THE FINANCE OF THE FINANCE OF INNOVATION : INNOVATION : BINOMIAL BINOMIAL

TREES, TREES, GAME THEORY &GAME THEORY &R&D VALUATIONR&D VALUATIONProf.Stephen OngProf.Stephen Ong

BSc(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 use of To understand the use of binomial trees in decision binomial trees in decision making;making;

To understand the use of To understand the use of game theory in the evaluation game theory in the evaluation of strategic options;of strategic options;

To understand the valuation To understand the valuation of R&D projects.of R&D projects.

1.Binomial Trees

Call Option in a Decision TreeCall Option in a Decision Tree

A 3-Step Binomial TreeA 3-Step Binomial Tree

Multi-step treesMulti-step trees

To solveTo solve1)1) Compute the key inputs: u, d, and p.Compute the key inputs: u, d, and p.

2)2) Build the Build the base treebase tree by solving by solving forwards forwards using the up and down movements.using the up and down movements.

3) Build the 3) Build the option treeoption tree by solving by solving backwards backwards using the risk-neutral using the risk-neutral probabilities.probabilities.

Base TreeBase Tree

Option TreeOption Tree

Cox, Ross, and Rubinstein (CRR) ModelCox, Ross, and Rubinstein (CRR) Model

Time length = tTime length = t Annualized volatility = Annualized volatility = σσ Riskless interest rate = rRiskless interest rate = r Then Then

u = u =

d = 1/u = d = 1/u =

p = (p = (eertrt – d) / (u – d) – d) / (u – d)

teσ

te σ−

Joe’s ProblemJoe’s Problem

AssumeAssumeStarting stock price = S = $100Starting stock price = S = $100Strike Price = X = $50Strike Price = X = $50Volatility = Volatility = σσ = 60% = 60%Riskfree rate = r = 5%Riskfree rate = r = 5%Time to expiration = T = 1Time to expiration = T = 13-step tree → N = 3 and t = 1/3 3-step tree → N = 3 and t = 1/3

Joe’s Problem, Base TreeJoe’s Problem, Base Tree

Joe’s Problem, Option TreeJoe’s Problem, Option Tree

Example 1Example 1Drugco is a publicly traded biotechnology company with several Drugco is a publicly traded biotechnology company with several drugs in development, but no products on the market. To raise drugs in development, but no products on the market. To raise capital for the development of Newdrug, Drugco enters a strategic capital for the development of Newdrug, Drugco enters a strategic alliance with Bigco. In return for marketing rights for Newdrug, alliance with Bigco. In return for marketing rights for Newdrug, Bigco will pay for clinical trials and will give Drugco up-front and Bigco will pay for clinical trials and will give Drugco up-front and milestone payments. Bigco also agrees to make an equity milestone payments. Bigco also agrees to make an equity investment in Drugco, purchasing ten million shares at the market investment in Drugco, purchasing ten million shares at the market price of $10 per share and also receiving warrants to purchase an price of $10 per share and also receiving warrants to purchase an additional 10 million shares. (The market price of $10 includes the additional 10 million shares. (The market price of $10 includes the market reaction to the Bigco alliance.) These warrants can either be market reaction to the Bigco alliance.) These warrants can either be exercised in exactly two years at a strike price of $20 per share or exercised in exactly two years at a strike price of $20 per share or in exactly five years, with a strike price of $50 per share. Drugco in exactly five years, with a strike price of $50 per share. Drugco does not pay dividends and has no plans (or cash) to do so for at does not pay dividends and has no plans (or cash) to do so for at least the next five years. The expected volatility of Drugco stock is least the next five years. The expected volatility of Drugco stock is 60 percent per year.60 percent per year.

Problem Problem What is the value of Bigco’s warrants?What is the value of Bigco’s warrants?

