Berlin, 04.01.2006Fußzeile1 Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of...

Berlin, 04.01.2006 Fußzeile 1

Professor Dr. Rainer Stachuletz

Corporate Finance

Berlin School of Economics

Capital Budgeting(Chapter 8)

Berlin, 18th of June, 2007 Fußzeile 2

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.


Capital Budgeting Decision Techniques

Payback period: most commonly used

Accounting rate of return (ARR): focuses on project’s impact on accounting profits

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


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.


Accounting Rate Of Return (ARR)

Can be computed from available accounting data

ARR uses accounting numbers, not cash flows; no time value of money.

vestmentAverage in

r taxesofits afteAverage prARR

Average profits after taxes

Average annual operating cash inflows

Average annual depreciation

= -

• 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.


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.


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.

NN

r

CF

r

CF

r

CF

r

CFCFNPV

)(...

)()()(

1111 33

221

0

Accept projects if NPV > 0.

Berlin, 04.01.2006 Fußzeile 8

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

$175Year 5 inflow

$160Year 4 inflow

$130Year 3 inflow

$80Year 2 inflow

$35Year 1 inflow

-$250Initial outlay

$32Year 5 inflow

$30Year 4 inflow

$25Year 3 inflow

$22Year 2 inflow

$18Year 1 inflow

-$50Initial outlay

Western Europe ($ millions) Southeast U.S. ($ millions)


Calculating NPVs for Global Wireless Projects

Assuming Global Wireless uses 18% discount rate, NPVs are:

5432 )18.1(

175

)18.1(

160

)18.1(

130

)18.1(

80

)18.1(

352503.75$ EuropeWesternNPV

5432.. )18.1(

32

)18.1(

30

)18.1(

25

)18.1(

22

)18.1(

18507.25$ SUSoutheastNPV

Western Europe project: NPV = $75.3 million

Southeast U.S. project: NPV = $25.7 million

Should Global Wireless invest in one project or both?


Pros and Cons of Using NPV as Decision Rule

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.

NPV is the “gold standard” of investment decision rules.


Internal Rate of Return

NN

r

CF

r

CF

r

CF

r

CFCFNPV

)(....

)()()(

11110

33

221

0

• IRR found by computer/calculator or manually by trial and error.

Internal rate of return (IRR) is the discount rate that results in a zero NPV for the project:

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.


Calculating IRRs for Global Wireless Projects

Western Europe project: IRR (rWE) = 27.8%

5432 )1(

175

)1(

160

)1(

130

)1(

80

)1(

352500

WEWEWEWEWE rrrrr

Southeast U.S. project: IRR (rSE) = 36.7%

5432 )1(

32

)1(

30

)1(

25

)1(

22

)1(

18500

SESESESESE rrrrr

Global Wireless will accept all projects with at least 18% IRR.


-100,0

-50,0

0,0

50,0

100,0

150,0

200,0

250,0

300,0

350,0

0,0% 5,0% 10,0% 15,0% 20,0% 25,0% 30,0% 35,0% 40,0% 45,0%

W.EuropeS. U.S.

Calculating IRRs for Global Wireless Projects

12

1211 NPVNPV

rrNPVrr IRR

%91.27

6.184.13

%25%306.18%25

27.91%


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


Multiple IRRs

NPV ($)

NPV<0

NPV>0

NPV>0

Discount rateNPV<

0

With multiple IRRs, which do we compare with the cost of capital to accept/reject the

project?

IRR

IRR

When project cash flows have multiple signchanges, there can be multiple IRRs.


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!


Conflicts Between NPV and IRR

NPV and IRR do not always agree when ranking competing projects.

$25.7 mn36.7%Southeast U.S.

$75.3 mn27.8%Western Europe

NPV (18%)IRRProject

• Southeast U.S. project has higher IRR, but doesn’t increase shareholders’ wealth as much as Western Europe project.

The scale problem:


The Timing Problem

• The NPV of the long-term project is more sensitive to the discount rate than the NPV of the short-term project is.

Discount rate

Short-term project

Long-term project

17%15%

NPV

13%

IRR = 15%

IRR = 17%

• 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%.


Profitability Index

Decision rule: Accept project with PI > 1.0, equal to NPV > 0

0

221

)1(...

)1()1(CF

r

CF

r

CF

r

CF

PIN

N

• Both projects’ PI > 1.0, so both acceptable if independent.

1.5$50 million$75.7 millionSoutheast U.S.

