FINANCE 7. Capital Budgeting (2) - PowerPoint PPT Presentation

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FINANCE7. 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?

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.

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

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

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

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

Scenario analysis

Consider plausible combinations of variables
Ex: If recession

market share low
variable cost high
price low

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

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

Simulated cash flows

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

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

Optimal timing for wine sale?

Calculate NPV(t): NPV at time 0 if wine sold in year t:

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

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?

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)

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

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