DividendsDividends

Consider again Joe’s three-step problem. Consider again Joe’s three-step problem. Now, let’s add a dividend in the second-to-last Now, let’s add a dividend in the second-to-last period (eight months into the year) that is period (eight months into the year) that is equal to 10 percent of the stock value. Now, if equal to 10 percent of the stock value. Now, if Joe decides to exercise after eight months, he Joe decides to exercise after eight months, he would receive the whole value of the stock would receive the whole value of the stock (including the 10 percent dividend). If, (including the 10 percent dividend). If, instead, he decides to wait until the full year is instead, he decides to wait until the full year is over, then the 10 percent dividend gets paid over, then the 10 percent dividend gets paid out after eight months, and the stock price out after eight months, and the stock price falls by 10 percent before making an up or falls by 10 percent before making an up or down move in the last period. down move in the last period.

Joe’s Problem, Base Tree, with DividendsJoe’s Problem, Base Tree, with Dividends

Joe’s Problem, Option Tree, with DividendsJoe’s Problem, Option Tree, with Dividends

Example 2Example 2Fuelco is considering a consumer application for their patented Fuelco is considering a consumer application for their patented fuel-cell technology. They have already completed several R&D fuel-cell technology. They have already completed several R&D projects with this technology, so they have eliminated the projects with this technology, so they have eliminated the technical risk for this new project. To begin producing and technical risk for this new project. To begin producing and marketing to the consumer market would require a new marketing to the consumer market would require a new investment of $200M. At the present time, Fuelco estimates that investment of $200M. At the present time, Fuelco estimates that the completed project would have a present value of $400M the completed project would have a present value of $400M (i.e., if Fuelco spent $200M to initiate the project, they believe (i.e., if Fuelco spent $200M to initiate the project, they believe they could spin off the initiated project for $400M). Fuelco can they could spin off the initiated project for $400M). Fuelco can delay starting the project for up to five years, during which time delay starting the project for up to five years, during which time they expect this value of the project to fluctuate, with an annual they expect this value of the project to fluctuate, with an annual volatility of 90 percent. Once initiated, the project is expected to volatility of 90 percent. Once initiated, the project is expected to generate annual cash flows equal to 10 percent of its value. generate annual cash flows equal to 10 percent of its value. Thus, if Fuelco delays the project, they will forego these cash Thus, if Fuelco delays the project, they will forego these cash flows. After five years, some important Fuelco patents will flows. After five years, some important Fuelco patents will expire, and they will not longer have the option to profitably expire, and they will not longer have the option to profitably enter this new market. If Fuelco does not enter the market, then enter this new market. If Fuelco does not enter the market, then Project C has no salvage value.Project C has no salvage value.

Problem Problem What is the NPV of Project C?What is the NPV of Project C?

Fuelco’s problem: Project C with dividends

Appendix: CRR model details

We have three unknowns, u, d, and p. To solve, we need three equations:

First, the expected return for asset i, , can be written as

(1 ) (1 )

Second, the variance of return, var(

i

rt rt

r

Se pSu p Sd e pu p d

r

= + − → = + −

2 2 2 2 2 2 2

) can be written as

( ) ( ) (1 ) [ (1 ) ]

CRR add an arbitrary third condition that 1/ .

i

i iE r E r t pu p d pu p d t

u d

σ σ− = → + − − + − =

=

These three conditions can be solved to obtain the CRR equations.

2. Game Theory

Game Theory ModelsGame Theory Models

A set of mathematical tools for A set of mathematical tools for analyzing situations in which players analyzing situations in which players make various strategic moves and make various strategic moves and have different outcomes or payoffs have different outcomes or payoffs associated with those moves.associated with those moves.

22

Game TheoryGame TheoryGame Theory = Multiplayer Decision Game Theory = Multiplayer Decision

ProblemsProblemsStrategiesStrategiesPayoffPayoffNormal FormNormal FormExtensive Form = Game TreeExtensive Form = Game TreeSimultaneous GameSimultaneous GameSequential GameSequential GameTypes of GamesTypes of Games

Arms RaceArms RaceZero-sum (“win-lose”)Zero-sum (“win-lose”)Coordination (“win-win”)Coordination (“win-win”)

