPV>0
NPV<0
NPV<0
Discount
rate
IRR
When project cash flows have multiple sign
changes, there can be multiple IRRs.
With multiple IRRs, which do we compare with the
cost of capital to accept/reject the project?
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Fußzeile
15
No Real Solution
Sometimes projects do not have a real IRR solution.
Modify Global Wireless’s Western Europe project to
include a large negative outflow (-$355 million) in
year 6.
• There is no real number that will make
NPV=0.........
so no real IRR.
Project is a bad idea based on NPV. At r =18%,
project has negative NPV, so reject!
Berlin, 18th of June, 2007
Fußzeile
16
Conflicts Between
NPV and IRR
NPV and IRR do not always agree when ranking
competing projects.
The scale problem:
Project
IRR
NPV (18%)
Western Europe
27.8%
$75.3 mn
Southeast U.S.
36.7%
$25.7 mn
• Southeast U.S. project has higher IRR, but doesn’t increase
shareholders’ wealth as much as Western Europe project.
Berlin, 18th of June, 2007
Fußzeile
17
The Timing Problem
NPV
Longterm
project
IRR = 15%
Shortterm
project
13% 15%
IRR = 17%
Discount
rate
17%
• The NPV of the long-term project is more sensitive to the
discount rate than the NPV of the short-term project is.
• Long-term project has higher NPV if the cost of capital is
less than 13%. Short-term project has higher NPV if the
cost of capital is greater than 13%.
Berlin, 18th of June, 2007
Fußzeile
18
Profitability Index
Calculated by dividing the PV of a project’s cash
inflows by the PV of its outflows:
CF1
CF2
CFN


...

