Chapter 8: Project Analysis

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Topic Project Analysis and Evaluation
Objectives

• NPV estimates depend on projected future cash
  flows
• Use sensitivity, scenario, and break-even
  analysis to see how project profitability would
  be affected by a change in forecasting
• Explain the concept of operating leverage

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Project Analysis

• Some What If Analyses
• Scenario Analysis
• Sensitivity Analysis
• Simulation Analysis
• Break-Even Analysis
• Additional Considerations in Capital Budgeting
• Managerial Options
• Capital Rationing

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Scenario Analysis

• The determination of what happens to NPV
  estimates when we ask what-if questions
• Allow managers to look at different but
  consistent combinations of variables, and compare
  one particular combination with another
• Forecasters usually prefer to give an estimate of
  revenues or costs under a particular scenario
  rather than giving some absolute optimistic or
  pessimistic value
• Scenario analysis allows variables to be
  interdependent

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Sensitivity Analysis

• Investigation of what happens to NPV when only
  one variable is changed
• e.g., sales, variable costs, fixed costs...
• Sensitivity analysis is useful in pinpointing
  those variables that deserve the most attention
• Sensitivity analysis assumes that the
  individual variables are independent of each
  other
• Simulation analysis a combination of scenario
  and sensitivity analyses

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Break-Even Analysis

• Question How bad do sales have to get before we
  actually loose money?
• Examines the relationship between sales volume
  and profitability
• Variable Costs costs that change when the
  quantity of output changes
• Fixed Costs costs that do not change when the
  quantity of output changes during a particular
  period

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Example A-Sensitivity Analysis

• A project currently generates sales of
  10million, variable
• costs equal to 50 of sales, and fixed costs of
  2million. The
• firms tax rate is 35. What are the effects of
  the following
• changes on after-tax profits and cash flows?
• a) Sales increase from 10million to 11million
• b) Variable costs increase to 60 of sales

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Example A
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Example A
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Operating Leverage

• Operating leverage the degree to which a project
  or firm is committed to fixed costs
• Degree of Operating Leverage (DOL) the change
  in operating cash flow relative to the change
  in the quantity sold
• DOL measures the sensitivity of OCF to the
  quantity sold. Since FC do not vary with sales, a
  small change in Q can be magnified into a large
  change in OCF
• The danger from incorrectly forecasting sales is
  directly related to its DOL. The higher the fixed
  costs, the greater the variation in operating
  cash flows given a change from estimated sales

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Operating Leverage

• Given that
• Can you prove (ignoring taxes) that
• Hint OCF(P-v)Q-FC, ignoring taxes, where P is
  unit price, v is unit cost, Q is sales and FC is
  fixed cost. Think about what happens when sales
  increases by 1.

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Operating Leverage
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NPV Break-Even Analysis

• NPV Break-Even analysis calculates the level of
  sales that generates an NPV of zero the
  textbook calls this the financial break-even.
• Sales higher than the zero NPV sales will produce
  positive NPV
• This is equivalent to finding the sales level for
  which the cost of the project equals the present
  value of the cash flows

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Simple Example, based on pp359

• Victoria Sailboats Limited is considering
  whether to launch its new Mona-class sailboat.
  The selling price would be 40,000 per boat and
  the cost per boat would be 20,000. Fixed costs
  would be 500,000 per year. The total investment
  needed to undertake this project would be 3.5 M
  for factory improvements. This amount will be
  depreciate straight-line over the 5-yr life of
  the equipment. The salvage value is zero, and
  there are no working capital consequences.
  Victoria has 20 required return on new projects.
• Calculate the NPV break-even ignoring taxes.
• Calculate the NPV break-even, assuming a tax rate
  of 35.

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Simple Example, based on pp359

• The initial investment is 3.5 M
• Ignoring taxes, the annual OCF is (P-v)Q-FC
  (40,000-20,000)Q- 500,000

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Example B

• Emperors Clothes Fashions can invest 5 million
  in a new plant for producing invisible makeup.
  The plant has an expected life of 5 years, and
  expected sales are 6 million jars of makeup a
  year. Fixed costs are 2 million a year, and
  variable costs are 1 per jar. The product will
  be priced at 2 per jar. The plant will be
  depreciated straight-line over 5 years to a
  salvage value of zero. The opportunity cost of
  capital is 12 and Tc is 40.
• a) What is the project NPV under the base-case
  assumptions?
• b) What is the NPV if variable costs turn out to
  be 1.20 per jar?
• c) At what price per jar would the NPV equal
  zero?
• d) Whats the NPV break-even sales per year?

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Example B,Part a)
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Example B,Part b)
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Example B,Part c)
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Example B,Part d)
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Topic Project Analysis and Evaluation
Objectives

• Analyze projects with alternative sequential
  decisions and possible outcomes by using decision
  trees
• Make investment timing decisions
• Choose between projects with different lives by
  comparing the equivalent annual costs of the
  projects
• Use equivalent annual costs to decide whether to
  replace an aging machine with a new one

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Example of a Decision Tree

• Your midrange guess as to the amount of oil in a
  prospective field is 10 million barrels, but in
  fact there is a 50 percent chance that the amount
  of oil is 15 million barrels, and a 50 percent
  chance of 5 million barrels. If the actual
  amount of oil is 15 million barrels, the present
  value of the cash flows from drilling will be 8
  million. If the amount is only 5 million
  barrels, the present value will be only 2
  million. It costs 3 million to drill the well.
  Suppose that a seismic test that costs 100,000
  can verify the amount of oil in the field. Is it
  worth paying for the test? Use a decision tree
  to justify your answer.

