Tfin 2009 06 Investment Decisions

8/13/2019 Tfin 2009 06 Investment Decisions

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Thorie Financire

6. Analyse de projets dinvestissementro esseur n r ar er


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NPV - Review

NPV: measure chan e in market value of com an if ro ect acce ted As market value of company V = PV(Future Free Cash Flows)

t FCF

V = V with project - V without project+t t r )1(

as ows o cons er: cash flows (not accounting numbers)

do not for et de reciation and chan es in WCR incremental (with project - without project)

forget sunk costs include opportunity costs include all incidental effects

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Investment rules

Net Present Value NPV Discounted incremental free cash flows

Rule: invest if NPV>0 IRR Internal Rate of Return (IRR)

IRR: discount rate such that NPV=0 r

u e: nves os o cap a Payback period

Numbers of ear to recou initial investment No precise rule

Profitability Index (PI) PI = NPV / Investment Useful to rank projects if capital spending is limited



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What do CFOs Use?

% Always or Almost Always

Internal Rate of Return 75.6% Net Present Value 74.9% ay ac per o . Discounted payback period 29.5% Accountin rate of return 30.3% Profitability index 11.9%

Based on a survey of 392 CFOs

Source: Graham, John R. and Harve R. Cam bell, The Theor and Practice of Cor orate Finance: Evidence from the Field,


Journal of Financial Economics 2001


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Internal Rate of Return IRR

Can be viewed as the ield to maturit of the ro ect Remember: the yield to maturity on a bond is the rate that set the

present value of the expected cash flows equal to its price Consider the net investment as the price of the project

The IRR is the rate that sets the present value of the expected cashflows e ual to the net investment

The IRR is the rate that sets the net present value equal to zero



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IRR Pitfall 1: Lendin or borrowin ?

Consider followin ro ects:

0 1 IRR NPV(10%)

IRR: borrowing or lending?

30.00 - . B +100 -120 20% -9.09

10.00

20.00

n t V a l u e

A: lending Rule IRR>r B: borrowing Rule IRR


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IRR Pitfall 2 Multi le Rates of Return

Consider the followin ro ect Year 0 1 2

CF -1,600 10,000 -10,000

Multiple Rates of Return

1500.00

2 IRRs : +25% & +400%500.00

1000.00

t V a l u e

This happens if more than one changein sign of cash flows-1000.00

-500.00

.

0 % 4 5 %

9 0 %

1 3 5 %

1 8 0 %

2 2 5 %

2 7 0 %

3 1 5 %

3 6 0 %

4 0 5 %

4 5 0 %

4 9 5 %

N e t P r e s e n

To overcome problem, use modifiedIRR method Reinvest all intermediate cash flows at the

-2000.00

-1500.00

Discount Rate

cost of capital till end of project Calculate IRR using the initial investment

and the future value of intermediate cash



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IRR Pitfall 3 - Mutuall Exclusive Pro ects

Scale Problem ( r = 10%) Timin Problem ( r = 10%)C 0 C 1 C 2 NPV IRR

A -100 +20 +120 17.4 20.0%0 1

Small -10 +20 8.2 100%Large -50 +80 22.7 60%

- . .

A-B 0 -60 +68 1.7 13.3%

To choose, look at incremental cashflows

C 0 C 1 NPV IRR

L-S -40 +60 14.5 50%



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Mutuall Exclusive Pro ect - Illustration

50.0

40.0

30.0

10.0

.

B

0.0

0.0% 2.5% 5.0% 7.5% 10.0% 12.5% 15.0% 17.5% 20.0% 22.5% 25.0% 27.5% 30.0% 32.5%

-20.0

-10.0



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Inflation

Be consistent in how ou handle inflation Discount nominal cash flows at nominal rate

Discount real cash flows at real rate Both approaches lead to the same result.

=

Inflation rate = 5% Real discount rate = 10%

Discount real cash flow using real rate

PV = 100 / (1.10)3 = 75.13Discount nominal cash flow using nominal rate

Nominal cash flow = 100 (1.05)3

= 115.76= = . . - .PV = 115.76 / (1.155)3 = 75.13



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Investment Pro ect Anal sis: BOF

Year 0 1 2 3

Initial Investment 60

Resale value 20

Sales 100 100

Corporate tax rate = 40%Working Capital Requirement = 25% SalesDiscount rate = 10%



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BOF: Free Cash Flow Calculation

Year 0 1 2 3

Sales 100 100

Cost of sales 50 50

EBITDA 50 50

Depreciation 30 30

EBIT 20 20

axes

Net income 12 12 -8

Net income 12 12 -8

Depreciation 30 30 0DWCR 25 0 -25

CFInvestment -60 20


ree as ow -


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BOF: o ahead?

NPV calculation:96.17

)10.1()10.1(10.160 32

=+++= NPV

Internal Rate of Return = 24%

ay ac per o = years



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BOF: checkin the numbers

Sensitivit anal sis What if expected sales below expected value?

Sales 60 70 80 90 100

NPV -22.11 -12.09 -2.07 7.95 17.96

Break-even oint What is the level of sales required to break even?