Example: Prisoner’s Example: Prisoner’s DilemmaDilemma

Two people, Al and Bob, have been arrested by the Two people, Al and Bob, have been arrested by the police and are being held in separate rooms. In each police and are being held in separate rooms. In each room an interrogator explains to the prisoner that he room an interrogator explains to the prisoner that he should make things easy for himself and “confess” should make things easy for himself and “confess” to the crime. (Whether Al and Bob are actually to the crime. (Whether Al and Bob are actually guilty is immaterial to the problem.) Each prisoner guilty is immaterial to the problem.) Each prisoner can choose whether or not to confess. If both can choose whether or not to confess. If both prisoners confess, then they will both go to jail for prisoners confess, then they will both go to jail for eight years. If neither prisoner confesses, then the eight years. If neither prisoner confesses, then the prosecutors will not be able to convict both prosecutors will not be able to convict both defendants of the highest crime, but they will still defendants of the highest crime, but they will still both go to jail for two years. If, however, only one both go to jail for two years. If, however, only one of the prisoners confesses, then the confessor will be of the prisoners confesses, then the confessor will be released without any jail time, while the other released without any jail time, while the other prisoner will get 10 years. prisoner will get 10 years.

Prisoner’s Dilemma, Extensive FormPrisoner’s Dilemma, Extensive Form

Dominant Strategies and the Prisoner’s Dilemma

This payoff matrix This payoff matrix shows the various shows the various prison terms for prison terms for Bonnie and Clyde Bonnie and Clyde that would result that would result from the from the combination of combination of strategies chosen strategies chosen when questioned when questioned about a crime spree.about a crime spree.

26

Prisoner’s Dilemma – Dominant Prisoner’s Dilemma – Dominant StrategyStrategy

A dominant A dominant strategy is one that strategy is one that results in the best results in the best outcome or outcome or highest payoff to a highest payoff to a given player no given player no matter what action matter what action or choice the other or choice the other player makes.player makes.

27

Nash EquilibriumNash Equilibrium

Nash equilibrium Nash equilibrium is a set of is a set of strategies from strategies from which all players which all players are choosing their are choosing their best strategy, best strategy, given the actions given the actions of the other of the other players.players.

28

Game Model ClassificationGame Model Classification

Number of players

Sum of all payoffs

Number of strategies employed

Two person (X, Y)

Zero sum, where sum of losses by one player = sum of gains by other player

Example : Duopoly of 2 StoresExample : Duopoly of 2 Stores There are only 2 lighting There are only 2 lighting

fixture stores, X and Y.fixture stores, X and Y. Owner of store X has 2 Owner of store X has 2

advertising strategies – advertising strategies – radio spots and newspaper radio spots and newspaper ads.ads.

Owner of store Y prepares Owner of store Y prepares to respond with radio spots to respond with radio spots and newspaper ads.and newspaper ads.

The 2x2 payoff matrix The 2x2 payoff matrix shows the effect on market shows the effect on market shares when both stores shares when both stores advertise.advertise.

30

Example : Duopoly Game OutcomesExample : Duopoly Game OutcomesStore X Store X StrategyStrategy

Store Y Store Y StrategyStrategy

Outcome Outcome (% Change in Market (% Change in Market

Share)Share)

X1X1 (Use Radio)(Use Radio)

Y1 Y1 (Use Radio)(Use Radio)

X wins 3X wins 3And Y loses 3And Y loses 3

X1 X1 (Use Radio)(Use Radio)

Y2 Y2 (Use Newspaper)(Use Newspaper)

X wins 5X wins 5And Y loses 5And Y loses 5

X2 X2 (Use Newspaper)(Use Newspaper)

Y1 Y1 (Use Radio)(Use Radio)

X wins 1X wins 1And Y loses 1And Y loses 1

X2 X2 (Use Newspaper)(Use Newspaper)

Y2 Y2 (Use Newspaper)(Use Newspaper)

X loses 2X loses 2And Y wins 2And Y wins 2

1- 31

3-32

Minimax CriterionUsed to find the strategy that minimises the

maximum loss, or maximizes the minimum payoff (maximin approach).

Locate the minimum payoff for each strategy. Select the strategy with the maximum number. The upper value of the game equal to the minimum of the

maximum values in the columns. The lower value of the game is equal to the maximum of the

minimum values in the rows.