(1  r ) (1  r ) 2
(1  r ) N
PI 
CF0
Decision rule: Accept project with PI > 1.0, equal to NPV > 0
Project
PV of CF (yrs1-5)
Initial Outlay
PI
Western Europe
$325.3 million
$250 million
1.3
Southeast U.S.
$75.7 million
$50 million
1.5
•
Both projects’ PI > 1.0, so both acceptable if independent.
Like IRR, PI suffers from the scale problem.
Berlin, 18th of June, 2007
Fußzeile
19
Some Extensions.............
•
The Tax Paradoxon
Tax payments affect the cash flows of a project in a negative way.
On the other hand, a discount rate after tax will be smaller than a
discount rate before tax. Under some circumstances fiscal policy –
i.e. Tax rate policy – may determine the ranking of investments.
•
Inflation
We always have to make sure, that nominal cash flows must refer
to nominal discount rates while real cash flows require real
discoount rates.
•
Exchange Rates
If global financial markets are working well, the effect of different
inflation rates will be perfectly substituted by a well functioning
exchange rate mechanism.
Berlin, 18th of June, 2007
Fußzeile
20
The Tax Paradoxon
Corporate tax will affect N.P.V.- calculation in
numerous aspects:
1. Tax payments reduce the cash flow
2. Depreciation and interest on debt diminish
the taxable income (don‘t confuse taxable
income with cash flow
3. As the cash flow now reflects after tax
figures, the concept of opportunity costs
also has to be adjusted to after tax interest
rates (rafter tax = rbefore tax x (1 – t);{t = tax rate}.
The Tax Paradoxon
Two mutually exclusive investment proposals show the
following cash flows over three years (without taxes):
0
1
Investment 1
-1500
+ 100
Investment 2
-1500 + 1000
2
3
+ 800 + 1000
+ 700
+ 100
0
1
2
3
NPV
Inv. 1
-1.500,0
90,9
661,2
751,3
3,38
Inv. 2
-1.500,0
909,1
578,5
75,1
62,73
r = 10%
s = 0%
The Tax Paradoxon
Discounted cash flows lead to following N.P.V.s. At
10% and no taxes, Investment 2 is clearly dominant.
+1,000
+700
+ 100
+3,38
- 1,500
0
1
2
3
N.P.V.
Inv.1
-1500
+ 100
+ 800
+ 1000
+ 3,38
Inv.2
-1500
+ 1000
+ 700
+ 100
+ 62,73
The Tax Paradoxon
At a given tax rate, the NPV is a continously decreasing
function of the opportunity cost of capital
500
NPV 1
NPV 2
400
NPV 2 > NPV 1
300
200
100
0
0%
-100
-200
-300
-400
5%
10%
15%
20%
25%
The Tax Paradoxon
Considering a corporate tax rate of 40 %, the NPV result
changes to:
0
1
2
3
Investment 1
-1500
+ 100
+ 800
+ 1000
Investment 2
-1500
+ 1000
+ 700
+ 100
-500
-500
-500
Depreciation
NPV
Tax payments 1
0
+ 160
-120
-200
Tax payments 2
0
-200
-80
+160
Cash flow after tax 1
-1500
+260
+680
+800
Cash flow after tax 2
-1500
+800
+620
+260
P.V. after tax 1
-1500
+245,3
+605,2
+671,7 + 22,2
P.V. after tax 2
-1500
+754,7
+551,8
+218,3 + 24,8
The Tax Paradoxon
NPV after tax can also be calculated in a step-by-step
mode, i.e. The project‘s NPV consists of the NPV of the
cash flows and the NPV of the tax payments:
0
1
2
3
Cash flow before tax
-1500
+ 100
+ 800
+ 1000
Present values
-1500
+ 94.34
+ 712
+ 839.62
Tax payments
0
- 40
- 320
- 400
Present values
0
- 37.73
-284.80
-335.85
+ 200
+ 200
+ 200
+ 188.68
+ 178
Tax shield
NPV
+ 145.96
- 658.38
(Depreciation x tax rate)
Present values
+ 167.92 + 534.60
22.2
The Tax Paradoxon
At a given discount rate, the first cash flows NPV starts
rising according to rising tax rates (Tax Paradox). A tax
rate of approx. 50% would affect the ranking order .... !!!
NPV after tax (rbefore tax = 10%)
70
NPV 1
NPV 2
60
50
40
30
20
10
0
0
10
20
30
40
50
Tax rates
60
70
80
90
100
Inflation Effects / FX Rates
Sometimes there is uncertainty about the question how to
include inflationary effects.
Basically nominal cash flows need to be discounted by nominal
(inflated) discount rates, while cash flows which reflect the
purchase power must be discounted using real rates.
Following nominal cash flows do include a yearly inflation rate of
15%. The expected real rate is supposed to be 10%:
Year
Cash Flow
(Nominal Values)
Present Values
at real rates
N.P.V.
0
-20.000.000
1
15.000.000
2
15.000.000
-20.000.000
13.636.364
12.396.694 6.033.058
Inflationary Effects
Year
Cash Flow
(Nominal Values)
Present Values
at real rates
N.P.V.
0
-20.000.000
1
15.000.000
2
15.000.000
-20.000.000
13.636.364
12.396.694 6.033.058
The use of nominal cash flows and real discount rates will not
lead to a correct result. A first solution would be, to inflate the
real discount rate:
1  rnom  1  rreal   1  d 
A second solution could mean, to deflate the nominal cash
flows and use the real discount rate:
CFt , real  CFt ,nom .
1

