Binomial Trees, Game Theory, R & D Valuation, Research and Development project evaluation

1. THE FINANCE OFTHE FINANCE OF
INNOVATION :INNOVATION : BINOMIALBINOMIAL
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 University
Academic 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

2. Today’s OverviewToday’s Overview

3. LEARNING OBJECTIVESLEARNING OBJECTIVES
To understand the use ofTo understand the use of
binomial trees in decisionbinomial trees in decision
making;making;
To understand the use ofTo understand the use of
game theory in the evaluationgame theory in the evaluation
of strategic options;of strategic options;
To understand the valuationTo understand the valuation
of R&D projects.of R&D projects.

4. 1.Binomial Trees

5. Call Option in a Decision TreeCall Option in a Decision Tree

6. A 3-Step Binomial TreeA 3-Step Binomial Tree

7. Multi-step treesMulti-step trees
To solveTo solve
1)1) Compute the key inputs: u, d, and p.Compute the key inputs: u, d, and p.
2)2) Build theBuild the base treebase tree by solvingby solving forwardsforwards
using the up and down movements.using the up and down movements.
3) Build the3) Build the option treeoption tree by solvingby solving
backwardsbackwards using the risk-neutralusing the risk-neutral
probabilities.probabilities.

8. Base TreeBase Tree

9. Option TreeOption Tree

10. 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
 ThenThen
u =u =
d = 1/u =d = 1/u =
p = (p = (eertrt
– d) / (u – d)– d) / (u – d)
t
eσ
t
e σ−

11. Joe’s ProblemJoe’s Problem
AssumeAssume
Starting stock price = S = $100Starting stock price = S = $100
Strike Price = X = $50Strike Price = X = $50
Volatility =Volatility = σσ = 60%= 60%
Riskfree rate = r = 5%Riskfree rate = r = 5%
Time to expiration = T = 1Time to expiration = T = 1
3-step tree → N = 3 and t = 1/33-step tree → N = 3 and t = 1/3

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

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

14. Example 1Example 1
Drugco is a publicly traded biotechnology company with severalDrugco is a publicly traded biotechnology company with several
drugs in development, but no products on the market. To raisedrugs in development, but no products on the market. To raise
capital for the development of Newdrug, Drugco enters a strategiccapital 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 andBigco will pay for clinical trials and will give Drugco up-front and
milestone payments. Bigco also agrees to make an equitymilestone payments. Bigco also agrees to make an equity
investment in Drugco, purchasing ten million shares at the marketinvestment in Drugco, purchasing ten million shares at the market
price of $10 per share and also receiving warrants to purchase anprice of $10 per share and also receiving warrants to purchase an
additional 10 million shares. (The market price of $10 includes theadditional 10 million shares. (The market price of $10 includes the
market reaction to the Bigco alliance.) These warrants can either bemarket reaction to the Bigco alliance.) These warrants can either be
exercised in exactly two years at a strike price of $20 per share orexercised 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. Drugcoin 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 atdoes 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 isleast the next five years. The expected volatility of Drugco stock is
60 percent per year.60 percent per year.
ProblemProblem What is the value of Bigco’s warrants?What is the value of Bigco’s warrants?

15. 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-lastNow, let’s add a dividend in the second-to-last
period (eight months into the year) that isperiod (eight months into the year) that is
equal to 10 percent of the stock value. Now, ifequal to 10 percent of the stock value. Now, if
Joe decides to exercise after eight months, heJoe decides to exercise after eight months, he
would receive the whole value of the stockwould 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 isinstead, he decides to wait until the full year is
over, then the 10 percent dividend gets paidover, then the 10 percent dividend gets paid
out after eight months, and the stock priceout after eight months, and the stock price
falls by 10 percent before making an up orfalls by 10 percent before making an up or
down move in the last period.down move in the last period.