3-33

Minimax Solution

STRATEGIESSTRATEGIES Y1Y1 Y2Y2 MINIMUMMINIMUM

X1X1 33 55 33

X2X2 11 -2-2 -2-2

MAXIMUMMAXIMUM 33 55

Saddle PointSaddle Point

An equilibrium or saddle point condition exists if An equilibrium or saddle point condition exists if the upper value of the game is equal to the lower the upper value of the game is equal to the lower value of the game. This is called the value of the value of the game. This is called the value of the game.game.

Minimum of maximumsMinimum of maximums Maximum of minimumsMaximum of minimums

3-34

Pure Strategy Game

STRATEGIESSTRATEGIES Y1Y1 Y2Y2 MINIMUMMINIMUM

X1X1 1010 66 66

X2X2 -12-12 22 -12-12

MAXIMUMMAXIMUM 1010 66

Saddle PointSaddle Point

When a saddle point is present, the strategy each When a saddle point is present, the strategy each player should follow will always be the same player should follow will always be the same regardless of the other player’s strategy.regardless of the other player’s strategy.

Minimum of maximumsMinimum of maximums Maximum of minimumsMaximum of minimums

3-35

Mixed Strategy Game

STRATEGIESSTRATEGIESY1Y1(P)(P)

Y2Y2(1 - P)(1 - P)

Expected Expected GainGain

X1 (Q)X1 (Q) 44 22 4P + 2(1-P)4P + 2(1-P)

X2 (1 - Q)X2 (1 - Q) 11 1010 1P + 10(1-P)1P + 10(1-P)

Expected Expected gaingain 4Q + 1(1-Q)4Q + 1(1-Q) 2Q + 10(1-Q)2Q + 10(1-Q)

When there is no saddle point, players will play When there is no saddle point, players will play each strategy for a certain percentage of the time each strategy for a certain percentage of the time (P, Q). To solve a mixed strategy game, use the (P, Q). To solve a mixed strategy game, use the expected gain or loss approach.expected gain or loss approach.

Mixed Strategy Game

The goal of this approach is for a player to play each strategy a particular percentage of the time so that the expected value of the game does not depend upon what the opponent does. This will only occur if the expected value of each strategy is the same.

For player Y,

4P + 2 (1 – P) = 1P + 10(1 – P)

P = 8/11

For player X,

4Q + 1(1 – Q) = 2Q + 10(1 – Q)

Q = 9/113-36

DominanceDominance The principle of dominance

can be used to reduce the size of the games by eliminating strategies that would never be played.

A strategy can be eliminated if all its game’s outcomes are the same or worse than the corresponding game outcomes of another strategy.

37

Example : DominanceExample : Dominance

1- 38

Y1Y1 Y2Y2 Y3Y3 Y4Y4

X1X1 -5-5 44 66 -3-3

X2X2 -2-2 66 22 -20-20

Nash EquilibriumNash Equilibrium

Each player must play a best response to the strategy of the other player.

Thus, in a Nash equilibrium, no player can improve his position by choosing a different strategy.

Everyone is playing “a best response to a best response”

Example: Advertising Arms RaceDrugco and Pharmco produce the two leading drugs to Drugco and Pharmco produce the two leading drugs to treat severe flu symptoms. These are strong medications treat severe flu symptoms. These are strong medications available only by prescription, and both firms market their available only by prescription, and both firms market their medicines heavily to physicians. Both firms are medicines heavily to physicians. Both firms are considering large direct-to-consumer advertising plans. considering large direct-to-consumer advertising plans. Advertising is very costly, but it would increase awareness Advertising is very costly, but it would increase awareness of the drugs and help each firm in its competitive position. of the drugs and help each firm in its competitive position. Each firm can independently choose to be aggressive in Each firm can independently choose to be aggressive in the direct-to-consumer market by choosing the direct-to-consumer market by choosing high high advertisingadvertising or to be less aggressive by choosing or to be less aggressive by choosing low low advertisingadvertising. If only one of the two firms chooses . If only one of the two firms chooses high high advertisingadvertising, then the NPV of that firm’s product , then the NPV of that firm’s product (including advertising costs) would be $500M, whereas (including advertising costs) would be $500M, whereas the NPV of the the NPV of the low advertisinglow advertising firm would be $100M. If firm would be $100M. If both firms choose both firms choose high advertisinghigh advertising, then the NPV of each , then the NPV of each product would be $200M. If both firms choose product would be $200M. If both firms choose low low advertisingadvertising, then the NPV of each product would be , then the NPV of each product would be $400M.$400M.

