gs503 vcf lecture 7 innovation finance i 300315

THE FINANCE OF THE FINANCE OF INNOVATION : R&D INNOVATION : R&D

FINANCING, FINANCING, MONTE CARLO MONTE CARLO SIMULATION& SIMULATION& REAL OPTIONSREAL OPTIONS

Prof.Stephen OngProf.Stephen OngBSc(Hons)Econs (LSE), MBA (Bradford)BSc(Hons)Econs (LSE), MBA (Bradford)

Visiting Professor, Shenzhen UniversityVisiting Professor, Shenzhen UniversityAcademic Fellow, Entrepreneurship & Innovation,Academic Fellow, Entrepreneurship & Innovation,

The Lord Ashcroft International Business School, The Lord Ashcroft International Business School, Anglia Ruskin University Cambridge UKAnglia Ruskin University Cambridge UK

MSC TECHNOPRENEURSHIP : MSC TECHNOPRENEURSHIP : VENTURE CAPITAL FINANCINGVENTURE CAPITAL FINANCING

Today’s Overview Today’s Overview

LEARNING OBJECTIVESLEARNING OBJECTIVES

To understand the financing of To understand the financing of R&D projects;R&D projects;

To understand the steps of To understand the steps of conducting Monte Carlo conducting Monte Carlo simulation in evaluation of project simulation in evaluation of project outcomes:outcomes:

To understand the use of decision To understand the use of decision trees in decision making in VC trees in decision making in VC investments.investments.

1.R&D Financing

R&D as a % of GDP

U.S. R&D Funding by Source

U.S. R&D by Source and Performer

R&D Definitions from the NSF

Basic researchBasic research: : The objective of basic research is to gain The objective of basic research is to gain more comprehensive knowledge or understanding of the more comprehensive knowledge or understanding of the subject under study without specific applications in mind. In subject under study without specific applications in mind. In industry, basic research is defined as research that advances industry, basic research is defined as research that advances scientific knowledge but does not have specific immediate scientific knowledge but does not have specific immediate commercial objectives, although it may be performed in fields commercial objectives, although it may be performed in fields of present or potential commercial interest. of present or potential commercial interest.

Applied researchApplied research: : The objective of applied research is to gain The objective of applied research is to gain the knowledge or understanding to meet a specific, the knowledge or understanding to meet a specific, recognized need. In industry, applied research includes recognized need. In industry, applied research includes investigations to discover new scientific knowledge that has investigations to discover new scientific knowledge that has specific commercial objectives with respect to products, specific commercial objectives with respect to products, processes, or services.processes, or services.

DevelopmentDevelopment: : Development is the systematic use of the Development is the systematic use of the knowledge directed toward the production of useful materials, knowledge directed toward the production of useful materials, devices, systems, or methods, including the design and devices, systems, or methods, including the design and development of prototypes and processes.development of prototypes and processes.

R&D Finance

ThemesThemesNonlinearities: Interactions between risks lead to Nonlinearities: Interactions between risks lead to

highly complex models that must be solved using highly complex models that must be solved using simulation;simulation;

Decisions made over time, leading to Decisions made over time, leading to real real options;options;

Multiple decision makers, so that we must use Multiple decision makers, so that we must use game theory game theory to model behavior.to model behavior.

This themes give rise to three types of riskThis themes give rise to three types of riskTechnical (=idiosyncratic, use simulation to solve)Technical (=idiosyncratic, use simulation to solve)Business (=systematic, use real options to solve)Business (=systematic, use real options to solve)Competitive (use game theory to solve)Competitive (use game theory to solve)

Pharmaceutical R&D

Pharmaceutical R&D: Data

Phase Mean Time to

Next Phase (in months)

Capitalized phase cost (in T $millions)

Probability of reaching phase (in percent)

I 12.3 30.5 100 I 26.0 41.6 71.4 III 33.8 119.2 31.4 Approval 18.0 NA 16.7

Sources: DeMasi et al (2003), Tufts CSDD Outlook 2005,

author’s calculations

Fuel Cell Project

Pharmaceutical R&D: Financing

How can we finance this cost? Main sources:How can we finance this cost? Main sources: Largeco: Internal fundsLargeco: Internal funds Mediumco: Public marketsMediumco: Public markets Smallco: Strategic alliances / licensingSmallco: Strategic alliances / licensing Newco: VCNewco: VC

Of course, each size does not exclusively use one Of course, each size does not exclusively use one type of financing.type of financing.

Government and non-profits can partially fund some Government and non-profits can partially fund some parts for all types of companies.parts for all types of companies.

Strategic Alliances and LicensingStrategic Alliances and Licensing

Alliance and licensing (a special type of Alliance and licensing (a special type of alliance) is the major source of funding (much alliance) is the major source of funding (much more than VC) for private and small public more than VC) for private and small public biopharma companies.biopharma companies.

Licensing deals can take a wide variety of Licensing deals can take a wide variety of structures, the most common components arestructures, the most common components areUpfront feesUpfront feesMilestone paymentsMilestone paymentsRoyaltiesRoyaltiesR&D fundingR&D fundingEquity investmentsEquity investments

Example of Strategic AllianceExample of Strategic Alliance Novartis gets the exclusive worldwide development, Novartis gets the exclusive worldwide development,

manufacturing, and marketing rights to Anadys’s manufacturing, and marketing rights to Anadys’s ANA975 and other [similar compounds] for chronic ANA975 and other [similar compounds] for chronic hepatitis B and C viruses and other infectious diseases… hepatitis B and C viruses and other infectious diseases…

Novartis will pay a Novartis will pay a $20M up-front license fee$20M up-front license fee, , $550M $550M in regulatory and commercial milestones for the in regulatory and commercial milestones for the development and marketing of ANA975, including development and marketing of ANA975, including $10M payment upon a successful IND submission (it $10M payment upon a successful IND submission (it anticipates a mid-2005 filing). anticipates a mid-2005 filing).

Novartis will provide funding for Novartis will provide funding for 80.5 percent of the 80.5 percent of the expensesexpenses associated with developing the lead candidate, associated with developing the lead candidate, with Anadys funding 19.5 percent of the costs. with Anadys funding 19.5 percent of the costs.

