Lecture note 5 Chapter 8

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Lecture note 5(Chapter 8)
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Outline

• 1.Decision Trees
• 2. Sensitivity Analysis, Scenario Analysis
• 3. Break-Even Analysis
• 4. Monte Carlo Simulation

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Decision Trees

• We often make decisions in a sequence. For
  example, when you makes a capital budgeting
  decision, you may first want to do test
  marketing. Then, depending on the result of test
  marketing, you either go ahead with full scale
  investment.
• In this case, you are making a sequence of two
  decisions First, you make a decision regarding
  whether you should do the test marketing.
  Second, depending on the test marketing you make
  a decision regarding whether you go ahead with
  the full scale project.

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Decision Trees (Contd)

• Decision tree makes it easy to represent such a
  sequence of decision making.
• In the following slides, we will use a simple
  example to illustrate a decision tree.

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Stewart Pharmaceuticals

• The Stewart Pharmaceuticals Corporation is
  considering investing in developing a drug that
  cures the common cold.
• A corporate planning group, including
  representatives from production, marketing, and
  engineering, has recommended that the firm go
  ahead with the test-and-development phase.
• This preliminary phase will last one year and
  cost 1 billion. Furthermore, the group believes
  that there is a 60 chance that tests will prove
  successful.
• If the initial tests are successful, Stewart
  Pharmaceuticals can go ahead with full-scale
  production. This investment phase will cost 1.6
  billion. Production will occur over the next 4
  years.
• Full scale production incurs a variable cost and
  fixed cost. Company estimates that the variable
  cost would be equal to 3/7 of the revenue for
  each year. The company also estimates that the
  fixed cost will be 1.8 billion per year.

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Stewart Pharmaceuticals (Contd)

• According to the description of the project, the
  capital budgeting involves a sequence of two
  decisions. The first decision is whether to go
  ahead with the test. The second decision is
  whether to go ahead with the full project.
• This sequence is illustrated in the decision tree
  given in the next slide.

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Decision Tree for Stewart Pharmaceutical (Contd)
Invest
Success (probability60)
Do not invest
Test
Invest
Failure (probability40)
Do not test
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Decision Tree for Stewart Pharmaceutical (Contd)

• Clearly, to make the initial decision of whether
  to invest in the test project, we should have
  some idea about the possible revenues and costs
  that would follow after the initial decision.
• To make the decision, the company further came up
  the following estimates about the possible
  revenue and costs from the project.
• See next page.

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Case 1 Revenue and cost estimation of Full-Scale
if the test is successful

• To assist the decision making, the company
  further came up with the following estimate in
  the case of successful test result.
• -If the test marketing is successful and, if
  the company goes ahead with the project, the
  revenue for each year will be 7 billion for the
  lifetime of the project. The revenue will start
  one year from the initial investment
• - Corporate tax rate is estimated to be 34.
• Exercise Assuming that the initial investment of
  1.6 billion is the only cash flow of the
  investment, and using a straight line
  depreciation schedule, compute the NPV of the
  full scale project at year 1. The discount rate
  is 10. Use the Table 1 of the Decision tree
  example

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Case 1 Revenue and cost estimation of Full-Scale
if the test is successful

• For case 1, NPV as of year 1 is 3.433 billion
• Also notice that if the company did not invest,
  the net present value would be zero. This means
  that, if the test result is successful, it is
  better to invest in the project. This in turn
  means that, given the successful outcome, the
  probability that you will invest in the full
  scale project is 100. Using conditional
  probability notation, we can illustrate this
  result in the decision tree.
• See next slide

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Decision Tree for Stewart Pharmaceutical (Contd)
P(InvestTest success) 100
NPV at year 1 3.43billion
Success (probability60)
P(Not invest Test Successl) 0
NPV at year 1 0
Test
Failure (probability40)
Invest
Do not test
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Case 2 Revenue and cost estimation of Full-Scale
if the test is unsuccessful

• Again, to assist the decision making, the company
  came up with the following estimate in the case
  of unsuccessful test result. If the test
  marketing turns out to be unsuccessful, but the
  company goes ahead with the production anyway,
  the company estimates that
• - Revenue per each year will be 4.05 billion.
• - Corporate tax rate is again estimated to be
  34.
• Assuming again that initial investment is the
  only cash flow from the investment, and assuming
  a straight line depreciation, compute the net
  present value of the full scale project at year
  1. Use Table 2 of the Decision Tree example.

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Case 2 Revenue and cost estimation of Full-Scale
if the test is unsuccessful

• The NPV at year 1 for case 2 is -0.092billion.
• Since the NPV at year 1 is negative, given the
  unsuccessful test result, it is better not to go
  ahead with the full scale project. This in turn
  means that, given the unsuccessful test result,
  the probability that the company go ahead with
  the project is 0.
• The result can be conveniently written in the
  decision tree using conditional probability
  notation.
• See
  next page.