Advertising Game, Extensive FormAdvertising Game, Extensive Form

Example: Standards GameExample: Standards GameGameco and Movieco are the leading developers of DVD technology. Gameco and Movieco are the leading developers of DVD technology. In the past, these two companies were able to agree on identical In the past, these two companies were able to agree on identical technical standards, but they are now embroiled in a fierce debate technical standards, but they are now embroiled in a fierce debate about the next generation of technology. Gameco believes that the about the next generation of technology. Gameco believes that the time is ripe for a revolutionary change in DVD technology that would time is ripe for a revolutionary change in DVD technology that would provide much larger storage capacity and allow for highly complex provide much larger storage capacity and allow for highly complex interactive games. Movieco, on the other hand, favours a more interactive games. Movieco, on the other hand, favours a more evolutionary change that would maintain a higher degree of backward evolutionary change that would maintain a higher degree of backward compatibility.compatibility.Because the companies are unable to agree on a standard technology, Because the companies are unable to agree on a standard technology, they have continued with separate development projects. Other they have continued with separate development projects. Other content providers are reluctant to choose sides, fearing that they may content providers are reluctant to choose sides, fearing that they may pick the wrong company to back. This delay is damaging the long-pick the wrong company to back. This delay is damaging the long-term sales potential of both technologies. If the two companies are term sales potential of both technologies. If the two companies are unable to settle on a single technology, then each project would be unable to settle on a single technology, then each project would be worth $2B. Both companies would do better if they could agree on a worth $2B. Both companies would do better if they could agree on a single standard—but which one? The revolutionary standard would single standard—but which one? The revolutionary standard would favour Gameco, with an expected NPV of $10B versus only $4B for favour Gameco, with an expected NPV of $10B versus only $4B for Movieco. The evolutionary standard would favour Movieco, with an Movieco. The evolutionary standard would favour Movieco, with an expected NPV of $10B versus only $4B for Gameco. Although this is expected NPV of $10B versus only $4B for Gameco. Although this is an ongoing battle with no clear endpoint, we choose to model it as a an ongoing battle with no clear endpoint, we choose to model it as a single-stage simultaneous game, where each company must decide on single-stage simultaneous game, where each company must decide on a standard.a standard.

Standards Game, Extensive FormStandards Game, Extensive Form

Example: Entry GameExample: Entry GameDrugco sells Drugco sells LeaufleauLeaufleau, the market-leading drug for hypertension. , the market-leading drug for hypertension. This drug is about to lose patent protection for its key ingredient. This drug is about to lose patent protection for its key ingredient. Generico, a maker of generic drugs, is considering entry into the Generico, a maker of generic drugs, is considering entry into the hypertension market with the chemical equivalent of hypertension market with the chemical equivalent of LeaufleauLeaufleau. . Under law, if Generico is the first company to gain approval for a Under law, if Generico is the first company to gain approval for a generic version of generic version of LeaufleauLeaufleau, then they will be allowed six months , then they will be allowed six months as the only generic competitor. After this six months is over, other as the only generic competitor. After this six months is over, other companies can enter the market with their own versions. As soon as companies can enter the market with their own versions. As soon as generic competition intensifies, the profits for both the incumbent generic competition intensifies, the profits for both the incumbent (Drugco) and the first generic (Generico) would fall significantly. (Drugco) and the first generic (Generico) would fall significantly. Drugco would like to postpone this date for as long as possible by Drugco would like to postpone this date for as long as possible by “scaring” Generico out of the market. As Generico plans to “scaring” Generico out of the market. As Generico plans to introduce their drug, Drugco files expensive lawsuits claiming introduce their drug, Drugco files expensive lawsuits claiming infringement of patents related to the manufacturing of infringement of patents related to the manufacturing of LeaufleauLeaufleau and prepares to drop the price of and prepares to drop the price of LeaufleauLeaufleau to keep consumers from to keep consumers from switching to the generic form during Generico’s six-month switching to the generic form during Generico’s six-month exclusivity period. If Drugco succeeds in scaring Generico away exclusivity period. If Drugco succeeds in scaring Generico away from entry, then Drugco will increase their NPV by $1B, and from entry, then Drugco will increase their NPV by $1B, and Generico will have an NPV of 0. If Generico enters the market and Generico will have an NPV of 0. If Generico enters the market and Drugco chooses to fight with these measures, then both companies Drugco chooses to fight with these measures, then both companies will lose $100M. If Generico enters and Drugco decides not to fight, will lose $100M. If Generico enters and Drugco decides not to fight, then both companies will make $100M. then both companies will make $100M.