Anadys has a co-promotion option to keep Anadys has a co-promotion option to keep 35 percent of 35 percent of the U.S. profits the U.S. profits if it pays that percentage of the if it pays that percentage of the marketing costs. marketing costs.

If Anadys declines the option, it will get royalties on If Anadys declines the option, it will get royalties on global sales of the resulting product. No equity was global sales of the resulting product. No equity was exchanged. (Sourceexchanged. (Source: In Vivo: In Vivo, July/August 2005, p.92), July/August 2005, p.92)

Trees and ToolsTrees and ToolsWe use event trees and We use event trees and Monte Carlo simulation Monte Carlo simulation

to handle problems that do not have sequential to handle problems that do not have sequential decisions decisions

We use decision trees and We use decision trees and real-options analysis real-options analysis to handle one-agent problems that have to handle one-agent problems that have sequential decisions sequential decisions

We use We use binomial trees binomial trees – a special case of – a special case of decision trees – to simplify complex problems decision trees – to simplify complex problems that have “standard” types of uncertainty that have “standard” types of uncertainty

We use game trees and We use game trees and game theory game theory to handle to handle multiple-agent decision problems multiple-agent decision problems

We combine game theory, real options analysis, We combine game theory, real options analysis, and Monte Carlo simulation for complex and Monte Carlo simulation for complex problems with sequential decisions and multiple problems with sequential decisions and multiple agentsagents

How does this all relate to VC?How does this all relate to VC?

1)1) R&D valuation is one of the most R&D valuation is one of the most important inputs into total valuation for important inputs into total valuation for VCs.VCs.

2)2) Monte Carlo simulation and real Monte Carlo simulation and real options analysis can be used more options analysis can be used more broadly to get better estimates for total broadly to get better estimates for total valuation.valuation.

3)3) Many VC-backed companies must Many VC-backed companies must negotiate license agreements and other negotiate license agreements and other strategic alliances. strategic alliances.

2. Monte Carlo Simulation

IntroductionIntroduction

Simulation is one of the most widely used quantitative analysis tools.

To simulate is to try to duplicate the features, appearance, and characteristics of a real system.

We will build a mathematical model that comes as close as possible to representing the reality of the system.

Physical models can also be built to test systems.


Using simulation, a manager should:Using simulation, a manager should:

1.1. Define a problem.Define a problem.

2.2. Introduce the variables associated with Introduce the variables associated with the problem.the problem.

3.3. Construct a simulation model.Construct a simulation model.

4.4. Set up possible courses of action for Set up possible courses of action for testing.testing.

5.5. Run the simulation experiment.Run the simulation experiment.

6.6. Consider the results.Consider the results.

7.7. Decide what courses of action to take.Decide what courses of action to take.

Process of SimulationProcess of Simulation

Define Problem

Introduce Important Variables

Construct Simulation Model

Specify Values of Variables to Be Tested

Conduct the Simulation

Examine the Results

Select Best Course of Action

Figure 14.1

Advantages and Disadvantages Advantages and Disadvantages of Simulationof Simulation

The main advantages of simulation are:The main advantages of simulation are:

1.1. It is relatively straightforward and flexible.It is relatively straightforward and flexible.

2.2. Recent advances in computer software make Recent advances in computer software make simulation models very easy to develop.simulation models very easy to develop.

3.3. Can be used to analyze large and complex real-world Can be used to analyze large and complex real-world situations.situations.

4.4. Allows “what-if?” type questions.Allows “what-if?” type questions.

5.5. Does not interfere with the real-world system.Does not interfere with the real-world system.

6.6. Enables study of interactions between components.Enables study of interactions between components.

7.7. Enables time compression.Enables time compression.

8.8. Enables the inclusion of real-world complications.Enables the inclusion of real-world complications.

Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall 14-23

Advantages and Disadvantages of Simulation

The main disadvantages of simulation are:

1. It is often expensive as it may require a long, complicated process to develop the model.

2. It does not generate optimal solutions; it is a trial-and-error approach.

3. It requires managers to generate all conditions and constraints of real-world problem.

4. Each model is unique and the solutions and inferences are not usually transferable to other problems.


Monte Carlo Simulation When systems contain elements that exhibit chance in their

behavior, the Monte Carlo method of simulation can be applied.

Some examples are:

1. Inventory demand.

2. Lead time for inventory.

3. Times between machine breakdowns.

4. Times between arrivals.

5. Service times.

6. Times to complete project activities.

7. Number of employees absent.


Monte Carlo Simulation The basis of the Monte Carlo simulation is experimentation

on the probabilistic elements through random sampling. It is based on the following five steps:

1. Establishing a probability distribution for important variables.

2. Building a cumulative probability distribution for each variable.

3. Establishing an interval of random numbers for each variable.

4. Generating random numbers.

5. Actually simulating a series of trials.

Example : Harry’s Auto TireExample : Harry’s Auto Tire

A popular radial tire accounts for a large portion of A popular radial tire accounts for a large portion of the sales at Harry’s Auto Tire.the sales at Harry’s Auto Tire.

Harry wishes to determine a policy for managing Harry wishes to determine a policy for managing this inventory.this inventory.

He wants to simulate the daily demand for a He wants to simulate the daily demand for a number of days.number of days.

Step 1: Establishing probability distributionsStep 1: Establishing probability distributions One way to establish a probability distribution One way to establish a probability distribution

for a given variable is to examine historical for a given variable is to examine historical outcomes.outcomes.

Managerial estimates based on judgment and Managerial estimates based on judgment and experience can also be used.experience can also be used.

Harry’s Auto Tire

Historical Daily Demand for Radial Tires at Historical Daily Demand for Radial Tires at Harry’s Auto Tire and Probability DistributionHarry’s Auto Tire and Probability Distribution

DEMAND FOR TIRES FREQUENCY (DAYS) PROBAILITY OF OCCURRENCE

0 10 10/200 = 0.05

1 20 20/200 = 0.10

2 40 40/200 = 0.20

3 60 60/200 = 0.30

4 40 40/200 = 0.20

5 30 30/200 = 0.15

200 200/200 = 1.00

Table 14.1

Harry’s Auto Tire

Step 2:Building a cumulative probability Step 2:Building a cumulative probability distribution for each variabledistribution for each variable

Converting from a regular probability to Converting from a regular probability to a cumulative distribution is an easy job.a cumulative distribution is an easy job.