Break even sales = 82



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BOF Pro ect with inflation rate = 100%

Nominal free cash flows

Year 0 1 2 3

Sales 200 400ost o sa es

EBITDA 100 200Depreciation 30 30

Taxes 28 68 64 Net income 42 102 -64

Net income 42 102 -64Depreciation 30 30 0

WCR 50 50 -100CFInvestment -60 160Free Cash Flow -60 22 82 196

Nominal discount rate = (1+10%)(1+100%)-1 = 120%


NPV = -14.65 IRR = 94%


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A ro ect is not a black box

Sensitivit anal sis: analysis of the effects of changes in sales, costs,.. on a project.

Scenario analysis: project analysis given a particular combination of assumptions.

Simulation analysis: es ma ons o e pro a es o eren ou comes.

Break even analysis anal sis of the level of sales at which the com an breaks even.



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Sensitivit anal sis

Year 0 Year 1-5Initial investment 1,500

Revenues 6,000Variables costs (3,000)Fixed costs (1,791)

eprec a onPretax Profit 909Tax T = 34% 309

Net Profit 600

Cash flow 900

NPV calculation (for r = 15%):


= - , . = ,


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Sensitivit anal sis usin Excel

=C12 Result to calculate

10

20

xcerecalculatesusing these

30

Values to use

(in cell B3 for

values



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Sensitivit anal sis

1. Identi ke variables

Revenues = Nb engines sold Price per engine 6,000 3,000 2 Nb engines sold = Market share Size of market , . , V.Cost =V.cost per unit Number of engines 3 000 1 3 000 Total cost = Variable cost + Fixed costs

4,791 3,000 1,791



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Sensitivit anal sis

2. Pre are essimistic best o timistic orecasts bo

Variable Pessimistic Best Optimistic Market size 5,000 10,000 20,000 Market share 20% 30% 50% r ce . . V.cost / unit 1.2 1 0.8 Fixed cost 1 891 1 791 1 741 Investment 1,900 1,500 1,000



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Scenario anal sis

Consider lausible combinations of variables Ex: If recession

- market share low- variable cost high- price low



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Monte Carlo simulation

Tool for considerin all combinations model the project

specify probabilities for forecast errors select numbers for forecast errors and calculate cash flows

u come: s mu a e s r u on o cas ows



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Standard normal random variable eneration

1.00

0.80

0.90

RAND()

0.60

0.70 ALEA()

0.40

0.50

0.20

0.30

0.00

0.10

NORMSINV(RAND())

LOI.NORMALE.STANDARD.INVERSE(ALEA())

September 15, 2009 Tfin 06 Capital budgeting |25 -

3 . 0

0

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2 . 8

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2 . 6

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2 . 4

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2 . 2

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-

2 . 0

0

-

1 . 8

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-

1 . 6

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1 . 4

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1 . 2

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-

1 . 0

0

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0


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Break even anal sis

Sales level to break-even? 2 views

Account Profit Break-Even Point:

Accountin rofit = 0

Present Value Break-Even Point:

NPV = 0



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Break even anal sis with Excel

Use Goal Seek Valeur cible

Tell Excel to change the value of one variable until NPV = 0



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Timin

Even ro ects with ositive NPV ma be more valuable if deferred. Example

You may sell a barrel of wine at anytime over the next 5 years.Given the future cash flows, when should you sell the wine?

0 1 2 3 4 5

as ow

% change 30% 20% 15% 12% 8%

Suppose discount rate r = 10%Wait NPV so now = 100

NPV if sold in year 1 = 130 / 1.10 = 118



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When to invest

Traditional NPV rule: invest if NPV>0. Is it alwa s valid? Suppose that you have the following project:

Cost I = 100 Present value of future cash flows V = 150 Possibility to mothball the project

ou you s ar e pro ec If you choose to invest, the value of the project is: Traditional NPV = 150 - 100 = 50 >0 What if you wait?



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To mothball or not to mothball?

Su ose that the ro ect mi ht be dela ed for one ear. One year later:

Cost is unchanged (I = 100) Present value of future cash flow = 160 NPV1 = 160 - 100 = 60 in year 1

o ec e: compare presen va ues a me . Invest now : NPV = 50 Invest one ear later: NPV = PV NPV = 60/1.10 = 54.5

Conclusion: you should delay the investment

+ Benefit from increase in present value of future cash flows (+10)+ Save cost of financing of investment (=10% * 100 = 10)- Lose return on real asset (=10% * 150 = 15)



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E uivalent Annual Cost

The cost er eriod with the same resent value as the cost of bu in andoperating a machine.

Equivalent Annual Cost = PV of costs / Annuity factor Example: cheap & dirty vs good but expensive Given a 10% cost of capital, which of the following machines

would ou bu ?C 0 C 1 C 2 C 3 PV EAC

A 15 4 4 4 24.95 10.03

B 10 6 6 20.41 11.76

EAC calculation:A: EAC = PV(Costs) / 3-year annuity factor = 24.95 / 2.487 = 10.03B: EAC = PV Costs / 2- ear annuit factor = 20.41 / 1.735 = 11.76



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The Decision to Re lace

When to re lace an existin machine with a new one? Calculate the equivalent annual cost of the new equipment

Calculate the yearly cost of the old equipment (likely to rise overtime as equipment becomes older) Replace just before the cost of the old equipment exceeds the EAC

on new e ui ment

Example Annual operating cost of old machine = 8 Cost of new machine : C 0 C 1 C 2 C 3

15 5 5 5 r = = .

EAC = 27.4 / 3-year annuity factor = 11 Do not re lace until o eratin cost of old machine exceeds 11


Tfin 2009 06 Investment Decisions

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