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?

• Project with different lifes: Equivalent Annual Cost MBA 2007 - Capital Budgeting (2) |

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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) |

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Sensitivity analysis

Initial investment Revenues Variables costs Fixed costs Depreciation Pretax Profit Tax (T C = 34%) Net Profit Cash flow Year 0 1,500 Year 1-5 6,000 (3,000) (1,791) (300) 909 (309) 600 900 • NPV calculation (for r = 15%): • NPV = - 1,500 + 900  3.3522 = + 1,517 MBA 2007 - Capital Budgeting (2) |

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Sensitivity analysis

•

1. Identify key variables

• Revenues = Nb engines sold  Price per engine • 6,000 3,000 • Nb engines sold = Market share  2 Size of market • 3,000 0.30

• V.Cost =V.cost per unit  • 3,000 1 10,000 Number of engines 3,000 • Total cost = Variable cost + • 4,791 3,000 Fixed costs 1,791 MBA 2007 - Capital Budgeting (2) |

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Sensitivity analysis

•

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

• Variable • Market size • Market share • Price • V.cost / unit • Fixed cost • Investment Pessimistic 5,000 20% 1.9

1.2

1,891 1,900 Best 10,000 30% 2 1 1,791 1,500 Optimistic 20,000 50% 2.2

0.8

1,741 1,000 MBA 2007 - Capital Budgeting (2) |

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Sensitivity analysis

•

3. Recalculate NPV changing one variable at a time

• Variable • Market size • Market share • Price • V.cost / unit • Fixed cost • Investment Pessimistic -1,802 -696 853 189 1,295 1,208 Best 1,517 1,517 1,517 1,517 1,517 1,517 Optimist 8,154 5,942 2,844 2,844 1,628 1,903 MBA 2007 - Capital Budgeting (2) |

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Scenario analysis

• Consider plausible

combinations

of variables • Ex: If recession - market share low - variable cost high - price low MBA 2007 - Capital Budgeting (2) |

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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) |

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Monte Carlo Simulation - Example

Model

Q t = Q t

-1 +

u t m t = m + v t CF t =

(

Q t m t - FC - Dep

)(1-

T C

)+

Dep

Procedure

1. Generate large number of evolutions 2. Calculate average annual cash flows 3. Discount using risk-adjusted rate

Notations

Q m t t FC quantity unit margin fixed costs Dep T C u t, ,v t depreciation corporate tax rate random variables

Random number generation

Random number

R i

on [0,1] : uniform distribution Use RAND in Excel To simulate   ~ N(0,1): 12 

i

  1

R i

 6 MBA 2007 - Capital Budgeting (2) |

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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 MBA 2007 - Capital Budgeting (2) 9 10 |

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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) |

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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 % change 100 130 30% 156 20% 180 15% 202 12% 218 8%

• 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) |

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Optimal timing for wine sale?

• Calculate NPV(

t

): NPV at time 0 if wine sold in year

t

: NPV(

t)

=

C t /

(1+

r

)

t

Cash flow NPV(

t

) 0 100 100 1 130 118.2

2 156 129 3 180 135 4 202 138 5 218 135 MBA 2007 - Capital Budgeting (2) |

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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) |

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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 • NPV 1 = 160 - 100 = 60 in year 1 • To decide: compare present values

at time

0.

• Invest now : NPV = 50 • Invest one year later: NPV 0 = PV(NPV 1 ) = 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) |

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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?

C

0

C

1

C

2

C

3 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

MBA 2007 - Capital Budgeting (2) |

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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 :

C

15 0

C

5 1

C

5 2

C

5 3 • 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 MBA 2007 - Capital Budgeting (2) |

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