1  d t
Inflation Effects / FX Rates
After inflating the real discount rate of 10% with an inflation
rate of 15%, the nominal discount rate is at:
1  rnom  1  0 ,10   1  0 ,15 
rnom  26 ,5%
Year
Cash Flow
(Nominal Values)
Present Values
at inflated rates
0
-20.000.000
1
15.000.000
2
15.000.000
N.P.V.
-20.000.000
11.857.708
9.373.682
1.231.389
Consequently, the N.P.V. will drop to 1,231 Mio €.
Inflation Effects / FX Rates
Another way round, we could also transfer nominal cash flows
into real figures:
CF2 , real
CF2 , real
1
 15 Mio 
2
1  0 ,15 
 11.342.155 €
Year
Cash Flow
(nominal)
Cash Flow
(real)
0
-20.000.000
1
15.000.000
2
15.000.000
-20.000.000
13.043.478
11.342.155
Present Values
(at real rates)
-20.000.000
11.857.708
9.373.682
Consequently the N.P.V. Now remains the same.
N.P.V.
1.231.389
Inflation Effects / FX Rates
Two alternative ways to avoid a wrong way of calculation:
All figures reflect „real“ data, i.e. real (not in - or deflated) cash
flows and real discount rates (expected grow of purchasing
power):
CFt , real  CFt ,nom .
1

t
1  d 
All figures reflect „nominal“ data, i.e. nominal (in- or deflated)
cash flows and nominal discount rates (usually inflated interest
rate):
1  rnom  1  rreal   1  d 
Inflation Effects / FX Rates
CF
rbef. tax
Tc
rafter tax
dlocal
dforeign
EXR0
s.u.
10%
50%
5%
2%
10%
1000:1
0
Investment
Cash Flow In
Cash Flow Out
Cash Flow before taxes
Depreciation
Corporate Taxes
Cash Flow after taxes
Present Values
1
2
-10.000.000
-10.000.000
-10.000.000
-10.000.000
12.000.000
-5.000.000
7.000.000
-5.000.000
-1.000.000
6.000.000
5.714.286
12.000.000
-5.000.000
7.000.000
-5.000.000
-1.000.000
6.000.000
5.442.177
Cash Flows (FC)
Depreciation (straight)
Tax rate 50%
Disc.rate(before tax) 10%
Disc.rate(after tax) 5%
NPV
1.156.463
In the view of the foreign country based subsidiary, the N.P.V. is at
1.156.463 Mrd.
Inflation Effects / FX Rates
CF
rbef. tax
Tc
rafter tax
dlocal
dforeign
EXR0
s.u.
10%
50%
5%
2%
10%
1000:1
The NPV can also be calculated as the sum of the cash flows
present values before taxes and the present value of the tax
payments:
Cash Flow before taxes
Corporate taxes
-10.000.000
7.000.000
-1.000.000
7.000.000
-1.000.000
PV Cash Flows
PV tax payments
-10.000.000
6.666.667
-952.381
6.349.206
-907.029
Adjusted Present Value
(A.P.V.)
NPV
3.015.873
-1.859.410
1.156.463
Inflation
Effects Effects
/ FX Rates
Inflationary
/ Foreign Exchange
Rates
CF
rbef. tax
Tc
rafter tax
dhome
dforeign
EXR0
s.u.
10%
50%
5%
2%
10%
1000:1
Regarding the foreign inflation rate, the local N.P.V. drops to 546,467. Cash
Flows increased but discount rate adjusted to 15,5% ( = 1,05*1,10 ).
date of payment
Investment
Cash Flow In
Cash Flow Out
Cash Flow before taxes
Depreciation
Corporate taxes
Cash Flow after taxes
Present Values
0
1
2
-10.000.000
-10.000.000
-10.000.000
-10.000.000
13.200.000
-5.500.000
7.700.000
-5.000.000
-1.350.000
6.350.000
5.497.835
14.520.000
-6.050.000
8.470.000
-5.000.000
-1.735.000
6.735.000
5.048.631
NPV
546.467
Inflation Effects / FX Rates
CF
rbef. tax
Tc
rafter tax
dlocal
dforeign
EXR0
s.u.
10%
50%
5%
2%
10%
1000:1
Considering the different sources of NPV it becomes clear, that
it is not the PV of the operational cash flow which has changed,
but the PV of tax payments. In our example the smaller NPV is
exclusively caused by higher tax payments.