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Decision Tree for Stewart Pharmaceutical (Contd)
P(InvestTest success) 100
NPV at year 1 3.43billion
Success (probability60)
P(Not invest Test Successl) 0
NPV at year 1 0
Test
Failure (probability40)
P(InvestTest fail) 0
NPV at year 1 ?0.092 billion
Do not test
NPV at year 10
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• Remember again that, the project requires a
  sequence of two decisions. The first decision is
  regarding whether to go ahead with the test. The
  second decision is whether to go ahead with the
  full scale project after the test result is
  obtained.
• What we have discussed so far is the decision
  making rule of the second decision Based on the
  estimates, we found that, if the test marketing
  is successful, the company should go ahead with
  the full scale project. If the result is not
  successful, we found that the company should not
  go ahead with the full scale project.
• Commonly, when a sequential decision making is
  necessarily, we solve the problem backward.
• Now, we will examine the first decision the
  decision to go ahead or not with the test.

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Decision to go ahead with the test

• To make a decision regarding whether to invest in
  the test project, we employ the concept of
  conditional expectation.
• See next page.

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Conditional expected value of the NPV of the full
scale project of given successful test outcome.

• (Note, all the NPV is evaluated at year 1 in
  this slide. )
• Conditional expected value of NPV given the
  successful outcome of the project
• NPV at year 1 when investP(InvestTest
  Success)
• NPV at year 1 when not investP(Not
  investTest Success)
• 3.433 billion100 003.433 billion
  --------------(1)

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Conditional expected value of the NPV of the full
scale project given unsuccessful test outcome.

• (Note, all the NPV is evaluated at year 1 in this
  slide. )
• Conditional expected value of NPV given
  unsuccessful outcome of the project
• NPV when investP(InvestTest Fail)
• NPV when not investP(Not investTest
  Fail)
• ?0.092 billion0 0100 0
  --------------(2)

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(Unconditional) Expected NPV of the project at
year 1.

• In the previous slide, we computed the expected
  value of the NPV of the full scale project when
  the test is successful (1), and the test is
  unsuccessful (2).
• To make the decision regarding whether or not to
  go ahead with the test, we need to compute the
  (unconditional) expected value of NPV at year 1.
  This is given in the next slide.

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(Unconditional) Expected NPV of the project at
year 1.

• The (unconditional) expected NPV of the full
  scale project at year 1 is given by
• Expected NPV when test is successP(Test
  success)
• Expected NPV when test is uncessfulP(Test
  unsuccessful)
• 3.433 billion60040
• 2.059 billion.
• This means that the expected NPV of the full
  scale project evaluated at year 1 if you go ahead
  with the test project is 2.059 billion.
• See Next slide.

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Decision Tree for Stewart Pharmaceutical (Contd)
Expected NPV of the full scale project at year 1
if you test 2.059billion
P(InvestTest success) 100
NPV at year 1 3.43billion
Success (probability60)
P(Not invest Test Successl) 0
NPV at year 1 0
Test
Failure (probability40)
P(InvestTest fail) 0
NPV at year 1 ?0.092 billion
Do not test
NPV at year 10
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Decision regarding whether to go ahead with test.

• Now, you can compute the NPV of the whole project
  evaluated at year 0 (the full scale project plus
  the test project ) if you go ahead with the test
  project. This is given by
• Combined NPV of the full scale project and
  test at year 0

NPV of full scale project if you go ahead with
test
Cost of test
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Decision regarding whether to go ahead with test.

• The net present value if you go ahead with the
  test is computed as 0.87 billion.
• Now, should you go ahead with the test? To answer
  to this question, you also have to consider the
  NPV if you do not go ahead with the project.
• If you do not go ahead with the project, the Net
  present value is 0 (No cost for test, but no cash
  flow from the full scale project). Thus, the
  expected net present value if you go ahead with
  the test marketing is greater than if you do not.
  Thus, you should go ahead with the project.

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Sensitivity Analysis-Stewart Pharmaceuticals
example-

• Sensitivity Analysis examines how sensitive the
  estimated NPV of the project is to the change in
  the underlying assumption.
• For example, in the Steward Pharmaceuticals
  example, we assumed that the yearly revenue when
  the test turns out to be successful is 7 billion
  dollars. Sensitivity analysis examines what if
  questions What if the estimate of the revenue is
  changed to 6.5 billion dollars instead?, etc. If
  NPV became negative for a small change in the
  estimated revenue, a conservative manager may not
  be convinced that the project is worthwhile to
  invest in. Next slide.

