Théorie Financière 6. Analyse de projets … 2009 06 Investment... · Théorie Financière 6....

Théorie Financière

6. Analyse de projets d’investissement

P f A d é F bProfesseur André Farber

NPV - Review

• NPV: measure change in market value of company if project acceptedN V: easu e c a ge a et va ue o co pa y p oject accepted• As market value of company V = PV(Future Free Cash Flows)

∑Δ

=Δ= tFCFVNPV

• ΔV = Vwith project - Vwithout project

• Cash flo s to consider:

∑+

=Δ=t tr

VNPV)1(

• Cash flows to consider:– cash flows (not accounting numbers)

• do not forget depreciation and changes in WCRg p g– incremental (with project - without project)

• forget sunk costs• include opportunity costs• include all incidental effects• beware of allocated overhead costs

September 15, 2009 Tfin 06 Capital budgeting |2

• beware of allocated overhead costs

Investment rules

• Net Present Value (NPV) NPVNet ese t Va ue (N V)– Discounted incremental free cash flows– Rule: invest if NPV>0

NPV

IRR

• Internal Rate of Return (IRR)– IRR: discount rate such that NPV=0

R le: in est if IRR > Cost of capital

r

– Rule: invest if IRR > Cost of capital• Payback period

– Numbers of year to recoup initial investmenty p– No precise rule

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


What do CFOs Use?

• % Always or Almost Always

• Internal Rate of Return 75.6%• Net Present Value 74.9%• Pa back period 56 7%• Payback period 56.7%• Discounted payback period 29.5%• Accounting rate of return 30.3%g• Profitability index 11.9%

• Based on a survey of 392 CFOs

Source: Graham, John R. and Harvey R. Campbell, “The Theory and Practice of Corporate Finance: Evidence from the Field”,


, y p , y p ,Journal of Financial Economics 2001

Internal Rate of Return IRR

• Can be viewed as the “yield to maturity” of the projectCa be v ewed as t e y e d to atu ty o t e p oject• 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 cash flows equal to the net investmentq

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


IRR Pitfall 1: Lending or borrowing?g g

• Consider following projects:g p j

• 0 1 IRR NPV(10%)A 100 +120 20% 9 09

IRR: borrowing or lending?

30.00• A -100 +120 20% 9.09• B +100 -120 20% -9.09

0 00

10.00

20.00

ent V

alue

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

-20.00

-10.00

0.00

0% 3% 6% 9%12% 15% 18% 21% 24% 27% 30%

Net P

rese

-30.00

Discount rate

Project A Project B


IRR Pitfall 2 Multiple Rates of Returnp

• Consider the following projectg p j• Year 0 1 2• CF -1,600 10,000 -10,000

Multiple Rates of Return

1500.00

• 2 “IRRs” : +25% & +400%

0 00

500.00

1000.00

t Val

ue

• This happens if more than one change in sign of cash flows

-1000.00

-500.00

0.00

0% 45%

90%

135%

180%

225%

270%

315%

360%

405%

450%

495%

Net

Pre

sen

• To overcome problem, use modified IRR 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 flows


flows

IRR Pitfall 3 - Mutually Exclusive Projectsy j

Scale Problem (r = 10%) Timing Problem (r = 10%)( )

C C NPV IRR

g ( )C0 C1 C2 NPV IRR

A -100 +20 +120 17.4 20.0%B 100 +80 +52 15 7 22 5%C0 C1 NPV IRR

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

B -100 +80 +52 15.7 22.5%

A-B 0 -60 +68 1.7 13.3%

To choose, look at incremental cash flows

C0 C1 NPV IRRL-S -40 +60 14.5 50%


Mutually Exclusive Project - Illustrationy j

50.0

40.0

A

20 0

30.0A

10.0

20.0

B

0.00.0% 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


20.0

Inflation

• Be consistent in how you handle inflatione co s ste t ow you a d e at o• Discount nominal cash flows at nominal rate• Discount real cash flows at real rate

– Both approaches lead to the same result.

