Advanced Corporate Finance
FINA 7330
Ronald F. Singer
Practical Problems in Capital
Budgeting
Lecture 3
Fall 2010
1
Topics Covered
• Sensitivity Analysis
– Break Even Analysis
• Monte Carlo Simulation
• Real Options and Decision Trees
What is Project Analysis
• At any one time the firm has a number of
projects that are possible.
• Typically, a number of projects are
recommended by division heads
• The problem: Which of the proposed projects
should be ultimately taken?
• Critical to this decision is what can go wrong:
– i.e. Uncertainty
How To Handle Uncertainty
• Sensitivity Analysis – What happens if certain
variables are forecasted incorrectly?
• Scenario Analysis – What happens if a logical set
of variables are forecasted incorrectly?
• Simulation Analysis – Alternative results when a
large number of different scenarios are proposed.
• Break Even Analysis – What is the minimum level
of sales (prices, costs) which still allows the
project a non-negative NPV
Steps in Sensitivity Analysis
•
•
•
•
•
Define Costs as a function of output
Define Revenue as a function of output
Define expected (initial) variables
Estimate worse and best case variables
Get NPV’s for expected and also for worst case
and best case situations
• Purpose: Determines where you might want to
concentrate your efforts to assure correct
forecasts
International Widget Company (IWC)
• The Company is thinking of introducing a new
version of widgets designed for the under 30
crowd. To do this requires an initial investment of
$150,000 and, at a production level of 10,000
units, it is expected to payoff $20,000 per year
for 10 years. At the end of the ten years IWC will
be able to sell the fixed assets and equipment for
$100,000. If the real Cost of Capital is 4%, is this
a good investment? All numbers are in real terms
• The NPV is: ???
Sensitivity Analysis
–
–
–
–
–
Initial Investment
Output (Q)
Life
Discount Rate
Terminal Value
• NPV
=
=
=
=
=
$150,000
10,000
10 years
4%
$100,000
=
$79,774.33
• But this is the EXPECTED NPV!. Sensitivity analysis asks what
happens in things are worse (better) than predicted
• To answer this you need to know what the production process looks
like (“model”).
Sensitivity Analysis
The Model
• Cost = Fixed Cost + Unit cost X Quantity
= $10,000 + $6Q
• Revenues = Price X Quantity =
$9Q
• Notice at output of 10,000:
Annual Payoff (Net Revenue)
Our original Scenario
Cost = $70,000
Revenue = $90,000
$20,000
Sensitivity Analysis
•
Pessimistic
–
–
–
–
–
–
–
–
–
Optimistic
Initial Investment 155
140
Sales price
8
10
Fixed cost
12
8
Unit Variable Cost
7
5
Output
9
13
Life
8
12
Discount Rate
5%
3%
Scrap Value
95
120
See excel file: International Widget Company
Sensitivity analysis
• What does Sensitivity analysis Tell You?
Scenario Analysis
• We have assumed that inflation, over the period will be zero. What
if we assume that the inflation rate is 1% per year
• We have to forecast the impact on the variables in the model.
Suppose we forecast that REAL variable costs, and revenues will
remain the same. But that the REAL fixed cost will decline by
$1,000.
• Then the impact of inflation on annual cash flow will be:
– Real CF will increase to $21,000
• Also we forecast that this will impact on the real terminal value of
the assets will decline to $90,000, from the original $100,000.
.
• What is the new NPV?
Breakeven Analysis
• Breakeven is that level of output for which the
investment “breaks even”
• What is meant by “breaks even”
– Where NPV = 0
• What is that in terms of output?
Break Even Analysis
• Notice that the (real) margin is $2 per unit, and Cash Flow is
the margin times the units sold,
– That is CF = (Sale price-Unit cost)*Units sold
= (Margin)*Units sold
= (2.00)* 10,000 = $20,000
– What is the minimum units you have to sell to “break even” in
PV terms? That is: what is the sales level which will give you a
zero NPV.
• The Cash Flow’s PV must equal $150,000
• How do you do this? Find the Payments that have a PV of
$150,000
• So Breakeven is:
– So quantity must be ???
Monte Carlo Simulation
Modeling Process
• Step 1: Modeling the Project
• Step 2: Specifying Probabilities
• Step 3: Simulate the Cash Flows
Monte Carlo Simulation
Flexibility & Real Options
Decision Trees
• Decision Trees - Diagram of sequential decisions and
possible outcomes.
• Embedded in a typical project are options which are
not adequately dealt with by the standard DCF
Analysis.
• These Options are typically contingent on observing
new information as time goes by.
• For example, options:
– To Expand,
– Contract
– Cease Operations or abandon
Flexibility & Real Options
• Decision trees help companies determine
their Options by showing the various choices
and outcomes.
• The ability to create an Option thus has value
that should be included in the PV of a project
Classic Analysis
• Search for projects with a positive NPV.
• Typically this entails generating a stream of
Expected Cash Flows and appropriately
discounting.
• However, this could miss some of the strategic
value associated with an investment
opportunity.
• That is, the ability to react to new information
after the project has begun.
The Strategic Approach
• Views the Firm in a dynamic setting
• Firm is searching for and capitalizing on its
comparative advantage
• Emphasis on the ability of the firm to react to
complex situations
• Emphasis on the firm’s reaction to change and
capitalizing on changing environment
Strategic Approach
• Typically the cash flow from an investment is
determined initially with no concept of
dynamic reactions.
• The use of Real Options allows us to integrate
the two concepts into project analysis.
International Widget Company
• Thinking of expanding into China: the plant will
cost $3 million to build and the marketing
department tells you that the market will
generate the equivalent of about $500,000 per
year forever if successful, but may produce as
little as $50,000 per year if unsuccessful. the
probability of success is 50%. At a 10% discount
rate, what is the NPV of the project.
• Accept or Reject this project?
Strategic Approach
• If you develop a pilot project it will only cost
$200,000 and if successful, then the pilot
project will generate $80,000 if unsuccessful it
will only generate $30,000, each outcome
equally likely . In either case, the pilot project
will not be able to be continued thereafter.
• Note that this is a losing project by itself, but it
does allow you to get valuable information
about the full scale production
Widget’s China Experiment
• Marketing people tell you that if the pilot project
is successful, then there is a 90% chance of the
full scale project being successful and generating
$500,000 and year, but if the pilot project is
unsuccessful then the full scale project will only
generate the $500,000 with a probability of 25%.
• Should we (1) undertake the Pilot Project, (2) go
immediately into production full scale, or (3) do
neither?
Decision Tree Analysis
5,000,000
-3,000,000
80,000
500,000
5,000,000
-200,000
-3,000,000
500,000
30,000
NPV = 0 (stop)
Decision Tree analysis
5,000,000
-3,000,000
80,000
500,000
NPV = 0
5,000,000
-200,000
-3,000,000
500,000
30,000
NPV = 0
Decision Tree analysis
5,000,000
-3,000,000
80,000
500,000
NPV = 0
5,000,000
-200,000
-3,000,000
500,000
30,000
NPV = 0
Decision Tree Analysis
NPV(1) = $1,550,000
80,000
-200,000
30,000
NPV = 0
Decision Tree
80,000 + 1,550,000 = $1,630,000
-200,000
NPV OF Total is: $740,909 + 13,636 -200,000 = 554,545
30,000