Finance Analyse de projets d’investissement by qfc86623

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									Finance
Analyse de projets d’investissement


Professeur André Farber
                    Investment decisions

• Objectives for this session :
• Review investment rules
       • NPV, IRR, Payback
• BOF Project
       • Free Cash Flow calculation
       • Inflation
• A project is not a black box: Sensitivity analysis, break even point
• Timing:
       • How long to invest?
       • When to invest?
       • Project with different lifes: Equivalent Annual Cost



September 8, 2010                        Capital budgeting (1)           |2
                    Investment rules

• Net Present Value (NPV)                                NPV
   – Discounted incremental free cash flows
   – Rule: invest if NPV>0                                       IRR

• Internal Rate of Return (IRR)
                                                                            r
   – IRR: discount rate such that NPV=0
   – Rule: invest if IRR > Cost of capital
• Payback period
   – Numbers of year to recoup initial investment
   – No precise rule
• Profitability Index (PI)
   – PI = NPV / Investment
   – Useful to rank projects if capital spending is limited


September 8, 2010                        Capital budgeting (1)         |3
                    Internal Rate of Return IRR

• Can be viewed as the “yield to maturity” of the project
       • 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 investment
       • The IRR is the rate that sets the net present value equal to zero




September 8, 2010                        Capital budgeting (1)          |4
                               What do CFOs Use?



•                                                       % Always or Almost Always

•    Internal Rate of Return                                          75.6%
•    Net Present Value                                                74.9%
•    Payback period                                                   56.7%
•    Discounted payback period                                        29.5%
•    Accounting rate of return                                        30.3%
•    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”,
     Journal of Financial Economics 2001

September 8, 2010                                                Capital budgeting (1)                            |5
                       IRR Pitfall 1: Lending or borrowing?

•    Consider following projects:
                                                                       IRR: borrowing or lending?

•        0 1     IRR NPV(10%)                                 30.00
•    A -100 +120 20%   9.09
                                                              20.00




                                          Net Present Value
•    B +100 -120 20% -9.09
                                                              10.00

                                                               0.00
•    A: lending   Rule IRR>r




                                                                 0%
                                                                 3%
                                                                           6%
                                                                           9%

                                                                            %
                                                                            %
                                                                            %
                                                                            %
                                                                            %
                                                                            %
                                                                            %
                                                              -10.00
•




                                                                          12
                                                                          15
                                                                          18
                                                                          21
                                                                          24
                                                                          27
                                                                          30
     B: borrowing Rule IRR<r
                                                              -20.00

                                                              -30.00
                                                                                   Discount rate

                                                                                 Project A    Project B




September 8, 2010                       Capital budgeting (1)                                             |6
                             IRR Pitfall 2 Multiple Rates of Return

•    Consider the following project
•    Year         0      1         2                                                     Multiple Rates of Return
•    CF      -1,600 10,000 -10,000
                                                                              1500.00
                                                                              1000.00
•    2 “IRRs” : +25% &             +400%




                                                          Net Present Value
                                                                               500.00
                                                                                  0.00
•    This happens if more than one change




                                                                                                          135%
                                                                                                                 180%
                                                                                                                        225%
                                                                                                                               270%
                                                                                                                                      315%
                                                                                                                                             360%
                                                                                                                                                    405%
                                                                                                                                                           450%
                                                                                                                                                                  495%
                                                                                              45%
                                                                                                    90%
                                                                                         0%
                                                                               -500.00
     in sign of cash flows
                                                                              -1000.00
                                                                              -1500.00
•    To overcome problem, use modified
                                                                              -2000.00
     IRR method
                                                                                                                 Discount Rate
      –    Reinvest all intermediate cash flows at the
           cost of capital till end of project
      –    Calculate IRR using the initial investment
           and the future value of intermediate cash
           flows

September 8, 2010                                        Capital budgeting (1)                                                                      |7
                          IRR Pitfall 3 - Mutually Exclusive Projects

Scale Problem (r = 10%)                    Timing Problem    (r = 10%)
                                                C0    C1  C2       NPV IRR
                                           A -100 +20 +120         17.4 20.0%
             C0      C1   NPV    IRR       B -100 +80 +52          15.7 22.5%
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 cash
   flows
         C0    C1 NPV IRR
L-S     -40 +60        14.5 50%




September 8, 2010                          Capital budgeting (1)               |8
                        Payback

• The payback period is the number of years it takes before the cumulative
  forcasted cash flows equals the initial investment.
• Example:      Year     0       1         2      3   Payback NPV
                                                                      r=10%
                    A     -1,000   500    500       1,000         2    619
                    B     -1,000    0    1,000          0         2   -174
                    C     -1,000   500    500           0         2   -132




•     A very flawed method, widely used
          • Ignores time value of money
          • Ignores cash flows after cutoff date



