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FINANCE 7. Capital Budgeting (2). Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2007. Investment decisions (2). Objectives for this session : A project is not a black box Timing: How long to invest? When to invest?

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finance 7 capital budgeting 2

FINANCE7. Capital Budgeting (2)

Professor André Farber

Solvay Business School

Université Libre de Bruxelles

Fall 2007

investment decisions 2
Investment decisions (2)
  • Objectives for this session :
      • A project is not a black box
      • Timing:
        • How long to invest?
        • When to invest?
      • Project with different lifes: Equivalent Annual Cost

MBA 2007 - Capital Budgeting (2)

a project is not a black box
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.

MBA 2007 - Capital Budgeting (2)

sensitivity analysis
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

MBA 2007 - Capital Budgeting (2)

sensitivity analysis1
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

MBA 2007 - Capital Budgeting (2)

sensitivity analysis2
Sensitivity analysis
  • 2. Prepare pessimistic, best, optimistic forecasts (bop)
  • VariablePessimistic 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

MBA 2007 - Capital Budgeting (2)

sensitivity analysis3
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

MBA 2007 - Capital Budgeting (2)

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

MBA 2007 - Capital Budgeting (2)

monte carlo simulation
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

MBA 2007 - Capital Budgeting (2)

monte carlo simulation example
Model

Qt = Qt-1 + ut

mt = m + vt

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

Procedure

1. Generate large number of evolutions

2. Calculate average annual cash flows

3. Discount using risk-adjusted rate

Notations

Qt quantity

mt unit margin

FC fixed costs

Dep depreciation

TC corporate tax rate

ut,,vt random variables

Random number generation

Random number Ri: uniform distribution on [0,1]

Use RAND in Excel

To simulate  ~ N(0,1):

Monte Carlo Simulation - Example

MBA 2007 - Capital Budgeting (2)

simulated cash flows
Simulated cash flows

MBA 2007 - Capital Budgeting (2)

break even analysis
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

MBA 2007 - Capital Budgeting (2)

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

Wait

MBA 2007 - Capital Budgeting (2)

optimal timing for wine sale
Optimal timing for wine sale?
  • Calculate NPV(t): NPV at time 0 if wine sold in year t:

NPV(t) = Ct / (1+r)t

MBA 2007 - Capital Budgeting (2)

when to invest
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?

MBA 2007 - Capital Budgeting (2)

to mothball or not to mothball
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)

MBA 2007 - Capital Budgeting (2)

equivalent annual cost
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?

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

MBA 2007 - Capital Budgeting (2)

the decision to replace
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 :
  • 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

C0C1C2 C315 5 5 5

MBA 2007 - Capital Budgeting (2)