February 1819

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Lecture 4

• February 18/19

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What do these have in common?

• New Coke
• XFL
• Waterworld (the movie)
• EuroDisney

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Outline

• How sure can we be about our projections?
• Sensitivity Analysis
• Scenario Analysis
• Breakeven Analysis
• Monte Carlo Simulation
• Recognize that accepting/rejecting a project is
  not necessarily a one-shot decision things
  evolve
• Decision Trees
• Real Options

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Sensitivity Analysis

• To this point we have assumed that all of our
  cash flow projections are perfect.
• Sensitivity analysis allows us to see how NPV
  calculations respond to changes in individual
  assumptions.
• Lets look more closely at Southwests
  projections for the Philly expansion (keep in
  mind, these numbers are fictional)

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Sensitivity Analysis-Southwest

• Suppose that Southwest made the following
  projections regarding its possible outcomes in
  the PHL market

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Sensitivity Analysis - Southwest

• How sensitive are the NPV calculations to each of
  the inputs?

See the spreadsheet (Go to the tab labeled
Sensitivity) for the calculations. Also, for
those of you that are interested in the _at_Risk
software, you will find that as _at_Risk does the
Monte Carlo simulation it performs a sensitivity
analysis. It presents to you the regression
coefficients from regressing the project NPV on
all of the input variables. This shows you how
sensitive the NPV is to changing each of the
inputs, holding all other variables constant.
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Scenario Analysis - Southwest

• Now suppose that you want to see how the project
  looks
• If everything goes perfectly?
• If everything goes badly?
• In general, if you believe a given set of factors
  might come together at one time.

See the Spreadsheet for the results from the
Southwest example (Go to the tabs labeled
Pessimistic, Expected, Optimistic).
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Monte Carlo Simulation

• Specify a distribution for the input variables
• Draw repeatedly from this distribution
• Look at the expected value of NPV after many
  draws.

Recall that we used the _at_Risk software to explore
Monte Carlo Simulation. I will not ask you to
run any Monte Carlo simulations, however, I do
hope that you have a firm grasp on what is
involved as well as the limitations of
itremember, garbage in, garbage out. If you
make bad assumptions in specifying the
distributions of your input variables, the
results are useless.
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Breakeven Analysis

• Breakeven analysis looks at the relation between
  sales and NPV in a different way How many units
  must we sell to achieve an NPV of 0?
• Formula for breakeven point
• Where does this equation come from?

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Breakeven analysis - Southwest

• Suppose that market size, price per seat,
  variable costs per seat, fixed costs per year,
  and the investment outlay are all at their
  expected levels. What market share must
  Southwest achieve in order to break even on a
  present value basis?
• Now suppose that market size, market share,
  variable costs, and fixed costs are all at their
  expected levels. What price per seat must
  Southwest charge in order to break even?

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Breakeven analysis-Southwest
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Breakeven analysis-Southwest
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Decision Trees

• Allow us to graphically represent the
  alternatives available to us in each period and
  the likely consequences of our actions
• Open circles represent decisions to be made
• Filled circles represent receipt of information
• The lines leading away from the circles represent
  the alternatives

Dont Invest
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Southwest (Lecture 3 example)

• Suppose now that you are deciding whether or not
  to do the marketing study which will cost 20
  million and will take 1 year to complete.
• If marketing study is successful (80
  probability), Southwest expects the project to
  have the 59 million NPV that we found last time.
  If the study is unsuccessful (20 probability),
  Southwest expects the PHL project to have an NPV
  of -22 million.

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Southwest Decision Tree
T0
T1
If the test indicates success, we will always
invest
Note that Im assuming the 59 and -22 NPVs are
t0 values
NPV-205939
(80 chance)
Cost of test20 million
NPV-20
NPV-20-22-42
(20 chance)
Dont Invest
NPV-20
If the test indicates failure, we will never
invest
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Southwest

• Should Southwest undertake the Philly marketing
  study?

Therefore, the NPV of testing is .80(39).20(-20)
27.2
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Real Options

• The option to expand
• Suppose that Southwest thinks there is a 50
  chance of ending up in the pessimistic
  scenario, and a 50 chance of ending up in the
  expected scenario. (Assume the test marketing
  has already been done and is a sunk cost.) What
  is the expected NPV to Southwest?

In this base case, without the option to expand,
the NPV is .5(-183.94).5(82.32)-50.81
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The option to expand

• Now suppose that after one year, Southwest can
  expand from 10 planes to 20. What is the value
  of Southwests option to expand?