September 8, 2010                         Capital budgeting (1)               |9
                    Profitability Index

• Profitability Index = PV(Future Cash Flows) / Initial Investment

• A useful tool for selecting among projects when capital budget limited.
• The highest weighted average PI




September 8, 2010                       Capital budgeting (1)         |10
                    NPV - Review

• NPV: measure change in market value of company if project accepted
• As market value of company V = PV(Future Free Cash Flows)
                                             FCFt
                            NPV  V  
                                                        t
                                           t (1  r )
• V = Vwith project - Vwithout project
• Cash flows to consider:
   – cash flows (not accounting numbers)
       • do not forget depreciation and changes in WCR
   – incremental (with project - without project)
       • forget sunk costs
       • include opportunity costs
       • include all incidental effects
       • beware of allocated overhead costs
September 8, 2010                     Capital budgeting (1)       |11
                          Inflation

• Be consistent in how you handle inflation
       • 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)
      – Inflation rate = 5%
      – Real discount rate = 10%

      Discount real cash flow using real rate       Discount nominal cash flow using nominal rate
      PV = 100 / (1.10)3 = 75.13                    Nominal cash flow = 100 (1.05)3 = 115.76
                                                    Nominal discount rate = (1.10)(1.05)-1 = 15.5%
                                                    PV = 115.76 / (1.155)3 = 75.13




September 8, 2010                                   Capital budgeting (1)              |12
                         Investment Project Analysis: BOF


         Big Oversea Firm is considering the project


    Year                           0            1                 2     3
    Initial Investment            60

    Resale value                                                        20

    Sales                                     100                 100

    Cost of sales                              50                 50

         Corporate tax rate = 40%
         Working Capital Requirement = 25% Sales
         Discount rate = 10%


September 8, 2010                         Capital budgeting (1)              |13
                            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

            Taxes                                                    8     8          8

            Net income                                              12    12          -8



            Net income                                              12    12          -8

            Depreciation                                            30    30          0

            DWCR                                                    25     0         -25

            CFInvestment                       -60                                   20

            Free Cash Flow                     -60                  17    42         37

September 8, 2010                           Capital budgeting (1)              |14
                    BOF: go ahead?

• NPV calculation:
                                    17     42         37
                     NPV  60                            17.96
                                   1.10 (1.10) 2          3
                                                   (1.10)

• Internal Rate of Return = 24%

• Payback period = 2 years




September 8, 2010                      Capital budgeting (1)          |15
                          BOF: checking the numbers

• Sensitivity analysis
       • 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 point
       • What is the level of sales required to break even?
       • Break even sales = 82




September 8, 2010                           Capital budgeting (1)             |16
                        Impact of inflation

• Recommendation:
        • discount nominal cash flow using a nominal discount rate.
• Inflation modifies the NPV because:

             • Depreciation tax shields are lower with inflation

             • WCR is influenced by inflation




September 8, 2010                            Capital budgeting (1)    |17
                           BOF Project with inflation rate = 100%

              Nominal free cash flows

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

        Net income                                            42        102    -64
        Depreciation                                          30         30      0
        WCR                                                  50         50   -100
        CFInvestment                           -60                             160
        Free Cash Flow                         -60            22        82    196
                    Nominal discount rate = (1+10%)(1+100%)-1 = 120%
                    NPV = -14.65   IRR = 94%
September 8, 2010                               Capital budgeting (1)            |18
                    A project is not a black box

• Sensitivity analysis:
   – 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 outcomes.
• Break even analysis
   – analysis of the level of sales at which the company breaks even.




September 8, 2010                        Capital budgeting (1)             |19
                        Sensitivity analysis

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

• NPV calculation (for r = 15%):
• NPV = - 1,500 + 900  3.3522 = + 1,517
September 8, 2010                         Capital budgeting (1)          |20
                      Sensitivity analysis using Excel


• Use Data|Table (Données|Table)

                                               =C12             Result to calculate


                               10
                                                               Excel
                                                               recalculates
                               20                              using these
    Values to use                                              values
    (in cell B3 for
    instance)                  30



September 8, 2010                      Capital budgeting (1)            |21
                    Sensitivity analysis

• 1. Identify key variables

•    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
•    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




September 8, 2010                          Capital budgeting (1)   |22
                     Sensitivity analysis

• 2. Prepare pessimistic, best, optimistic forecasts (bop)

•    Variable             Pessimistic         Best               Optimistic
•    Market size          5,000               10,000             20,000
•    Market share         20%                 30%                50%
•    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




September 8, 2010                        Capital budgeting (1)           |23
                     Sensitivity analysis

• 3. Recalculate NPV changing one variable 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
•    V.cost / unit        189                1,517              2,844
•    Fixed cost           1,295              1,517              1,628
•    Investment           1,208              1,517              1,903




