Project Interactions

1
Project Interactions
2
Applying the models

• So far we have discussed simple projects that are
  mutually exclusive and made some assumptions
• Competing projects have the same lives
• We know the future cash flows with certainty
• Management does not have the ability to make
  decisions that change the cash flows after the
  project is started.
• This chapter expands on the basic decision
  variables (NPV, IRR etc) in cases where projects
  with different lives are compared, cash flows are
  uncertain, and we discuss the value impact of
  management.

3
Capital Rationing

• Choosing among projects when limited by the
  amount of resources available.
• Previously we assumed that the firm could
  undertake any positive NPV project, however it
  may be limited by available resources.

4
Spending Limits

• Assume that the company has a limit on the amount
  of funds that it believes it can raise.
• Example 3 projects Spending limit of 12M
• Project Investment NPV
• A 12,000,000 18,000,000
• B 7,000,000 14,000,000
• C 5,000,000 10,000,000
• Which project(s) should it undertake?

5
Using Profitability Index

• Given the spending limits, the firm should also
  look at the return per dollar invested.
• Project Investment NPV PI
• A 12,000,000 18,000,000 1.5
• B 7,000,000 14,000,000 2.0
• C 5,000,000 10,000,000 2.0
• While B C have a lower NPV individually they
  both have a higher profitability index.

6
Problems

• Profitability index can be misleading if looked
  at alone.
• Project Investment NPV PI
• A 10,000,000 14,000,000 1.4
• B 5,000,000 6,000,000 1.2
• C 5,000,000 10,000,000 2.0
• The firm should still look at the total amount of
  NPV!

7
Problems with Profitability Index

• If more than one constraint is to be rationed
  then PI can be misleading. For example, if one
  project depends upon another.
• Also PI ignores the amount of wealth created.

8
Comparing Projects with Unequal Lives

• Replacement Chain Approach
• Repeat projects until they have the same life
  span.
• Compare a two year project with a four year
  project by repeating the two year project

9
Comparing Projects with Unequal Lives

• Equivalent Annual Annuity (finding an annualized
  NPV)
• To Find EA
• find the NPV of the Project
• Use the NPV as the PV of an annuity and solve for
  payment
• Choose the project with the highest EAA

10
Abandonment Decisions

• Often one question is when to stop a project. By
  quitting at different points in time the NPV and
  EAA will vary due to the changes in salvage
  value.
• Use EAA and treat each abandonment time as a
  separate project.

11
Uncertain Cash Flows

• So far we have assumed that we can estimate the
  cash flows from the project with certainty.
• However, it is difficult to correctly forecast
  future cash flows how can the risks associated
  with changes in the economic environment and the
  difficulties with forecasting cash flows be
  accounted for?

12
Three Types of Risk

• Stand Alone Risk
• Views project in isolation
• With-in firm (Corporate Risk)
• Looks at the firms portfolio of projects and how
  they interact
• Market Risk
• Risk from the view of a well diversified
  investor.

13
Definitions

• Risk
• Exposure to a chance of injury or loss
• Probability
• The likelihood an event occurs
• Risk vs. Uncertainty
• Risk the probability of the outcome is known
• Uncertainty includes judgment concerning the
  probability

14
Definitions and Terms Continued

• Objective Prob can measure prob. precisely
• Subjective Prob. Includes judgment or opinion
• Variation Risk We want to look at a range of
  possible outcomes

15
Issues in Risk Measurement

• Stand Alone Risk is the easiest to measure
• Market Risk is the most important to the
  shareholder
• To evaluate risk you need three things
• Standard deviation of the projects forecasted
  returns
• Correlation of the projects forecasted returns
  with the firms other assets
• Correlation of the projects forecasted returns
  with the market

16
Issues in Risk Management cont

• Using the numbers in 3) you can find the
  corporate beta and market beta coefficient (equal
  to ((s/s)r)
• Most projects have a correlation with other
  projects and a coefficient lt 1
• Most projects are positively correlated with the
  market with coefficient lt 1
• Corporate risk should also be examined
• More important to small business
• Investors may look at things other than market
  risk
• Firm Stability is important to creditors,
  suppliers etc

17
Stand Alone Risk (Review)

• The easiest approach to measuring stand alone
  risk is to use the standard deviation of the
  projects returns.
• Just like security analysis you need to be
  careful looking at only standard deviation
  dont forget coefficient of variation