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Sensitivity Analysis (Contd)-Stewart
Pharmaceuticals example-

• Therefore, it is often important to see how
  sensitive the result is to the change in the
  underlying assumptions.
• As an exercise, compute the NPV of the project if
  the revenue from the full scale project were
  5billion, 6 billion or 6.5 billion. All the other
  assumptions are unaltered.

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Sensitivity Analysis (Contd)-Stewart
Pharmaceuticals example-
As can be seen from this sensitivity analysis,
even if you estimate the revenue as
conservatively as 5 billion, you still have
positive NPV. Such analysis may be used to
increase the convincingness of the project.
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Scenario Analysis Stewart Pharmaceuticals

• A variation on sensitivity analysis is the
  scenario analysis.
• For example, the following three scenarios could
  apply to Stewart Pharmaceuticals
• The next years each have heavy cold seasons, and
  sales exceed expectations, but labor costs
  skyrocket.
• The next years are normal and sales meet
  expectations.
• The next years each have lighter than normal cold
  seasons, so sales fail to meet expectations.
• Scenario analysis simply calculates the NPV for
  each Scenario. Your confidence in the project
  increases if NPV is still positive for a
  pessimistic scenario. Your confidence may
  decrease if NPV is only positive for a very
  optimistic scenario.

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Break-Even Analysis Stewart Pharmaceuticals

• Another way to examine variability in our
  forecasts is break-even analysis.
• In the Stewart Pharmaceuticals example, we could
  be concerned with break-even revenue, that is
  the level of annual revenue that is necessary to
  cover the initial cost, (or in other words,
  annual revenue at which the NPV is equal to
  zero).
• This is another way to look at the sensitivity of
  the NPV calculation to the underlying assumption.

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Break-Even AnalysisExercise 1

• Using Stewart Pharmaceuticals, find the net
  annual cash flow necessary to cover the initial
  cost.

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Break-Even AnalysisExercise 2

• Using the Stewart Pharmaceuticals example, find
  the break even revenue

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Monte Carlo Simulation

• When the assumptions underlying the capital
  budgeting are complex, it becomes difficult to
  find the expected value of the NPV.
• For such a case, Monte Carlo Simulation can help
  find the expected value of the project.
• Moreover, you can visualize the distribution of
  NPV easily by using Monte Carlo Simulation.
• In the following slides, we will use an example
  to illustrate how a Monte Carlo Simulation can be
  used.

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Monte Carlo Simulation-Example-

• Backyard Barbeque Inc (BBI) is considering an
  project to produce a new grill that cooks with
  compressed hydrogen.
• For simplicity, let us assume that the lifetime
  of the project is 2 years. The discount rate is
  10
• The company came up with the following
  assumptions for the purpose of capital budgeting.

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Monte Carlo Simulation-Example Contd-

• Assumptions 1
• The revenue from the new grill will be given by
• RevenueThe number grills sold by the entire
  market
• Market share of BBIs hydrogen grill
  Price per hydrogen gril

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Monte Carlo Simulation-Example Contd-

• Assumption 2
• The initial cost is estimated to be 50 million
• Assumption 3
• The operating cost per year will be
• Fixed Cost Variable Cost
• Fixed cost is estimated to be 5 million per
  year. Variable cost is estimated to be 40 of the
  revenue.

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Monte Carlo Simulation-Example Contd-

• Assumption 4
• The probability distribution of the next years
  industry wide unit sales of grills is given by

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Monte Carlo Simulation-Example Contd-

• Assumption 5
• Distribution of the market share of BBI in
  each year is given by

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Monte Carlo Simulation-Example Contd-

• Assumption 6
• The price of the grill per unit for each year is
  given by
• Price 190 0.98(Industry wide unit sales in
  million) (random component)
• Where (random component)3 with probability
  50 and ?3 with probability 50

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Monte Carlo Simulation-Example Contd-

• Assumption 7
• Growth rate of industry wide unit sale is also
  assumed to be a random number. The distribution
  of the growth rate for each year is given by

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Monte Carlo Simulation-Example Contd-

• Assumption 8 There is no tax.
• This is just an assumption to make the
  computation easy.

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Monte Carlo Simulation exercise 1

• Open Monte Carlo example
• Ex 1 Compute the NPV for the following
  condition.
• Year 1market wide unit sale 10million
• Year 1 market share 2
• Year 1 price error component is 3
• Growth rate of the market unit sales is 3
• Year 2 market share 1
• Year 2 price error component ?3

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Monte Carlo Simulation exercise 1

• Ex 2
• Generate each variable 500 times (Monte Carlo
  Simulation with 500 repetitions). Then compute
  the expected net present value of the project.
  Also make a histogram to show the distribution of
  the net present value of the project.

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Monte Carlo Result
The result of Monte Carlo simulation (500 random
draws) shows that the probability that the
project will have negative net present value is
very small. The expected value of NPV is about
14.5 million dollars. This would give the
company confidence about the project.