FINANCE 7. Capital Budgeting (2)

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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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### FINANCE7. Capital Budgeting (2)

Professor André Farber

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?
• Project with different lifes: Equivalent Annual Cost

MBA 2007 - Capital Budgeting (2)

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

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

MBA 2007 - Capital Budgeting (2)

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)

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

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

MBA 2007 - Capital Budgeting (2)

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
• 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?
• 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
• 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?
• 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
• 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
• 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)