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Decision Tree
Big oil field (.5)
NPV 8 3 5 million
Test (cost .1m)
NPV 0 (abandon)
Small oil field (.5)
Big oil field (.5)
NPV 8 3 5 million
Do not test
NPV 2 3 - 1 million
Small oil field (.5)
EV(test) -.1M .5x5M .5x0 2.4M EV (no test)
.5x5M .5x(-1) 2.0M
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Decision Tree - Part II

• Suppose the probability of the oil field being
  large is p. For what value of p would you be
  indifferent between paying for the test and not
  paying for it?

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Decision Tree - Part II
EV(test) -.1M px5M (1-p)x0 (5p-.1)M EV (no
test) px5M (1-p)x(-1)M (6p-1)M EV(test)
EV (no test) (5p-.1)M(6p-1)M p0.9
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Investment Timing Decision

• When to make an investment is a difficult
  decision in a dynamic world, where new
  cost-saving technology is always improving and
  NPVs are greater if delayed until later.
• Decision Rule
• - compute NPVs for each possible year of
  investment
• - compare NPVs computed all in t 0 values
• - choose the time that gives the highest NPV0

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Example on Investment Timing

• You can purchase an optical scanner today for
  400. The
• scanner provides benefits worth 60 a year. The
  expected life
• of the scanner is 10 years. Scanners are
  expected to decrease
• in price by 20 percent per year. Suppose the
  discount rate is
• 10. What is the best purchase time?

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Example on Investment Timing

• Time Cost PV of Benefits till Purchase
  at Purchase Date
• 60x(1/.1)x(1-1/1.110)
• 0 400 368.67
• 1 320 368.67
• 2 256 368.67
• 3 204.8 368.67
• 4 163.84 368.67
• 5 131.07 368.67
• 6 104.86 368.67
• 7 83.88 368.67

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Example on Investment Timing

• Time NPV at NPV at till
  Purchase Purchase Date Time 0
• 0 -31.33 -31.33 -31.33
• 1 48.67 48.67/(1.1) 44.25
• 2 112.67 112.67/(1.1)2 93.12
• 3 163.87 163.87/(1.1)3 123.12
• 4 204.83 204.83/(1.1)4 139.90
• 5 237.60 237.60/(1.1)5 147.53
• 6 263.81 263.81/(1.1)6 148.91
• 7 284.79 284.79/(1.1)7 146.14

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Example on Investment Timing -II

• How does your answer change when the cost of
  scanners decreases by 50 each year?

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Example on Investment Timing -II
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Long-lived versus Short-lived Equipment

• When comparing mutually exclusive projects that
  have unequal project lives, one must analyze the
  present value of investment outlays and operating
  costs of the projects
• Decision Rule (between two machines w/ different
  lives)
• - calculate the equivalent annual cost (EAC) of
  both machines
• - the equivalent annual cost is the cost per
  period with the same PV as the cost of buying and
  operating a machine
• - choose the machine with the lowest EAC

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Example on Long- vs. Short-Lived Machines

• Suppose your firm must decide which machine to
  buy to produce widgets. Machines A and B have
  identical capacity and do exactly the same job.
  Machine A costs 100,000, lasts 4 years, and
  costs 20,000 per year to operate. Machine B
  costs 75,000, will last only 3 years, and costs
  35,000 per year to operate. Which machine would
  you purchase? The opportunity cost of capital is
  10.

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Example on Long- vs. Short-Lived Machines

• PV of costs for A
• PV of costs for B
• Why cant we compare A and B yet?

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To compare costs of projects with different lives
use EAC Project A (life of 4 years) Annuity
factor1-1/1.14/.103.17 EAC163,397/3.1751,5
47 Project B (life of 3 years) Annuity
factor1-1/1.13/.102.49 EAC162,040/2.4965,1
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Replacing an Old Machine

• Most equipment is replaced before the end of its
  useful economic life. Replacement decisions most
  often involve replacing old by new with different
  useful cash flow lives
• Decision Rule
• calculate the EAC of the new project, and compare
  to the period cost of the old project.
• if the EAC of the new project is less than the
  period cost of the old project, accept the new

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Example on Replacing an Old Machine

• Suppose that a new machine has developed and it
  costs 20,000 and its economic life is 3 years.
  The existing machine will last at most for 2 more
  years. The annual operating costs of the two
  machines are given below. Both machines produce
  identical output. The opportunity cost of capital
  is 10. When should you replace the existing
  machine with the new one?
• Annual Operating Cost
• Machine 1 2 3
• Old 10,000 15,000
• New 4,000 6,000 8,000

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Example on Replacing an Old Machine

• The firm has 3 mutually exclusive alternatives
• Replace immediately
• Replace in 1 year
• Replace in 2 years
• First step compute EACNEW

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Example on Replacing an Old Machine

• 1. Immediate replacement (today)
• 2. Replace in 1 year
• 3. Replace in 2 years!!

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Example on Replacing an Old Machine

• Replace after 1 yr.

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A Quick Summary

• Optimal investment timing
• - Compare the NPV0 of all future NPVs
• Mutually exclusive equipment with different
  lives
• - Compare the EACs of the two equipment pieces
• Replacing an old machine
• - Compare the EAC of a new machine with the
  period cost of the old machine