In this case, Southwest can start the project,
and after one year decide whether or not to
expand. The decision tree looks like (see next
page)
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Southwest Decision Tree
T0
T1
If we end up in the expected state, we will
always expand
The NPV of 140.12 comes from the NPV of investing
at t0, finding out at t1 that you are in the
expected state, and then expanding by buying 10
more planes. I assume that market share and
fixed costs double in each year after the
expansion, and the whole operation will be shut
down at t10.
Expand
NPV140.12
(50 chance)
Expected
The NPV of 82.32 comes from the standard base
case NPV of buying 10 planes at t0 and operating
for 10 years in the expected state.
Dont Expand
NPV82.32
Expand
NPV-350.33
(50 chance)
The NPV of -350.33 comes from the NPV of
investing at t0, finding out at t1 that you are
in the pessimistic state, and then expanding by
buying 10 more planes. I assume that market
share and fixed costs double in each year after
the expansion, and the whole operation will be
shut down at t10.
Pessimistic
Dont Expand
NPV-183.94
If we end up in the pessimistic state, we will
never expand
The NPV of -183.94 comes from the standard base
case NPV of buying 10 planes at t0 and operating
for 10 years in the pessimistic state.
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Option to Expand
So the NPV with the option to expand
is .5(140.12).5(-183.94)-21.91 Therefore the
value of the option to expand is given by the
difference between the NPV of the project with
the option to expand and the NPV of the project
without the option to expand Option
valueNPV(with option) NPV (without option)
-21.91 (-50.81) 28.90
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Real Options

• The option to abandon
• Now suppose that in the pessimistic scenario,
  Southwest actually experiences negative after-tax
  cash flow in the future
• T0 -350 million
• T1 through 10 -50 million.
• So if there is a 50 chance of ending up in the
  optimistic scenario (NPV608) and a 50 chance of
  ending up in the pessimistic scenario (which now
  has an NPV-632), what is the NPV to Southwest?

In this base case, without the option to abandon,
the NPV is .5(608) .5(-632) -12.38
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The option to abandon

• Now supposed that Southwest has the option to
  abandon the project after one year. What is the
  value of Southwests option to abandon? (Ignore
  salvage values and assume Southwest is unable to
  expand operations.)

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Southwest Decision Tree
T0
T1
If we end up in the optimistic state, we will
never abandon
The NPV of -198.65 comes from the NPV of
investing at t0, finding out at t1 that you are
in the OPTIMISTIC state, and then abandoning the
project. Here you have the 350 initial
investment, then one positive cash inflow of
198.65
Abandon
NPV-198.65
(50 chance)
Optimistic
The NPV of 608 comes from the standard base case
NPV of buying 10 planes at t0 and operating for
10 years in the OPTIMISTIC state.
Dont Abandon
NPV608
Abandon
NPV-394.64
(50 chance)
The NPV of -394.64 comes from the NPV of
investing at t0, finding out at t1 that you are
in the PESSIMISTIC state, and then abandoning the
project. Essentially you have the 350
investment, and then one outflow of 50 after tax
at t1 which you need to discount back at 12.
Pessimistic
Dont Abandon
NPV-632
If we end up in the pessimistic state, we will
always abandon
The NPV of -632 comes from the standard base case
NPV of buying 10 planes at t0 and operating for
10 years in the PESSIMISTIC state.
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Option to Abandon
So the NPV with the option to abandon
is .5(608).5(-394.64)106.56 Therefore the
value of the option to abandon is given by the
difference between the NPV of the project with
the option to abandon and the NPV of the project
without the option to abandon Option
valueNPV(with option) NPV (without option)
106.56 (-12.38) 118.93
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Real Options

• Timing Option
• Even if a project appears to be negative NPV now,
  it may have value due to some possibility of a
  future positive event.
• Suppose that Southwest can buy the rights to use
  6 gates at Philadelphia airport for 20 million.
  However, anyone using those gates can expect to
  lose money in the current market situation.
  Should Southwest buy the gate rights?
• What if there is some possibility that US Airways
  will liquidate, making the Philadelphia market
  suddenly profitable?

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Timing Option
The illustration here is that while it might
first seem that Southwest should not pay for the
gate rights (given that they can only lose money
by starting operations), the timing option is
valuable. That is, Southwest can delay
commencing operations until market conditions are
favorable. This option to delay the project may
make it worth it to Southwest to pay for the gate
rights. For an excellent discussion on the use
of real options at Merck, see the article on my
website in the Miscellaneous section.