Corporate taxes
PV Cash Flows
PV Tax payments
-10.000.000
-1.350.000
-1.735.000
6.666.667
-1.168.831
6.349.206
-1.300.575
3.015.873
-2.469.406
546.467
Inflation Effects / FX Rates
• Inflation alone, under certain circumstances, (completely
passed on to customers and suppliers, no supply- or demandshifts) does not change the valuation of an investment. A
smaller NPV then will be exclusively caused by higher tax
payments (taxation of pseudo-profits). Tax authorities profit
from inflation.
• The investegated negative impact of inflation on the
economical attractiveness of investment proposals could be
avoided, if tax authorities would refrain from taxation of
pseudo profits.
• In the simplest way inflationary effects could be cancelled out
by depreciation on the basis of higher, inflated purchase
costs.
Inflation Effects / FX Rates
If purchasing costs are continously inflated and
depreciation is calculated on the basis of
increasing current costs (per year + 10%) :
Investment (Reproduction Value)
AfA (Reproduction Value
Date of Payment
Investment
Cash Flow In
Cash Flow Out
Cash Flow before taxes
Depreciation
Corporate taxes
Cash Flow after taxes
Present Values
0
0
10.000.000
-5.000.000
1
1
11.000.000
-5.500.000
2
12.100.000
-6.050.000
2
-10.000.000
-10.000.000
-10.000.000
-10.000.000
13.200.000
-5.500.000
7.700.000
-5.500.000
-1.100.000
6.600.000
5.714.286
14.520.000
-6.050.000
8.470.000
-6.050.000
-1.210.000
7.260.000
5.442.177
NPV
1.156.463
Inflation Effects / FX Rates
Tax deductible depreciation based on current market prices,
would neutralize the negative effects of inflation on N.P.V.
Cash Flow before taxes
Corporate taxes
-10.000.000
7.700.000
-1.100.000
8.470.000
-1.210.000
PV Cash Flows
PV Tax payments
-10.000.000
6.666.667
-952.381
6.349.206
-907.029
Cash Flow before taxes
Corporate taxes
-10.000.000
7.000.000
-1.000.000
7.000.000
-1.000.000
PV Cash Flows
PV Tax payments
-10.000.000
6.666.667
-952.381
6.349.206
-907.029
NPV
3.015.873
-1.859.410
1.156.463
NPV
3.015.873
-1.859.410
1.156.463
Inflation Effects / FX Rates
What will be the effect of inflated cash flows in foreign currencies, if the foreign cash flows are transferred at the end of
each period ?
If international interest rate differences are perfectly reflected
by a perfectly (unregulated) working foreign exchange rate
mechanism, future exchange rates (EXR) are to be calculated
using the „Fisher Equation“:
EXRt
 EXR0

1  dinside t
t
1  d outside 

1  0 ,02
1
1  0 ,10
in example for t1:
1
EXR1
 EXR0

EXR0  0 ,9273
Inflation Effects / FX Rates
1  0 ,02 
1  0 ,10 
2
EXR 2
Investment
Cash Flow In
Cash Flow Out
Cash Flow before taxes
Depreciation
Tax payments
Cash Flow a. taxes (LC)
Exchange Rates (€/B)
Cash Flow in Euro

EXR 0

2
 EXR 0  0 ,8598
-10.000.000
-10.000.000
-10.000.000
1,0000
-10.000.000
13.200.000
-5.500.000
7.700.000
-5.000.000
-1.350.000
6.350.000
0,9273
5.888.182
14.520.000
-6.050.000
8.470.000
-5.000.000
-1.735.000
6.735.000
0,8598
5.790.987
NPV
Present Values
at 7,1 % out of ((1,02*1,05)-1) -10.000.000
5.497.835
5.048.631
546.467
If an exchange rate mechanism is perfectly working, the profitability (in terms of NPV) of real investment projects are not affected. Lower Cash Flows – due to impaired exchange rates –
are then perfectly substituted by lower discount rates.