18
Measuring Stand Alone Risk

• Sensitivity Analysis
• Scenario Analysis
• Monte Carlo Simulation

19
Sensitivity Analysis

• Looks at the change in your decision variable
  (NPV or IRR) when one input changes.
• For example what if the cost of capital changes
  (or sales or salvage value of the equipment or)

20
Example 1 Change ONLY cost of capital

• Time CF
• 0 -5000
• 1 4000
• 2 4000
• 3000
• NPV _at_ 10 4196.09
• NPV _at_ 11 4043.67
• NPV _at_ 9 4352.99

21
Example 2 change ONLYfuture cash flows

• Time CF CF 10 CF 10
• 0 -5000 -5000 -5000
• 1 4000 4400 3600
• 2 4000 4400 3600
• 3000 3300 2700
• NPV_at_10 4196.09 5155.70
  3276.48

22
Sensitivity Analysis

• Usually the results are represented in a table
  where the response of the decision variable to
  changes in more than one individual variable are
  reported.
• Then you can compare across variables to see
  which one has the largest impact on your decision

23
Example Results

• NPV When there is a change in
• Change from Cost of Future
• Base Case Capital Cash Flows
• -10 4352.99 3276.48
• Base 4196.09 4196.09
• 10 4043.67 5115.70

156.90
919.61
152.42
919.61
24
Sensitivity Analysis

• Benefits
• Easy to Calculate and Understand
• Measures risk associated with individual inputs
• Weaknesses
• Ignores probability of event
• Ignores interaction among the variables
• Ignores gains from diversification

25
Scenario Analysis

• Differences from Sensitivity Analysis
• Allows you to change more than one variable at a
  time
• Look at a group of scenarios (best case, base
  case, and worst case) for example worst case
  what if all variables change against us by 20.
• Includes probability estimates of each scenario

26
Scenario Analysis

• Now let both the future cash flows and the cost
  of capital change.
• Worst Case Scenario Best Case Scenario
• (WACChCFi) (WACCiCFh)
• -5000 -5000
• 3600 4400
• 3600 4400
• 2700 3300
• NPV_at_11 3139.30 NPV _at_ 9 5288.29

27
Scenario Analysis

• Now let both the future cash flows and the cost
  of capital change.
• Scenario NPV
• Worst (WACChCFi) 3139.30
• Base 4196.09
• Best (WACCiCFh) 5288.29

28
Scenario Analysis

• Given the NPV and Probability you can find the
  expected NPV and standard deviation
• Scenario NPV Prob. NPV(Prob)
• Worst 3193.30 .25 784.825
• Base 4196.09 .50 2,098.045
• Best 5288.29 .25 1,322.0725
• Expected NPV 4,204.94
• Standard Deviation 741.38

29
Interpreting the Results

• The project has an expected return on 4204.94
  with standard deviation of 741.38
• This implies a 68 confidence interval of
  (3463.56 to 4946.32) a large range of possible
  outcomes
• The coefficient of variation would be .1763 (you
  are accepting .1763 units of risk for each unit
  of return)

30
Scenario Analysis

• Benefits
• More than one variable changes at a time
• Accounts for probability
• Easy to perform
• Weaknesses
• Small number of scenarios is unrealistic
• Probability distributions difficult to estimate

31
Monte Carlo Simulation

• A more advanced form of scenario analysis
• Utilizes the computer to make random choices for
  each variable input then calculate the expected
  return and standard deviation

32
Mont Carlo Simulation

• Construct a model of the firms cash flows and
  NPVs
• Specify a probability distribution for each
  uncertain variable (characterized by mean and
  standard dev) and correlation among variables.
• Allow computer to select a random draw form the
  distribution for each variable
• Calculate NPV (this is one scenario).
• Repeat 3) an 4) (10,000 or 100,000 times) equal
  chance of each scenario Calculate expected NPV
  and standard deviation.

33
Monte Carlo Simulation

• Benefits
• More realistic selection of variables
• Easy to understand results
• Weaknesses
• Only as good as probability estimate and
  correlation of variables

34
Quick Review

• Sensitivity Analysis Scenario Analysis and Monte
  Carlo Simulation were all used to measure stand
  alone risk
• Each is designed to provide more information
  about the uncertainty associated with the project
  they do not provide a clear cut decision rule.