• Example: Real cash flow in year 3 = 100 (based on price level at time 0)• Example: Real cash flow in year 3 = 100 (based on price level at time 0)– 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 = 115.76Nominal discount rate = (1 10)(1 05)-1 = 15 5%Nominal discount rate = (1.10)(1.05)-1 = 15.5%PV = 115.76 / (1.155)3 = 75.13


Investment Project Analysis: BOFj y

Big Oversea Firm is considering the project

Year 0 1 2 3

Big Oversea Firm is considering the project

Initial Investment 60

Resale value 20

Sales 100 100

Cost of sales 50 50Cost of sales 50 50

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


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

T 8 8 8Taxes 8 8 8

Net income 12 12 -8

Net income 12 12 -8

Depreciation 30 30 0

DWCR 25 0 -25

CFInvestment -60 20

F C h Fl 60 17 42 37


Free Cash Flow -60 17 42 37

BOF: go ahead?g

• NPV calculation: 374217N V ca cu at o :96.17

)10.1(37

)10.1(42

10.11760 32 =+++−=NPV

• Internal Rate of Return = 24%

• Pa back period 2 ears• Payback period = 2 years


BOF: checking the numbersg

• Sensitivity analysisSe s t v ty a a ys s• 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 pointp• What is the level of sales required to break even?• Break even sales = 82


BOF Project with inflation rate = 100%j

Nominal free cash flows

Year 0 1 2 3Sales 200 400C f l 100 200Cost of sales 100 200EBITDA 100 200Depreciation 30 30EBIT 70 170EBIT 70 170Taxes 28 68 64Net income 42 102 -64

Net income 42 102 -64Depreciation 30 30 0ΔWCR 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%

A project is not a black boxp j

• Sensitivity analysis:Se s t v ty a a ys s:– analysis of the effects of changes in sales, costs,.. on a project.

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

• Simulation analysis:estimations of the probabilities of different o tcomes– estimations of the probabilities of different outcomes.

• Break even analysis– analysis of the level of sales at which the company breaks even.y p y


Sensitivity analysisy y

Year 0 Year 1-5ea 0 ea 5Initial investment 1,500Revenues 6,000Variables costs (3,000)Fixed costs (1,791)Depreciation (300)Depreciation (300)Pretax Profit 909Tax (TC = 34%) (309)( C ) ( )Net Profit 600Cash flow 900

• NPV calculation (for r = 15%): • NPV = 1 500 + 900 × 3 3522 = + 1 517September 15, 2009 Tfin 06 Capital budgeting |17

• NPV = - 1,500 + 900 × 3.3522 = + 1,517

Sensitivity analysis using Excely y g

• Use Data|Table (Données|Table)Use Data|Table (Données|Table)

=C12 Result to calculate

10E l

20

Excel recalculates using these

30

Values to use

(in cell B3 for instance)

values

30instance)



• 1. Identify key variables. dentify key va iables

• Revenues = Nb engines sold × Price per engine• 6,000 3,000 2• Nb engines sold = Market share × Size of market• 3 000 0 30 10 000• 3,000 0.30 10,000• 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



• 2. Prepare pessimistic, best, optimistic forecasts (bop). epa e pessimistic, best, optimistic fo ecasts (bop)

• Variable Pessimistic Best Optimistic• Market size 5,000 10,000 20,000• Market share 20% 30% 50%• Price 1 9 2 2 2• Price 1.9 2 2.2• V.cost / unit 1.2 1 0.8• Fixed cost 1,891 1,791 1,741, , ,• Investment 1,900 1,500 1,000



• 3. Recalculate NPV changing one variable at a time3. ecalculate N V changing one va iable at a time

• Variable Pessimistic Best Optimist• Market size -1,802 1,517 8,154• Market share -696 1,517 5,942• Price 853 1 517 2 844• Price 853 1,517 2,844• V.cost / unit 189 1,517 2,844• Fixed cost 1,295 1,517 1,628, , ,• Investment 1,208 1,517 1,903


Scenario analysisy

• Consider plausible combinations of variablesCo s de p aus b e combinations o va ab es• Ex: If recession

- market share low- variable cost high- price low


Monte Carlo simulation

• Tool for considering all combinationsoo o co s de g a co b at o s• model the project• specify probabilities for forecast errors• select numbers for forecast errors and calculate cash flows

• O tcome: sim lated distrib tion of cash flo s• Outcome: simulated distribution of cash flows