A cumulative probability is the A cumulative probability is the probability that a variable will be less probability that a variable will be less than or equal to a particular value.than or equal to a particular value.

A cumulative distribution lists all of the A cumulative distribution lists all of the possible values and the probabilities, as possible values and the probabilities, as shown in Table 14.2. shown in Table 14.2.

Harry’s Auto Tire

Cumulative Probabilities for Radial TiresCumulative Probabilities for Radial Tires

DAILY DEMAND PROBABILITY CUMULATIVE PROBABILITY

0 0.05 0.05

1 0.10 0.15

2 0.20 0.35

3 0.30 0.65

4 0.20 0.85

5 0.15 1.00

Table 14.2

Harry’s Auto TireHarry’s Auto Tire

Step 3: Setting random number intervalsStep 3: Setting random number intervals Assign a set of numbers to represent each Assign a set of numbers to represent each

possible value or outcome.possible value or outcome.These are These are random number intervals.random number intervals.

A A random numberrandom number is a series of digits that is a series of digits that have been selected by a totally random have been selected by a totally random process.process.

The range of the random number intervals The range of the random number intervals corresponds corresponds exactlyexactly to the probability of the to the probability of the outcomes as shown in Figure 14.2.outcomes as shown in Figure 14.2.

14-31


Graphical Representation of the Cumulative Graphical Representation of the Cumulative Probability Distribution for Radial TiresProbability Distribution for Radial Tires

– 00

8685

6665

3635

1615060501

––

––

––

––

–––

Ran

dom

N

umbe

rs

Represents 4 Tires Demanded

Represents 1 Tire Demanded0.05

0.15

0.35

0.65

0.85

1.001.00 –

0.80 –

0.60 –

0.40 –

0.20 –

0.00 –

0 1 2 3 4 5

Daily Demand for Radials

Cum

ulat

ive

Pro

babi

lity

Figure 14.2


Assignment of Random Number Intervals Assignment of Random Number Intervals for Harry’s Auto Tirefor Harry’s Auto Tire

DAILY DEMAND PROBABILITY CUMULATIVE PROBABILITY

INTERVAL OF RANDOM NUMBERS

0 0.05 0.05 01 to 05

1 0.10 0.15 06 to 15

2 0.20 0.35 16 to 35

3 0.30 0.65 36 to 65

4 0.20 0.85 66 to 85

5 0.15 1.00 86 to 00

Table 14.3

Harry’s Auto TireHarry’s Auto TireStep 4: Generating random numbersStep 4: Generating random numbers Random numbers can be generated in several Random numbers can be generated in several

ways.ways. Large problems will use computer program to Large problems will use computer program to

generate the needed random numbers.generate the needed random numbers. For small problems, random processes like For small problems, random processes like

roulette wheels or pulling chips from a hat may roulette wheels or pulling chips from a hat may be used.be used.

The most common manual method is to use a The most common manual method is to use a random number table.random number table.

Because Because everythingeverything is random in a random is random in a random number table, we can select numbers from number table, we can select numbers from anywhere in the table to use in the simulation.anywhere in the table to use in the simulation.

Harry’s Auto Tire

Table of random numbers (partial)Table of random numbers (partial)

52 06 50 88 53 30 10 47 99 37

37 63 28 02 74 35 24 03 29 60

82 57 68 28 05 94 03 11 27 79

69 02 36 49 71 99 32 10 75 21

98 94 90 36 06 78 23 67 89 85

96 52 62 87 49 56 59 23 78 71

33 69 27 21 11 60 95 89 68 48

50 33 50 95 13 44 34 62 64 39

88 32 18 50 62 57 34 56 62 31

90 30 36 24 69 82 51 74 30 35

Table 14.4

Harry’s Auto Tire

Step 5: Simulating the experimentStep 5: Simulating the experimentWe select random numbers from We select random numbers from

Table 14.4.Table 14.4.The number we select will have a The number we select will have a

corresponding range in Table 14.3.corresponding range in Table 14.3.We use the daily demand that We use the daily demand that

corresponds to the probability range corresponds to the probability range aligned with the random number.aligned with the random number.


Ten-day Simulation of Demand for Radial TiresTen-day Simulation of Demand for Radial Tires

DAY RANDOM NUMBER SIMULATED DAILY DEMAND

1 52 3

2 37 3

3 82 4

4 69 4

5 98 5

6 96 5

7 33 2

8 50 3

9 88 5

10 90 5

39 = total 10-day demand

3.9 = average daily demand for tires

Table 14.5

Harry’s Auto TireHarry’s Auto TireNote that the average demand from this Note that the average demand from this simulation (3.9 tires) is different from the simulation (3.9 tires) is different from the expectedexpected daily demand. daily demand.

Expected Expected daily demanddaily demand ( ) ( )tires of Demandtires of yProbabilit

5

0

iii∑

==

== (0.05)(0) + (0.10)(1) + (0.20)(2) + (0.30)(3) + (0.20)(4) + (0.05)(0) + (0.10)(1) + (0.20)(2) + (0.30)(3) + (0.20)(4) + (0.15)(5)(0.15)(5)

== 2.95 tires2.95 tires

If this simulation were repeated hundreds or If this simulation were repeated hundreds or thousands of times it is much more likely thousands of times it is much more likely the average the average simulatedsimulated demand would be demand would be nearly the same as the nearly the same as the expectedexpected demand. demand.