35
Applying Sensitivity and Scenario Analysis

• In our examples we simplified the problem by
  changing the aggregate cash flows.
• When evaluating the project, any assumptions
  about inputs can change impacting the
  incremental cash flows.
• A few of many possible examples
• Changes in variable input costs
• Changes in sales
• Changes in tax laws

36
Probability Review

• Mutually exclusive events
• If A occurs then B cannot. Example considering
  building a new sports arena. There are two sites
  North and South.
• Prob North .5 Prob South .25
• This implies the prob that the stadium is built
  is
• .5 .25 .75

37
Probability Review 2

• Independent Events
• Example Exxon is considering two drilling sites,
  gulf coast and Alaska
• P(A) New oil from gulf coast .7
• P(B) Prob of oil in Alaska .4
• Event B No Event B
• (.4) (.6)
• Event A (.7) .28 .42
• No event A (.3) .12 .18

38
Probability Review 3

• Dependent Events Prob of one event depends upon
  the other
• North Side is voting on bonds for the new arena,
  80 chance of the bond passing If passed there is
  a 60 chance the stadium gets built in North. If
  the bonds fail there is a 30 chance that the
  stadium gets built in North

39
Prob Review 3 cont

• North North
• Selected Rejected
• Bond (.8)(.6) (.8)(.4)
• Passes (.8) .48 .32
• Bond (.2)(.3) (.2)(.7)
• Fails (.2) .06 .14

40
Decision Trees

• So far our decision making has ignored the role
  of management.
• We know that things change as a project
  progresses and decision trees attempt to account
  for this.

41
Project Example

• Peripherals Inc. is considering making a new
  copier/printer.
• Stage 1 Conduct a market study to investigate
  potential sales, cost 500,000
• Stage 2 If sizable market exists at time t1
  spend 1,000,000 to build prototype (80 prob)
• Stage 3 If it passes all test spend 10,000,000
  at time t2 60 prob
• Stage 4 Year t 3 to t 6
• High demand (20 prob) 12M in CF each yr
• Avg Demand (60 prob) 5M in CF each yr
• Low Demand (20 prob) 2M in CF each yr

42
Building the decision tree

• t 0 t 1
• -1,000,000
• 80
• -500,000
• 20
• 0
• Stage 1 and Stage 2 represented on the tree

43
Building the decision tree

• t 1 t 2
• -10,000,000
• 60
• -1,000,000
• 40
• 0
• Stage 2 and Stage 3 represented on the tree

44
Stage 1 to 3

• t0 t1 t2
• 
  -10,000,000
• 60
• -1,000,000
• 80
• -500,000 40
  
• 0
• 20
• 0

45
Decision Tree

• Continue to Build the tree (on the board in
  class)
• When finished find the NPV of each branch and
  multiply it times the probability for each branch
  to find the expected NPV.

46
Real Options

• Opportunities arise that present the management
  with the ability to make a choice. The decision
  points in the above decision tree represent this.
• For example At time t2, if we realize that the
  project is going to produce only
• -2,000,000 each year we would not proceed with
  the project. There is an option to abandon the
  project.

47
Real Options

• Three main components
• Determining the value of a real option.
• Identifying the optimal response to changing
  conditions.
• Structuring projects to create real options.

48
Valuing a Real Option Using the Decision Tree

• In the earlier decision tree. Assume we can
  abandon the project if we find out that it is
  going to result in 2,000,000 CF each year.
• We would need to recalculate the NPV of that
  branch without the 2,000,000 CFs
• NPV -9,364,795.92
• instead of 14,207,508.52
• The total NPV is then 1,235,339.21 instead of
  770,438.80 an increase of 464,900.41

49
Other Benefits

• If the reduction in uncertainty decreases the
  risk the firm can lower the WACC increasing the
  NPV even further.
• The key is building the decision points into the
  capital budgeting process from the beginning

50
Real Options and Financial Management

• Flexibility Option -- Switch inputs during the
  production process.
• Capacity options Ability to manage capacity in
  response to changing economic conditions.
• New Product Options May accept initial negative
  NPV if it allows rights to future goods.
• Timing Options Allow you to postpone or
  increase production.

51
Value of Real Options

• In each case the option can add value to the
  project.
• You would want to compare the added value of the
  option to the cost of implementing the option.
• Example it costs an extra 10Million to build a
  plant that could allow inputs to be switched.
  Given the volatility in the price of the inputs
  you estimate the real option to switch inputs is
  worth 20 Million

52
Characteristics of Real Options

• Real options often increase the value of a
  project
• The value of most real options increases
• As the longer the amount of time that exists
  before the option needs to be exercised increases
• The source of risk becomes more volatile
• If interest rates increase.