1.3$250 million$325.3 millionWestern Europe

PIInitial OutlayPV of CF (yrs1-5)

Project

Calculated by dividing the PV of a project’s cash inflows by the PV of its outflows:

Like IRR, PI suffers from the scale problem.

Some Extensions.............


• The Tax ParadoxonTax 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.

• InflationWe always have to make sure, that nominal cash flows must refer to nominal discount rates while real cash flows require real discoount rates.

• Exchange RatesIf global financial markets are working well, the effect of different inflation rates will be perfectly substituted by a well functioning exchange rate mechanism.

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

0 1 2 3

Investment 1 -1500 + 100 + 800 + 1000

Investment 2 -1500 + 1000 + 700 + 100r = 10%s = 0%

Two mutually exclusive investment proposals show the following cash flows over three years (without taxes):

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

Discounted cash flows lead to following N.P.V.s. At 10% and no taxes, Investment 2 is clearly dominant.

0 1 2 3 N.P.V.

Inv.1 -1500 + 100 + 800 + 1000 + 3,38

Inv.2 -1500 + 1000 + 700 + 100 + 62,73

- 1,500

+ 100

+700+1,000

+3,38

The Tax Paradoxon

The Tax Paradoxon

At a given tax rate, the NPV is a continously decreasing function of the opportunity cost of capital

-400

-300

-200

-100

0

100

200

300

400

500

0% 5% 10% 15% 20% 25%

NPV 1 NPV 2

NPV 2 > NPV 1

The Tax Paradoxon

Considering a corporate tax rate of 40 %, the NPV result changes to:

0 1 2 3 NPV

Investment 1 -1500 + 100 + 800 + 1000

Investment 2 -1500 + 1000 + 700 + 100

Depreciation -500 -500 -500

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 + 22,2P.V. after tax 2 -1500 +754,7 +551,8 +218,3 + 24,8

The Tax ParadoxonNPV 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 NPV

Cash flow before tax -1500 + 100 + 800 + 1000

Present values -1500 + 94.34 + 712 + 839.62 + 145.96

Tax payments 0 - 40 - 320 - 400

Present values 0 - 37.73 -284.80 -335.85 - 658.38

Tax shield(Depreciation x tax rate)

+ 200 + 200 + 200

Present values + 188.68 + 178 + 167.92 + 534.60

22.2

The Tax Paradoxon

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

NPV 1 NPV 2

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 .... !!!

Tax rates

NP

V a

fter

tax

(rb

efor

e ta

x =

10

%)

Year 0 1 2 N.P.V.Cash Flow -20.000.000 15.000.000 15.000.000(Nominal Values)Present Values -20.000.000 13.636.364 12.396.694 6.033.058at real rates

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 0 1 2 N.P.V.Cash Flow -20.000.000 15.000.000 15.000.000(Nominal Values)Present Values -20.000.000 13.636.364 12.396.694 6.033.058at real rates

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:

A second solution could mean, to deflate the nominal cash flows and use the real discount rate:

drr realnom 111

tnomtrealtd

CFCF

1

1.,,

Inflationary Effects

Year 0 1 2 N.P.V.Cash Flow -20.000.000 15.000.000 15.000.000(Nominal Values)Present Values -20.000.000 11.857.708 9.373.682 1.231.389at inflated rates

%,

,,

526

150110011

nom

nom

r

r

After inflating the real discount rate of 10% with an inflation rate of 15%, the nominal discount rate is at:

Consequently, the N.P.V. will drop to 1,231 Mio €.


Another way round, we could also transfer nominal cash flows into real figures:

Year 0 1 2 N.P.V.Cash Flow -20.000.000 15.000.000 15.000.000(nominal)Cash Flow -20.000.000 13.043.478 11.342.155(real)

Present Values -20.000.000 11.857.708 9.373.682 1.231.389(at real rates)

Consequently the N.P.V. Now remains the same.

€..