QM for Windows Output Screen for QM for Windows Output Screen for Simulation of Harry’s Auto Tire ExampleSimulation of Harry’s Auto Tire Example

Program 14.1

Simulation with Excel SpreadsheetsSimulation with Excel Spreadsheets

Using Excel 2010 to Simulate Tire Demand Using Excel 2010 to Simulate Tire Demand for Harry’s Auto Tire Shopfor Harry’s Auto Tire Shop

Program 14.2


Using Excel 2010 to Simulate Tire Demand for Using Excel 2010 to Simulate Tire Demand for Harry’s Auto Tire ShopHarry’s Auto Tire Shop

Program 14.2


Generating Normal Random Numbers in Excel

Program 14.3

14-42


Excel QM Simulation of Harry’s Auto Tire ExampleExcel QM Simulation of Harry’s Auto Tire Example

Program 14.4

Some TerminologySome Terminology

SimulationSimulationMonte Carlo simulationMonte Carlo simulation

Discrete random variablesDiscrete random variablesContinuous random variablesContinuous random variablesEvent treesEvent trees

Risk nodesRisk nodesBranchesBranchesTerminal nodesTerminal nodes

Example 1Example 1Drugco has just begun Phase I trials for Newdrug. Drugco has just begun Phase I trials for Newdrug.

1.1. Phase I takes one year and costs $10M. Drugco’s scientists estimate Phase I takes one year and costs $10M. Drugco’s scientists estimate that the R&D has a 50 percent chance of successfully completing that the R&D has a 50 percent chance of successfully completing Phase I and moving to Phase II. Phase I and moving to Phase II.

2.2. Phase II takes one year and costs $30M. If Newdrug enters Phase Phase II takes one year and costs $30M. If Newdrug enters Phase II, the scientists estimate a 40 percent chance of successfully II, the scientists estimate a 40 percent chance of successfully completing Phase II and moving to Phase III. completing Phase II and moving to Phase III.

3.3. Phase III takes three years (including the time waiting for FDA Phase III takes three years (including the time waiting for FDA approval) and costs $60M. If Newdrug enters Phase III, the approval) and costs $60M. If Newdrug enters Phase III, the scientists estimate a 50 percent chance of success (= FDA scientists estimate a 50 percent chance of success (= FDA approval). approval).

4.4. Drugco management estimates an NPV of $1B at the time of Drugco management estimates an NPV of $1B at the time of approval. If the drug fails, then it would be worth nothing. The approval. If the drug fails, then it would be worth nothing. The discount rate is equal to the riskfree rate of 5 percent per year. All discount rate is equal to the riskfree rate of 5 percent per year. All development costs must be paid at the beginning of the respective development costs must be paid at the beginning of the respective phase.phase.

ProblemsProblemsa)a) Draw the event tree for the Newdrug project.Draw the event tree for the Newdrug project.b)b) Find and solve the formula for the NPV of the Newdrug project.Find and solve the formula for the NPV of the Newdrug project.c)c) Build a Monte Carlo simulation for Newdrug and confirm the same Build a Monte Carlo simulation for Newdrug and confirm the same

(average) NPV solution as obtained in part (b).(average) NPV solution as obtained in part (b).

Event Tree

Example 2Example 2Drugco has just begun Phase III trials for Newdrug. For Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we are sure the drug has no side simplicity, we assume that we are sure the drug has no side effects, so all that matters for FDA approval is its efficacy. effects, so all that matters for FDA approval is its efficacy. Efficacy is distributed Efficacy is distributed EE ~ ~ UU [0,1] and will be learned during [0,1] and will be learned during three years of Phase III trails. The NPV of the drug after 3 three years of Phase III trails. The NPV of the drug after 3 years is $1B * years is $1B * EE22 (i.e., even with a low efficacy and a high (i.e., even with a low efficacy and a high likelihood of FDA failure, we are still allowing for some likelihood of FDA failure, we are still allowing for some salvage value for the project). The discount rate is equal to the salvage value for the project). The discount rate is equal to the riskfree rate of 5 percent per year. The total cost of R&D is riskfree rate of 5 percent per year. The total cost of R&D is $100M and must be paid at the beginning of development.$100M and must be paid at the beginning of development.

ProblemsProblemsa)a) Draw an event tree for the Newdrug project.Draw an event tree for the Newdrug project.b)b) What is the NPV of Newdrug if efficacy is set equal to its What is the NPV of Newdrug if efficacy is set equal to its

expected value?expected value?c)c) Use Monte Carlo simulation to solve for the NPV of the Use Monte Carlo simulation to solve for the NPV of the

Newdrug project.Newdrug project.d)d) Why is the answer to part (b) different than the answer to part Why is the answer to part (b) different than the answer to part

(c)?(c)?

Event Tree

Example 3Example 3 Drugco has just begun Phase III trials for Newdrug at Drugco has just begun Phase III trials for Newdrug at

a cost of $100Ma cost of $100M Phase III trials expected to take two years, and FDA Phase III trials expected to take two years, and FDA

decision one year after that.decision one year after that. Efficacy unknown: N(40,20).Efficacy unknown: N(40,20). FDA approval expected if E > 30.FDA approval expected if E > 30. Best alternative has efficacy of 50, but could get better Best alternative has efficacy of 50, but could get better

over next three years: T(50,100,50).over next three years: T(50,100,50). Initial market size unknown: N(1000M,100M).Initial market size unknown: N(1000M,100M). Market growth of 6 percent per year thereafter.Market growth of 6 percent per year thereafter. Market share: EMarket share: E22 / (E / (E22 + A + A22)) Marketing costs of $300M in first year, increasing at 6% Marketing costs of $300M in first year, increasing at 6%

per year thereafter.per year thereafter. Ten years of patent life remain after approval, NPV of Ten years of patent life remain after approval, NPV of

zero after patent expiration.zero after patent expiration. Discount rate of 5 percent per year.Discount rate of 5 percent per year.

Event TreeEvent Tree

3. Real Options Analysis


What is involved in making a good What is involved in making a good decision?decision?

Decision theory is an analytic and Decision theory is an analytic and systematic approach to the study systematic approach to the study of decision making.of decision making.

A good decision is one that is based A good decision is one that is based on logic, considers all available on logic, considers all available data and possible alternatives, and data and possible alternatives, and the quantitative approach the quantitative approach described here.described here.

The Six Steps in Decision MakingThe Six Steps in Decision Making

1.1. Clearly define the problem at hand.Clearly define the problem at hand.

2.2. List the possible alternatives.List the possible alternatives.

3.3. Identify the possible outcomes or states of Identify the possible outcomes or states of nature.nature.

4.4. List the List the payoffpayoff (typically profit) of each (typically profit) of each combination of alternatives and outcomes.combination of alternatives and outcomes.