Monte Carlo Simulation - Examplep

Model Notations

Qt = Qt-1 + ut

Qt quantitymt unit marginFC fi d t

mt = m + vt

FC fixed costsDep depreciationTC corporate tax rate

CFt = (Qtmt - FC - Dep)(1-TC)+Dep

Procedure

ut,,vt random variables

Random number generationProcedure1. Generate large number of evolutions2. Calculate average annual cash flows

Random number generationRandom number Ri : uniform distribution on

[0,1]U RAND() i E l3. Discount using risk-adjusted rate Use RAND() in ExcelTo simulate ε ~ N(0,1): NORMSINV(Rand())


Standard normal random variable generation

1.00

g

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())


-3.0

0

-2.8

0

-2.6

0

-2.4

0

-2.2

0

-2.0

0

-1.8

0

-1.6

0

-1.4

0

-1.2

0

-1.0

0

-0.8

0

-0.6

0

-0.4

0

-0.2

0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

2.80

3.00

Simulated cash flows

Cash flow simulation

120,000

80,000

100,000

60,000

40,000

0

20,000


1 2 3 4 5 6 7 8 9 10

Break even analysisy

• Sales level to break-even? 2 viewsSa es eve to b ea eve ? v ews

• Account Profit Break-Even Point:» Accounting profit = 0» Accounting profit 0

• Present Value Break-Even Point:» NPV = 0» NPV 0


Break even analysis with Excely

• Use Goal Seek (Valeur cible)Use Goa See (Va eu c b e)

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


Timingg

• Even projects with positive NPV may be more valuable if deferred.ve p ojects w t pos t ve N V ay be o e va uab e de e ed.• 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

C h fl 100 130 156 180 202 218Cash flow 100 130 156 180 202 218

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

• Suppose discount rate r = 10%NPV if ld 100

Wait• NPV if sold now = 100• NPV if sold in year 1 = 130 / 1.10 = 118


Optimal timing for wine sale?p g

• Calculate NPV(t): NPV at time 0 if wine sold in year t:Ca cu ate N V(t): N V at t e 0 w e so d yea t:NPV(t) = Ct / (1+r)t

0 1 2 3 4 5

Cash flow 100 130 156 180 202 218Cash flow 100 130 156 180 202 218

NPV(t) 100 118.2 129 135 138 135


When to invest

• Traditional NPV rule: invest if NPV>0. Is it always valid?ad t o a N V u e: vest N V 0. s t a ways va d?• Suppose that you have the following project:

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

• Should you start the project?• Should you start the project? • If you choose to invest, the value of the project is:• Traditional NPV = 150 - 100 = 50 >0• What if you wait?


To mothball or not to mothball?

• Suppose that the project might be delayed for one year.Suppose t at t e p oject g t be de ayed o o e yea .• One year later:

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

• To decide: compare present values t ti 0• To decide: compare present values at time 0.• Invest now : NPV = 50• Invest one year later: NPV0 = PV(NPV1) = 60/1.10 = 54.5y 0 ( 1)

• 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)


Equivalent Annual Costq

• The cost per period with the same present value as the cost of buying and e cost pe pe od w t t e sa e p ese t va ue as t e cost o buy g a doperating 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 you buy?y y

C0 C1 C2 C3 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-year annuity factor = 20.41 / 1.735 = 11.76


B: EAC PV(Costs) / 2 year annuity factor 20.41 / 1.735 11.76

The Decision to Replacep

• When to replace an existing machine with a new one?W e to ep ace a e st g ac e w t a ew o e?• Calculate the equivalent annual cost of the new equipment• Calculate the yearly cost of the old equipment (likely to rise over

time as equipment becomes older)• Replace just before the cost of the old equipment exceeds the EAC

on new equipment q p• Example• Annual operating cost of old machine = 8• Cost of new machine :

• PV of cost (r = 10%) = 27 4

C0 C1 C2 C315 5 5 5

• PV of cost (r = 10%) = 27.4• EAC = 27.4 / 3-year annuity factor = 11• Do not replace until operating cost of old machine exceeds 11


p p g

Théorie Financière 6. Analyse de projets … 2009 06 Investment... · Théorie Financière 6....

Documents

Transcript of Théorie Financière 6. Analyse de projets … 2009 06 Investment... · Théorie Financière 6....