53
Options

• Call Option the right to buy an asset at some
  point in the future for a designated price.
• Put Option the right to sell an asset at some
  point in the future at a given price

54
Call Option Profit

• Call option as the price of the asset increases
  the option is more profitable.
• Once the price is above the exercise price
  (strike price) the option will be exercised
• If the price of the underlying asset is below the
  exercise price it wont be exercised you only
  loose the cost of the option.
• The Profit earned is equal to the gain or loss on
  the option minus the initial cost.

55
Profit Diagram Call Option

• Profit
• Spot
• Cost Price

S-X-C
S
X
56
Call Option Intrinsic Value

• The intrinsic value of a call option is equal to
  the current value of the underlying asset minus
  the exercise price if exercised or 0 if not
  exercised.
• In other words, it is the payoff to the investor
  at that point in time (ignoring the initial cost)
  
• the intrinsic value is equal to
• max(0, S-X)

57
Payoff Diagram Call Option

• Payoff
• Spot
• Price

S-X
X
S
X
58
Put Option Profits

• Put option as the price of the asset decreases
  the option is more profitable.
• Once the price is below the exercise price
  (strike price) the option will be exercised
• If the price of the underlying asset is above the
  exercise price it wont be exercised you only
  loose the cost of the option.

59
Profit Diagram Put Option

• Profit
• Spot Price
• Cost

X-S-C
S
X
60
Put Option Intrinsic Value

• The intrinsic value of a put option is equal to
  exercise price minus the current value of the
  underlying asset if exercised or 0 if not
  exercised.
• In other words, it is the payoff to the investor
  at that point in time (ignoring the initial cost)
  
• the intrinsic value is equal to
• max(X-S, 0)

61
Payoff Diagram Put Option

• Profit
• Spot Price
• Cost

X-S
S
X
62
Pricing an Option

• Black Scholes Option Pricing Model
• Based on a European Option with no dividends
• Assumes that the prices in the equation are
  lognormal.

63
Inputs you will need

• S Current value of underlying asset
• X Exercise price
• t life until expiration of option
• r riskless rate
• s2 variance

64
PV and FV in continuous time

• e 2.71828 y lnx x ey
• FV PV (1k)n for yearly compounding
• FV PV(1k/m)nm for m compounding periods per
  year
• As m increases this becomes
• FV PVern PVert let t n
• rearranging for PV PV FVe-rt

65
Black Scholes

• Value of Call Option SN(d1)-Xe-rtN(d2)
• S Current value of underlying asset
• X Exercise price
• t life until expiration of option
• r riskless rate
• s2 variance
• N(d ) the cumulative normal distribution (the
  probability that a variable with a standard
  normal distribution will be less than d)

66
Black Scholes (Intuition)

• Value of Call Option
• SN(d1) - Xe-rt N(d2)
• The expected PV of cost Risk Neutral
• Value of S of investment Probability of
• if S gt X S gt X

67
Black Scholes

• Value of Call Option SN(d1)-Xe-rtN(d2)
• Where

68
Application to Real Options

• Investment
• Option Real Option
• Stock Price PV of projects Cash Flows
• Exercise Price Expenditure required to
  acquire projects assets
• Time to Expire Length of time the decision
  can be deferred
• Variance Riskiness of projects assets

69
Example

• Disney Can spend 100M to create a Spanish
  version of the Disney channel
• PV of future CFs 80M
• Initial investment 100M
• The resulting NPV of the project is
• 80M 100M -20 Million

70
A Real Option

• Assume the expansion will provide political
  connections resulting in an advantage if they
  expand into South America. Assume the expansion
  would cost 150M and could be taken at any time
  over the next ten years The firm believes that
  the NPV of expanding is 100M.
• S 100M X 150M r .065 Variance .40

71
Plugging into the Black Scholes Model

• Value of Call Option SN(d1)-Xe-rtN(d2)
• 100(.8648) 150e(-.065)(10)(.435)
• 52.3 Million
• Original NPV 80M 100M - 20M
• Add the value of the option Total Value of
  Project
• -20M52.3 32.3M

72
Put Option

• The black scholes value is similar for a put
  option
• Value of put option Xe-rtN(-d2)-SN(-d1)

73
Option to Abandon

• An example of a real option that corresponds to a
  put option would be an option to abandon a
  project in the future.

74
Developing Prob Estimates

• History What happened last year
• Experiments Test programs, market surveys etc
• Judgment Subjective adjustment

75
Structuring Project Cash Flows to Help Manage
Risk

• Variable and Fixed Costs
• Pricing Strategy
• Sequential Investment
• Financial Leverage

76
Measuring Corporate and Market Risk

• Corporate and Market betas