5.5. Select one of the mathematical decision Select one of the mathematical decision theory models.theory models.

6.6. Apply the model and make your decision.Apply the model and make your decision.

Example : Thompson Lumber CompanyExample : Thompson Lumber CompanyStep 1 –Step 1 – Define the problem.Define the problem.

The company is considering expanding The company is considering expanding by manufacturing and marketing a new by manufacturing and marketing a new product – backyard storage sheds.product – backyard storage sheds.

Step 2 –Step 2 – List alternatives.List alternatives. Construct a large new plant.Construct a large new plant. Construct a small new plant.Construct a small new plant. Do not develop the new product line at Do not develop the new product line at

all.all.

Step 3 –Step 3 – Identify possible outcomes.Identify possible outcomes. The market could be favourable or The market could be favourable or

unfavourable.unfavourable.

Thompson Lumber CompanyThompson Lumber CompanyStep 4 –Step 4 – List the payoffs.List the payoffs.

Identify Identify conditional valuesconditional values for the for the profits for large plant, small plant, and profits for large plant, small plant, and no development for the two possible no development for the two possible market conditions.market conditions.

Step 5 –Step 5 – Select the decision model.Select the decision model. This depends on the environment and This depends on the environment and

amount of risk and uncertainty.amount of risk and uncertainty.

Step 6 –Step 6 – Apply the model to the data.Apply the model to the data. Solution and analysis are then used to Solution and analysis are then used to

aid in decision-making.aid in decision-making.

Thompson Lumber CompanyThompson Lumber Company

STATE OF NATURESTATE OF NATURE

ALTERNATIVEALTERNATIVEFAVOURABLE FAVOURABLE

MARKET ($)MARKET ($)UNFAVOURABLEUNFAVOURABLE

MARKET ($)MARKET ($)

Construct a large Construct a large plantplant 200,000200,000 ––180,000180,000

Construct a small Construct a small plantplant 100,000100,000 ––20,00020,000

Do nothingDo nothing 00 00

Table 3.1

Decision Table with Conditional Values Decision Table with Conditional Values for Thompson Lumberfor Thompson Lumber

Types of Decision-Making EnvironmentsTypes of Decision-Making EnvironmentsType 1:Type 1: Decision making under certaintyDecision making under certainty

The decision maker The decision maker knows with certaintyknows with certainty the the consequences of every alternative or decision consequences of every alternative or decision choice.choice.

Type 2:Type 2: Decision making under uncertaintyDecision making under uncertainty The decision maker The decision maker does not knowdoes not know the the

probabilities of the various outcomes.probabilities of the various outcomes.

Type 3:Type 3: Decision making under riskDecision making under risk The decision maker The decision maker knows the probabilitiesknows the probabilities of of

the various outcomes.the various outcomes.

Decision Making Under UncertaintyDecision Making Under Uncertainty

1.1. Maximax (optimistic)Maximax (optimistic)

2.2. Maximin (pessimistic)Maximin (pessimistic)

3.3. Criterion of realism (Hurwicz)Criterion of realism (Hurwicz)

4.4. Equally likely (Laplace) Equally likely (Laplace)

5.5. Minimax regretMinimax regret

There are several criteria for making There are several criteria for making decisions under uncertainty:decisions under uncertainty:

1. Maximax1. MaximaxUsed to find the alternative that Used to find the alternative that maximizes the maximum payoff.maximizes the maximum payoff.

Locate the maximum payoff for each alternative.Locate the maximum payoff for each alternative. Select the alternative with the maximum number.Select the alternative with the maximum number.


ALTERNATIVEALTERNATIVEFAVORABLE FAVORABLE MARKET ($)MARKET ($)

UNFAVORABLE UNFAVORABLE MARKET ($)MARKET ($)

MAXIMUM IN MAXIMUM IN A ROW ($)A ROW ($)

Construct a large Construct a large plantplant 200,000200,000 ––180,000180,000 200,000200,000

Construct a small Construct a small plantplant 100,000100,000 ––20,00020,000 100,000100,000

Do nothingDo nothing 00 00 00

Table 3.2

MaximaxMaximax

2. MaximinUsed to find the alternative that maximizes the minimum payoff.

Locate the minimum payoff for each alternative. Select the alternative with the maximum number.

STATE OF NATURE


MARKET ($)MARKET ($)UNFAVOURABLUNFAVOURABLE MARKET ($)E MARKET ($)

MINIMUM IN MINIMUM IN A ROW ($)A ROW ($)

Construct a large Construct a large plantplant 200,000200,000 ––180,000180,000 ––180,000180,000

Construct a small Construct a small plantplant 100,000100,000 ––20,00020,000 ––20,00020,000


Table 3.3 MaximinMaximin

3.Criterion of Realism (Hurwicz)3.Criterion of Realism (Hurwicz)This is a This is a weightedweighted average average compromise compromise between optimism and pessimism.between optimism and pessimism.

Select a coefficient of realism Select a coefficient of realism αα, with 0≤ , with 0≤ αα ≤1.≤1. A value of 1 is perfectly optimistic, while a value A value of 1 is perfectly optimistic, while a value

of 0 is perfectly pessimistic.of 0 is perfectly pessimistic. Compute the weighted averages for each Compute the weighted averages for each

alternative.alternative. Select the alternative with the highest value.Select the alternative with the highest value.

Weighted average =Weighted average =αα (maximum in row) (maximum in row) + (1 – + (1 – αα)(minimum in row))(minimum in row)

3.Criterion of Realism (Hurwicz) For the large plant alternative using For the large plant alternative using αα = 0.8: = 0.8:

(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000 For the small plant alternative using For the small plant alternative using αα = 0.8: = 0.8:

(0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000(0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000STATE OF NATURE


MARKET ($)MARKET ($)UNFAVOURABLE UNFAVOURABLE

MARKET ($)MARKET ($)

CRITERION CRITERION OF REALISM OF REALISM

((αα = 0.8) $ = 0.8) $




Table 3.4

RealismRealism

4.Equally Likely (Laplace)Considers all the payoffs for each Considers all the payoffs for each alternative alternative

Find the average payoff for each Find the average payoff for each alternative.alternative.