,

,

,

15534211

1501

115

2

22

real

real

CF

MioCF


Two alternative ways to avoid a wrong way of calcu-lation:

All figures reflect „real“ data, i.e. real (not in - or deflated) cash flows and real discount rates (expected grow of purchasing power):

All figures reflect „nominal“ data, i.e. nominal (in- or deflated) cash flows and nominal discount rates (usually inflated interest rate):

drr realnom 111

tnomtrealtd

CFCF

1

1.,,


0 1 2Investment -10.000.000Cash Flow In 12.000.000 12.000.000Cash Flow Out -5.000.000 -5.000.000Cash Flow before taxes -10.000.000 7.000.000 7.000.000Depreciation -5.000.000 -5.000.000Corporate Taxes -1.000.000 -1.000.000Cash Flow after taxes -10.000.000 6.000.000 6.000.000

NPVPresent Values -10.000.000 5.714.286 5.442.177 1.156.463

CF rbef. tax Tc rafter tax dlocal dforeign EXR0

s.u. 10% 50% 5% 2% 10% 1000:1

In the view of the foreign country based subsidiary, the N.P.V. is at 1.156.463 Mrd.


Cash Flows (FC)Depreciation (straight)Tax rate 50%Disc.rate(before tax) 10%Disc.rate(after tax) 5%

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 -10.000.000 7.000.000 7.000.000 NPVCorporate taxes -1.000.000 -1.000.000

PV Cash Flows -10.000.000 6.666.667 6.349.206 3.015.873PV tax payments -952.381 -907.029 -1.859.410

1.156.463

Adjusted Present Value (A.P.V.)


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 0 1 2Investment -10.000.000Cash Flow In 13.200.000 14.520.000Cash Flow Out -5.500.000 -6.050.000Cash Flow before taxes -10.000.000 7.700.000 8.470.000Depreciation -5.000.000 -5.000.000Corporate taxes -1.350.000 -1.735.000Cash Flow after taxes -10.000.000 6.350.000 6.735.000

NPVPresent Values -10.000.000 5.497.835 5.048.631 546.467

Inflationary Effects / Foreign Exchange Rates

CF rbef. tax Tc rafter tax dhome 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 -1.350.000 -1.735.000

PV Cash Flows -10.000.000 6.666.667 6.349.206 3.015.873PV Tax payments -1.168.831 -1.300.575 -2.469.406

546.467


s.u. 10% 50% 5% 2% 10% 1000:1


•Inflation alone, under certain circumstances, (completely passed on to customers and suppliers, no supply- or demand-shifts) 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.


0 1 2Investment (Reproduction Value) 10.000.000 11.000.000 12.100.000AfA (Reproduction Value -5.000.000 -5.500.000 -6.050.000

Date of Payment 0 1 2Investment -10.000.000Cash Flow In 13.200.000 14.520.000Cash Flow Out -5.500.000 -6.050.000Cash Flow before taxes -10.000.000 7.700.000 8.470.000Depreciation -5.500.000 -6.050.000Corporate taxes -1.100.000 -1.210.000Cash Flow after taxes -10.000.000 6.600.000 7.260.000

NPVPresent Values -10.000.000 5.714.286 5.442.177 1.156.463

If purchasing costs are continously inflated and depreciation is calculated on the basis of increasing current costs (per year + 10%) :


Cash Flow before taxes -10.000.000 7.700.000 8.470.000 NPVCorporate taxes -1.100.000 -1.210.000

PV Cash Flows -10.000.000 6.666.667 6.349.206 3.015.873PV Tax payments -952.381 -907.029 -1.859.410

1.156.463

Tax deductible depreciation based on current market prices, would neutralize the negative effects of inflation on N.P.V.

Cash Flow before taxes -10.000.000 7.000.000 7.000.000 NPVCorporate taxes -1.000.000 -1.000.000

PV Cash Flows -10.000.000 6.666.667 6.349.206 3.015.873PV Tax payments -952.381 -907.029 -1.859.410

1.156.463


What will be the effect of inflated cash flows in foreign curren-cies, 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“:

t

outside

tinside

td

dEXREXR

1

10 in example for t1:

9273,0EXR

10,01

02,01EXREXR 01

1

01


Investment -10.000.000Cash Flow In 13.200.000 14.520.000Cash Flow Out -5.500.000 -6.050.000Cash Flow before taxes -10.000.000 7.700.000 8.470.000Depreciation -5.000.000 -5.000.000Tax payments -1.350.000 -1.735.000Cash Flow a. taxes (LC) -10.000.000 6.350.000 6.735.000Exchange Rates (€/B) 1,0000 0,9273 0,8598Cash Flow in Euro -10.000.000 5.888.182 5.790.987

NPVPresent Valuesat 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 profit-ability (in terms of NPV) of real investment projects are not af-fected. Lower Cash Flows – due to impaired exchange rates – are then perfectly substituted by lower discount rates.

8598,0EXR

10,01

02,01EXREXR

02

2

02


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