Entry Game, Extensive FormEntry Game, Extensive Form

Subgame-Perfect Nash EquilibriumSubgame-Perfect Nash Equilibrium

Step 1) Identify all “subgames” in Step 1) Identify all “subgames” in the extensive form.the extensive form.

Step 2) Solve backwards, using NE Step 2) Solve backwards, using NE in each subgame.in each subgame.

Entry Game, Extensive Form,Entry Game, Extensive Form,with Subgame Perfect Strategies Circledwith Subgame Perfect Strategies Circled

Entry Game, with CommitmentEntry Game, with CommitmentExtensive FormExtensive Form

3. R&D Valuation

Evaluating R&D projectsEvaluating R&D projects

60 ideas are evaluated for: 60 ideas are evaluated for: Technical feasibility Technical feasibility Financial feasibility Financial feasibility

SuitabilitySuitability

12 ideas worthy of evaluation 12 ideas worthy of evaluation through: Technical evaluation and through: Technical evaluation and

market research analysismarket research analysis

6 potential products worthy of 6 potential products worthy of further development and further development and analysisanalysis

3 prototypes for technical and 3 prototypes for technical and market testingmarket testing

2 products 2 products launchedlaunched

1 1 successful successful

productproduct

Evaluation of research project ideasEvaluation of research project ideas

Number Number of of

research research ideasideas

Intr

od

uct

ion

Intr

od

uct

ion

GrowthGrowth

MaturityMaturity

DeclineDecline

Development:Development:demonstration ofdemonstration ofapplication andapplication and

product engineeringproduct engineering

Applied research:Applied research:laboratory laboratory verificationverification

Basic Basic research:research:scientific scientific suggestion, suggestion, discovery,discovery,recognition,recognition,new concept.new concept.

Time

0-2-4-6-8-10-12 2 4 6

Accumulated investmentAccumulated investment

ROIROI

RevenueRevenue

InvestmentInvestment

Lab to Market : Product life cycleLab to Market : Product life cycle

Example: Real Options and Competition

Fuelco 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. To technology, so they have eliminated the technical risk for this new project. To begin producing and marketing to the consumer market would require a new begin producing and marketing to the consumer market would require a new investment of $200M, to be paid in one year. The value of Project C depends on investment of $200M, to be paid in one year. The value of Project C depends on consumer demand and also depends on whether a competitor, Cellco, also enters consumer demand and also depends on whether a competitor, Cellco, also enters this market. To keep things (relatively) simple, we assume that the beta for the this market. To keep things (relatively) simple, we assume that the beta for the project is zero and that the risk-free rate is also zero, so all discount rates are zero project is zero and that the risk-free rate is also zero, so all discount rates are zero for the both firms.for the both firms.At time 0, Cellco and Fuelco each decide whether to invest or wait. If one firm At time 0, Cellco and Fuelco each decide whether to invest or wait. If one firm invests and the other waits, then the investing firm will get the whole market and invests and the other waits, then the investing firm will get the whole market and have an NPV of $300M, whereas the waiting firm will have an NPV of $0. If have an NPV of $300M, whereas the waiting firm will have an NPV of $0. If both firms invest, then competition will drive down the profits of both firms, both firms invest, then competition will drive down the profits of both firms, which will each have an NPV of $50M. If both firms wait, then they both get to which will each have an NPV of $50M. If both firms wait, then they both get to observe whether demand is “high” or “low”, after which each firm decides observe whether demand is “high” or “low”, after which each firm decides whether or not to invest. If demand is “high” (50 percent chance) and only one whether or not to invest. If demand is “high” (50 percent chance) and only one firm chooses to invest, then that firm receives an NPV of $700M, and the other firm chooses to invest, then that firm receives an NPV of $700M, and the other firm receives an NPV of $0. If neither firm invests, then both firms receive an firm receives an NPV of $0. If neither firm invests, then both firms receive an NPV of $0. If both firms invest, then each firm receives an NPV of $200M. If NPV of $0. If both firms invest, then each firm receives an NPV of $200M. If demand is “low” (50 percent chance), and only one firm chooses to invest, then demand is “low” (50 percent chance), and only one firm chooses to invest, then that firm receives a negative NPV of –$100M, and the other firm receives an that firm receives a negative NPV of –$100M, and the other firm receives an NPV of $0. If neither firm invests, then both firms receive an NPV of $0. If both NPV of $0. If neither firm invests, then both firms receive an NPV of $0. If both firms invest, then each firm receives a negative NPV of –$100M.firms invest, then each firm receives a negative NPV of –$100M.