Select the alternative with the highest Select the alternative with the highest average.average.


ALTERNATIVEALTERNATIVEFAVOURABLFAVOURABLE MARKET ($)E MARKET ($)

UNFAVOURABLE UNFAVOURABLE MARKET ($)MARKET ($)

ROW ROW AVERAGE ($)AVERAGE ($)




Table 3.5

Equally likelyEqually likely

3-63

5.Minimax RegretBased on Based on opportunity lossopportunity loss or or regretregret, this is the , this is the difference between the optimal profit and actual difference between the optimal profit and actual payoff for a decision.payoff for a decision.

Create an opportunity loss table by determining the Create an opportunity loss table by determining the opportunity loss from not choosing the best opportunity loss from not choosing the best alternative.alternative.

Opportunity loss is calculated by subtracting each Opportunity loss is calculated by subtracting each payoff in the column from the best payoff in the payoff in the column from the best payoff in the column.column.

Find the maximum opportunity loss for each Find the maximum opportunity loss for each alternative and pick the alternative with the alternative and pick the alternative with the minimum number.minimum number.

5.Minimax Regret


FAVOURABLE FAVOURABLE MARKET ($)MARKET ($)


200,000 200,000 – 200,000– 200,000 0 0 – (–180,000)– (–180,000)

200,000 200,000 – 100,000– 100,000 00 – (–20,000) – (–20,000)

200,000 200,000 – 0– 0 00 – 0 – 0

Table 3.6

Determining Opportunity Losses for Thompson Lumber

5.Minimax Regret

Table 3.7


ALTERNATIVEALTERNATIVEFAVOURABLE FAVOURABLE MARKET ($)MARKET ($)


Construct a large plantConstruct a large plant 00 180,000180,000

Construct a small plantConstruct a small plant 100,000100,000 20,00020,000

Do nothingDo nothing 200,000200,000 00

Opportunity Loss Table for Thompson Lumber

3-66

5.Minimax Regret

Table 3.8




MARKET ($)MARKET ($)MAXIMUM IN MAXIMUM IN

A ROW ($)A ROW ($)

Construct a large Construct a large plantplant 00 180,000180,000 180,000180,000

Construct a small Construct a small plantplant 100,000100,000 20,00020,000 100,000100,000

Do nothingDo nothing 200,000200,000 00 200,000200,000MinimaxMinimax

Thompson’s Minimax Decision Using Thompson’s Minimax Decision Using Opportunity LossOpportunity Loss

3-67

Decision Making Under Risk This is decision making when there are several possible

states of nature, and the probabilities associated with each possible state are known.

The most popular method is to choose the alternative with the highest expected monetary value (EMV).expected monetary value (EMV).This is very similar to the expected value calculated in probability distribution.

EMVEMV (alternative (alternative ii)) = (payoff of first state of nature)= (payoff of first state of nature)x (probability of first state of nature)x (probability of first state of nature)+ (payoff of second state of nature)+ (payoff of second state of nature)x (probability of second state of nature)x (probability of second state of nature)+ … + (payoff of last state of nature)+ … + (payoff of last state of nature)x (probability of last state of nature)x (probability of last state of nature)

EMV for Thompson Lumber Suppose each market outcome has a

probability of occurrence of 0.50. Which alternative would give the highest EMV? The calculations are:

EMVEMV (large plant)= ($200,000)(0.5) + (–$180,000)(0.5) (large plant)= ($200,000)(0.5) + (–$180,000)(0.5) = $10,000= $10,000

EMVEMV (small plant)= ($100,000)(0.5) + (–$20,000)(0.5) (small plant)= ($100,000)(0.5) + (–$20,000)(0.5) = $40,000= $40,000

EMVEMV (do nothing)= ($0)(0.5) + ($0)(0.5) (do nothing)= ($0)(0.5) + ($0)(0.5) = $0= $0

3-69

EMV for Thompson Lumber




MARKET ($)MARKET ($) EMVEMV ($) ($)




ProbabilitiesProbabilities 0.500.50 0.500.50

Table 3.9 Largest Largest EMVEMV

Using Excel

Program 3.1A

Input Data for the Thompson Lumber Problem Using Input Data for the Thompson Lumber Problem Using Excel QMExcel QM

Using ExcelOutput Results for the Thompson Lumber Output Results for the Thompson Lumber Problem Using Excel QMProblem Using Excel QM

Decision Trees Any problem that can be presented in a decision

table can also be graphically represented in a decision tree.decision tree.

Decision trees are most beneficial when a sequence of decisions must be made.

All decision trees contain decision pointsdecision points or nodes, nodes, from which one of several alternatives may be chosen.

All decision trees contain state-of-nature pointsstate-of-nature points or nodes, nodes, out of which one state of nature will occur.

Five Steps ofDecision Tree Analysis

1. Define the problem.

2. Structure or draw the decision tree.

3. Assign probabilities to the states of nature.

4. Estimate payoffs for each possible combination of alternatives and states of nature.

5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node.

Structure of Decision Trees

Trees start from left to right. Trees represent decisions and outcomes in

sequential order.Squares represent decision nodes.Circles represent states of nature nodes.Lines or branches connect the decisions nodes and

the states of nature.

