finance 7. capital budgeting (2) professor andré farber solvay business school université libre de...

FINANCE7. Capital Budgeting (2)

Professor André Farber

Solvay Business SchoolUniversité Libre de BruxellesFall 2007

MBA 2007 - Capital Budgeting (2) |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


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)

• 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



• 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


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):

12

16

iiR


Simulated cash flows

Cash flow simulation

0

20,000

40,000

60,000

80,000

100,000

120,000

1 2 3 4 5 6 7 8 9 10


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

0 1 2 3 4 5

Cash flow 100 130 156 180 202 218

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

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

0 1 2 3 4 5

Cash 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?

• 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?

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


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

C0 C1 C2 C3

15 5 5 5

finance 7. capital budgeting (2) professor andré farber solvay business school université libre de...

Documents

capital budgeting

project analysis

total cost

equivalent annual cost

cost unit1891

variable cost fixed

cash flowsoutcome

simulation analysis