Fuelco’s Project C, with competition

Fuelco’s Project C, with competition, prunedFuelco’s Project C, with competition, pruned

Pharmaceutical Alliances

Drugco is about to begin Phase II trials for Newdrug, at a cost of $50M.

If the drug continues to Phase III trials, then these trials would cost an additional $100M.

Bigco, a potential partner, has proposed two possible deal structures. Deal 1: Up-front payment of $200M, milestone payment of $150M

upon entering Phase III, 5 percent royalty on all sales, plus Bigco pays all development costs

Deal 2: Up-front payment of $100M, $300M milestone if Bigco decides to market the product, 10 percent royalties. Drugco absorbs 20 percent of Phase III costs but has decision rights for Phase III continuation.

Alliance: DetailsAlliance: Details EfficacyEfficacy

Phase II: E’ ~ N(40,40)Phase II: E’ ~ N(40,40) Phase III: E ~ N(E’, 20)Phase III: E ~ N(E’, 20)

Alternative efficacyAlternative efficacy Phase II: A’ ~ T(40,70,40)Phase II: A’ ~ T(40,70,40) Phase III: A ~ T(A’, A’+50, A’)Phase III: A ~ T(A’, A’+50, A’)

Market sizeMarket size Phase II: M’ ~ N(1000,50)Phase II: M’ ~ N(1000,50) Phase III: M ~ N(M’, 100)Phase III: M ~ N(M’, 100)

Market Share = EMarket Share = E22 / (E / (E22 + A + A22)) Each dose will sell for $1, with production cost of $0.25.Each dose will sell for $1, with production cost of $0.25. Discount rate = riskfree rate of 5 percent.Discount rate = riskfree rate of 5 percent. Ten years of patent life would remain after approval.Ten years of patent life would remain after approval. Marketing costs of $300M in first year, increase with 6 Marketing costs of $300M in first year, increase with 6

percent market growth rate.percent market growth rate.

Bigco NPV as of Phase IIIBigco NPV as of Phase III

-200

0

200

400

600

800

1000

1200

20 25 30 35 40 45 50 55 60

E'

Big

co N

PV

NPV = 0

Bigco Zero-Profit Curve, M’ = 1000Bigco Zero-Profit Curve, M’ = 1000

0

10

20

30

40

50

40 45 50 55 60 65 70

A'

E'

Bigco Zero-Profit Curves, Deal 1Bigco Zero-Profit Curves, Deal 1

0

10

20

30

40

50

60

70

80

90

100

40 45 50 55 60 65 70

A'

E'

M' = 600

M' = 700

M' = 800

M' = 900

M' = 1000

M' = 1100

M' = 1200

M' = 1300

M' = 1400

Bigco Zero-Profit Curves, Deal 2

-10

-5

0

5

10

15

20

25

30

35

40

40 45 50 55 60 65 70

A'

E'

M' = 600

M' = 700

M' = 800

M' = 900

M' = 1000

M' = 1100

M' = 1200

M' = 1300

M' = 1400

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?