Thompson’s Decision Tree

Favourable Market

Unfavourable Market

Favourable Market

Unfavourable Market

Do Nothing

Construct

Large Plant

11

Construct

Small Plant22

Figure 3.2

A Decision Node

A State-of-Nature Node

Thompson’s Decision Tree

Favourable Market

Unfavourable Market

Favourable Market

Unfavourable Market

Do Nothing

Construct

Large Plant

1

Construct

Small Plant2

Alternative with best Alternative with best EMVEMV is selected is selected

Figure 3.3

EMVEMV for Node 1 for Node 1 = $10,000= $10,000

= (0.5)($200,000) + (0.5)(–$180,000)

EMV for Node 2 = $40,000

= (0.5)($100,000) + (0.5)(–$20,000)

PayoffsPayoffs

$200,000$200,000

––$180,000$180,000

$100,000$100,000

––$20,000$20,000

$0$0

(0.5)(0.5)

(0.5)(0.5)

(0.5)(0.5)

(0.5)(0.5)

Thompson’s Complex Decision Tree

First Decision First Decision PointPoint

Second Decision Second Decision PointPoint

Favourable Market (0.78)

Unfavourable Market (0.22)










Unfavourable Market (0.50)Large Plant

Small Plant

No Plant

6

7

Condu

ct M

arke

t Sur

vey

Do Not Conduct Survey

Large Plant

Small Plant

No Plant

2

3

Large Plant

Small Plant

No Plant

4

5

1Resu

lts

Favora

ble

ResultsNegative

Survey (

0.45)

Survey (0.55)

PayoffsPayoffs

–$190,000

$190,000190,000

$90,000

–$30,000

–$10,000

–$180,000

$200,000

$100,000

–$20,000

$0

–$190,000

$190,000

$90,000

–$30,000

–$10,000

Figure 3.4

Thompson’s Complex Decision Tree1.1. Given favourable survey results,Given favourable survey results,

EMVEMV(node 2)= (node 2)= EMVEMV(large plant | positive (large plant | positive survey)survey)= (0.78)($190,000) + (0.22)(–$190,000) = = (0.78)($190,000) + (0.22)(–$190,000) = $106,400$106,400EMVEMV(node 3)= (node 3)= EMVEMV(small plant | positive (small plant | positive survey)survey)

= (0.78)($90,000) + (0.22)(–$30,000) = = (0.78)($90,000) + (0.22)(–$30,000) = $63,600$63,600EMVEMV for no plant = –$10,000 for no plant = –$10,000

2.2. Given negative survey results,Given negative survey results,EMVEMV(node 4)= (node 4)= EMVEMV(large plant | negative (large plant | negative survey)survey)= (0.27)($190,000) + (0.73)(–$190,000) = –= (0.27)($190,000) + (0.73)(–$190,000) = –$87,400$87,400EMVEMV(node 5)= (node 5)= EMVEMV(small plant | negative (small plant | negative survey)survey)

= (0.27)($90,000) + (0.73)(–$30,000)= (0.27)($90,000) + (0.73)(–$30,000) = $2,400= $2,400

EMVEMV for no plant = –$10,000 for no plant = –$10,000


3.3. Compute the expected value of the market Compute the expected value of the market survey,survey,EMVEMV(node 1)= (node 1)= EMVEMV(conduct survey)(conduct survey)

= (0.45)($106,400) + (0.55)($2,400)= (0.45)($106,400) + (0.55)($2,400)= $47,880 + $1,320 = $49,200= $47,880 + $1,320 = $49,200

4.4. If the market survey is not conducted,If the market survey is not conducted,EMVEMV(node 6)= (node 6)= EMVEMV(large plant)(large plant)

= (0.50)($200,000) + (0.50)(–$180,000) = (0.50)($200,000) + (0.50)(–$180,000) = $10,000= $10,000

EMVEMV(node 7)= (node 7)= EMVEMV(small plant)(small plant)= (0.50)($100,000) + (0.50)(–$20,000) = (0.50)($100,000) + (0.50)(–$20,000) = $40,000= $40,000

EMVEMV for no plant = $0 for no plant = $0

5.5. The best choice is to seek marketing The best choice is to seek marketing informationinformation


Figure 3.5

First Decision First Decision PointPoint

Second Decision Second Decision PointPoint












Unfavourable Market (0.50)Large Plant

Small Plant

No Plant

Condu

ct M

arke

t Sur

vey

Do Not Conduct Survey

Large Plant

Small Plant

No Plant

Large Plant

Small Plant

No Plant

Results

Favora

ble

ResultsNegative

Survey (

0.45)

Survey (0.55)

PayoffsPayoffs

–$190,000

$190,000

$90,000

–$30,000

–$10,000

–$180,000

$200,000

$100,000

–$20,000

$0

–$190,000

$190,000

$90,000

–$30,000

–$10,000

$40,

000

$40,

000

$2,4

00$2

,400

$106

,400

$106

,400

$49,

200

$49,

200

$106,400

$63,600

–$87,400

$2,400

$10,000

$40,000

CommutingCommuting

highway

1

backroads

20

2

traffic

no traffic

40%

60%

15

30

Commuting Options, with exitCommuting Options, with exit

Commuting Options, prunedCommuting Options, pruned

Types of Real OptionsTypes of Real Options

DelayDelayExpandExpandExtendExtendAbandonAbandonShrinkShrinkSwitchSwitch

Example: Fuelco Project AExample: Fuelco Project AFuelco is considering a development project using its patented fuel-Fuelco is considering a development project using its patented fuel-cell technology. cell technology.

1.1. If Fuelco pays $200M to start the project, then they are permitted to If Fuelco pays $200M to start the project, then they are permitted to bid for a government contract. The objective probability of winning bid for a government contract. The objective probability of winning the contract is 50 percent, and there is no beta risk for the the contract is 50 percent, and there is no beta risk for the government’s decision. government’s decision.

2.2. If Fuelco’s bid is accepted (one year later), then they can choose to If Fuelco’s bid is accepted (one year later), then they can choose to finish the project by accepting the contract (cost = $300M), when finish the project by accepting the contract (cost = $300M), when they will earn an NPV (as of one year from now) of $600M (not they will earn an NPV (as of one year from now) of $600M (not including the $300M cost of finishing the project). including the $300M cost of finishing the project).

3.3. If they do not receive the contract, then they can still finish the If they do not receive the contract, then they can still finish the development project (cost = $300M), but they could only receive development project (cost = $300M), but they could only receive $200M for the project by selling it to some nongovernmental buyer $200M for the project by selling it to some nongovernmental buyer (not including the $300M cost of finishing the project). The risk-(not including the $300M cost of finishing the project). The risk-free rate is zero.free rate is zero.