September 8, 2010                       Capital budgeting (1)          |24
                    Scenario analysis

• Consider plausible combinations of variables
• Ex: If recession
        - market share low
        - variable cost high
        - price low




September 8, 2010                       Capital budgeting (1)   |25
                    Monte Carlo simulation

• Tool for considering all combinations
       • model the project
       • specify probabilities for forecast errors
       • select numbers for forecast errors and calculate cash flows

• Outcome: simulated distribution of cash flows




September 8, 2010                       Capital budgeting (1)          |26
                     Monte Carlo Simulation - Example

Model                                    Notations
                                         Qt       quantity
Qt = Qt-1 + ut                           mt       unit margin
                                         FC       fixed costs
mt = m + vt                              Dep      depreciation
                                         TC       corporate tax rate
CFt = (Qtmt - FC - Dep)(1-TC)+Dep        ut,,vt   random variables

Procedure                                Random number generation
1. Generate large number of evolutions   Random number Ri : uniform distribution on
2. Calculate average annual cash flows      [0,1]
3. Discount using risk-adjusted rate     Use RAND() in Excel
                                         To simulate  ~ N(0,1): NORMSINV(Rand())



September 8, 2010                          Capital budgeting (1)          |27
                                                          Standard normal random variable generation
   1.00


   0.90


   0.80
                                                                                                  RAND()
   0.70
                                                                                                   ALEA()
   0.60


   0.50


   0.40


   0.30


   0.20
                                                                                                  LOI.NORMALE.STANDARD.INVERSE(ALEA())
   0.10

                                                                                                                                                                            NORMSINV(RAND())
   0.00
                                                                                                                                  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
          -3.00
                  -2.80
                          -2.60
                                  -2.40
                                          -2.20
                                                  -2.00
                                                          -1.80
                                                                  -1.60
                                                                          -1.40
                                                                                  -1.20
                                                                                          -1.00
                                                                                                  -0.80
                                                                                                          -0.60
                                                                                                                  -0.40
                                                                                                                          -0.20




September 8, 2010                                                                                                                 Capital budgeting (1)                                                                      |28
                            Simulated cash flows

                                        Cash flow simulation


     120,000




     100,000




      80,000




      60,000




      40,000




      20,000




          0
                    1   2      3    4           5         6          7      8   9   10



September 8, 2010                                   Capital budgeting (1)           |29
                      Break even analysis

• Sales level to break-even? 2 views
             • Account Profit Break-Even Point:
                    » Accounting profit = 0
             • Present Value Break-Even Point:
                    » NPV = 0




September 8, 2010                         Capital budgeting (1)   |30
                    Break even analysis with Excel

• Use Goal Seek (Valeur cible)

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




September 8, 2010                       Capital budgeting (1)    |31
                          Timing

• Even projects with positive NPV may 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
                    Cash flow   100    130        156          180   202     218
                    % change           30%       20%           15%   12%     8%


• Suppose discount rate r = 10%
                                                                      Wait
      • NPV if sold now = 100
      • NPV if sold in year 1 = 130 / 1.10 = 118


September 8, 2010                            Capital budgeting (1)            |32
                             Optimal timing for wine sale?

• Calculate NPV(t): NPV at time 0 if wine sold in year t:
                              NPV(t) = Ct / (1+r)t


                                   0     1         2            3        4    5
                    Cash flow     100   130      156          180       202   218
                    NPV(t)        100   118.2    129          135       138   135




September 8, 2010                               Capital budgeting (1)               |33
                    When to invest

• Traditional NPV rule: invest if NPV>0.         Is it always valid?
• 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?
• If you choose to invest, the value of the project is:
• Traditional NPV = 150 - 100 = 50 >0
• What if you wait?




September 8, 2010                         Capital budgeting (1)        |34
                    To mothball or not to mothball?

• Suppose that the project might be delayed for one year.
• 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 at time 0.
       • Invest now : NPV = 50
       • Invest one year later: NPV0 = PV(NPV1) = 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)


September 8, 2010                       Capital budgeting (1)            |35
                       Equivalent Annual Cost

• The cost per period with the same present value as the cost of buying and
  operating 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?
                    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 = 10.03
           B: EAC = PV(Costs) / 2-year annuity factor = 20.41 / 1.735 = 11.76
September 8, 2010                            Capital budgeting (1)                   |36
                    The Decision to Replace

• When to replace an existing 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 over
          time as equipment becomes older)
       • Replace just before the cost of the old equipment exceeds the EAC
          on new equipment
• Example
• Annual operating cost of old machine = 8
• Cost of new machine :              C0       C1       C2       C3
                                     15       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

September 8, 2010                       Capital budgeting (1)        |37

								
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