ProblemsProblemsa)a) Draw the tree for Fuelco’s problem under the assumption that it Draw the tree for Fuelco’s problem under the assumption that it

starts the project.starts the project.b)b) Compute the NPV for the project. Should Fuelco start the project?Compute the NPV for the project. Should Fuelco start the project?

Fuelco’s Decision Tree (Project A)Fuelco’s Decision Tree (Project A)

Example: Fuelco Project BExample: Fuelco Project BIn addition to Project A, Fuelco is also considering a separate investment in In addition to Project A, Fuelco is also considering a separate investment in fuel-cell technology designed to replace oil-based energy for some types of fuel-cell technology designed to replace oil-based energy for some types of engines . engines .

1.1. By investing $100M today to start the project, Fuelco would maintain the By investing $100M today to start the project, Fuelco would maintain the option to finish the project with a further investment (= $200M) in one year. option to finish the project with a further investment (= $200M) in one year.

2.2. If oil prices are at least $60 per barrel in one year (objective probability = If oil prices are at least $60 per barrel in one year (objective probability = 50%), then on completion of the project, Fuelco would have an NPV (as of 50%), then on completion of the project, Fuelco would have an NPV (as of one year from now) of $1000M (not including the $200M cost of finishing the one year from now) of $1000M (not including the $200M cost of finishing the project). project).

3.3. If oil prices are less than $60 a barrel in one year (objective probability = If oil prices are less than $60 a barrel in one year (objective probability = 50%), then the project would not be economical for most applications and 50%), then the project would not be economical for most applications and would have an NPV (one year from now) of $300M (not including the $200M would have an NPV (one year from now) of $300M (not including the $200M cost of finishing the project). cost of finishing the project).

4.4. If Fuelco decides not to finish the project, then they can sell the technology to If Fuelco decides not to finish the project, then they can sell the technology to a competitor for $200M, regardless of the price of oil. The beta for the project a competitor for $200M, regardless of the price of oil. The beta for the project is unknown, but we do have some information about oil prices: the market is unknown, but we do have some information about oil prices: the market price of a European binary call option (payoff = $1) on oil with a strike price price of a European binary call option (payoff = $1) on oil with a strike price of $60 per barrel, and an expiration of 1 year is 25 cents. of $60 per barrel, and an expiration of 1 year is 25 cents.

ProblemsProblemsa) Draw the tree for Fuelco’s problem under the assumption that it starts the project.a) Draw the tree for Fuelco’s problem under the assumption that it starts the project.b) Compute the NPV for the project. Should Fuelco start the project?b) Compute the NPV for the project. Should Fuelco start the project?

Fuelco’s Decision Tree (Project B)Fuelco’s Decision Tree (Project B)

Fuelco’s Decision Tree (Project B, pruned)Fuelco’s Decision Tree (Project B, pruned)

Alternative Solution: Risk-neutral probabilitiesAlternative Solution: Risk-neutral probabilities

If everyone in the world was risk If everyone in the world was risk neutral, what probabilities would neutral, what probabilities would have to go into the tree?have to go into the tree?

These probabilities are a fiction. These probabilities are a fiction. They are make-believe. They are They are make-believe. They are fantasy. They are not real. fantasy. They are not real.

Fuelco’s Decision Tree (Project B, pruned) Fuelco’s Decision Tree (Project B, pruned) Risk-Neutral WorldRisk-Neutral World

Example: Fuelco Project CExample: Fuelco Project CFuelco is considering a consumer application for their patented fuel-cell Fuelco is considering a consumer application for their patented fuel-cell technology. They have already completed several R&D projects with this technology. They have already completed several R&D projects with this technology, so they have eliminated the technical risk for this new project. technology, so they have eliminated the technical risk for this new project.

1.1. To begin producing and marketing to the consumer market would require a To begin producing and marketing to the consumer market would require a new investment of $200M, to be paid in one year. new investment of $200M, to be paid in one year.

2.2. The value of Project C depends on consumer demand. If demand is “high” (50 The value of Project C depends on consumer demand. If demand is “high” (50 percent chance), then the value of the project would be $600M (one year from percent chance), then the value of the project would be $600M (one year from now). now).

3.3. If demand is “low” (50 percent chance), then the value of the project would be If demand is “low” (50 percent chance), then the value of the project would be $200M. $200M.

4.4. If Fuelco chooses not to undertake the project, then they can still sell some of If Fuelco chooses not to undertake the project, then they can still sell some of the related patents to another firm. If demand is “high” (50 percent chance), the related patents to another firm. If demand is “high” (50 percent chance), then the salvage value of these patents would be $300M (one year from now).then the salvage value of these patents would be $300M (one year from now).

5.5. If demand is “low” (50 percent chance), then the salvage value of these patents If demand is “low” (50 percent chance), then the salvage value of these patents would be $100M. Selling the patents has no effect on any of Fuelco’s other would be $100M. Selling the patents has no effect on any of Fuelco’s other projects. projects.

We will use the CAPM to estimate expected returns in this problem, where the We will use the CAPM to estimate expected returns in this problem, where the expected market premium is 7 percent, and the risk-free rate is 5 percent. expected market premium is 7 percent, and the risk-free rate is 5 percent.

Fuelco’s Decision Tree, Project CFuelco’s Decision Tree, Project C

Fuelco’s Decision Tree, prunedFuelco’s Decision Tree, pruned

Fuelco’s event tree, after node 3 Fuelco’s event tree, after node 3 Risk-Neutral World, β = 1Risk-Neutral World, β = 1

Further ReadingFurther Reading

Metrick, Andrew and Yasuda, Ayako (2011) Venture Capital & the Finance of Innovation. 2nd Edition. John Wiley & Sons.

Lerner,Losh, Hardymon, Felda and Leamon, Ann (2012). Venture Capital and Private Equity : A Casebook. 5th Edition. John Wiley & Sons.

Dorf, R.C. and Byers, T.H. (2008) Technology Ventures – From Idea to Enterprise 2nd Edition, McGraw Hill

QUESTIONS?

gs503 vcf lecture 7 innovation finance i 300315

Business

rd financingexhibit

rd financethemesnonlinearities

systematic use

financing of rd projectsto

nsfbasic research

objective of applied

objective of basic research

use of decision trees