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

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

18. Example 2Example 2
Fuelco is considering a consumer application for their patentedFuelco is considering a consumer application for their patented
fuel-cell technology. They have already completed several R&Dfuel-cell technology. They have already completed several R&D
projects with this technology, so they have eliminated theprojects with this technology, so they have eliminated the
technical risk for this new project. To begin producing andtechnical risk for this new project. To begin producing and
marketing to the consumer market would require a newmarketing to the consumer market would require a new
investment of $200M. At the present time, Fuelco estimates thatinvestment of $200M. At the present time, Fuelco estimates that
the completed project would have a present value of $400Mthe 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 canthey could spin off the initiated project for $400M). Fuelco can
delay starting the project for up to five years, during which timedelay starting the project for up to five years, during which time
they expect this value of the project to fluctuate, with an annualthey expect this value of the project to fluctuate, with an annual
volatility of 90 percent. Once initiated, the project is expected tovolatility 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 cashThus, if Fuelco delays the project, they will forego these cash
flows. After five years, some important Fuelco patents willflows. After five years, some important Fuelco patents will
expire, and they will not longer have the option to profitablyexpire, and they will not longer have the option to profitably
enter this new market. If Fuelco does not enter the market, thenenter this new market. If Fuelco does not enter the market, then
Project C has no salvage value.Project C has no salvage value.
ProblemProblem What is the NPV of Project C?What is the NPV of Project C?

19. Fuelco’s problem: Project C with dividends

20. 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.

21. 2. Game Theory

22. Game Theory ModelsGame Theory Models
A set of mathematical tools forA set of mathematical tools for
analyzing situations in which playersanalyzing situations in which players
make various strategic moves andmake various strategic moves and
have different outcomes or payoffshave different outcomes or payoffs
associated with those moves.associated with those moves.
22

23. Game TheoryGame Theory
Game Theory = Multiplayer DecisionGame Theory = Multiplayer Decision
ProblemsProblems
StrategiesStrategies
PayoffPayoff
Normal FormNormal Form
Extensive Form = Game TreeExtensive Form = Game Tree
Simultaneous GameSimultaneous Game
Sequential GameSequential Game
Types of GamesTypes of Games
Arms RaceArms Race
Zero-sum (“win-lose”)Zero-sum (“win-lose”)
Coordination (“win-win”)Coordination (“win-win”)

24. Example: Prisoner’sExample: Prisoner’s
DilemmaDilemma
Two people, Al and Bob, have been arrested by theTwo people, Al and Bob, have been arrested by the
police and are being held in separate rooms. In eachpolice and are being held in separate rooms. In each
room an interrogator explains to the prisoner that heroom 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 actuallyto the crime. (Whether Al and Bob are actually
guilty is immaterial to the problem.) Each prisonerguilty is immaterial to the problem.) Each prisoner
can choose whether or not to confess. If bothcan choose whether or not to confess. If both
prisoners confess, then they will both go to jail forprisoners confess, then they will both go to jail for
eight years. If neither prisoner confesses, then theeight years. If neither prisoner confesses, then the
prosecutors will not be able to convict bothprosecutors will not be able to convict both
defendants of the highest crime, but they will stilldefendants of the highest crime, but they will still
both go to jail for two years. If, however, only oneboth go to jail for two years. If, however, only one
of the prisoners confesses, then the confessor will beof the prisoners confesses, then the confessor will be
released without any jail time, while the otherreleased without any jail time, while the other
prisoner will get 10 years.prisoner will get 10 years.

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

26. Dominant Strategies and the
Prisoner’s Dilemma
This payoff matrixThis payoff matrix
shows the variousshows the various
prison terms forprison terms for
Bonnie and ClydeBonnie and Clyde
that would resultthat would result
from thefrom the
combination ofcombination of
strategies chosenstrategies chosen
when questionedwhen questioned
about a crime spree.about a crime spree.
26

27. Prisoner’s Dilemma – DominantPrisoner’s Dilemma – Dominant
StrategyStrategy
A dominantA dominant
strategy is one thatstrategy is one that
results in the bestresults in the best
outcome oroutcome or
highest payoff to ahighest payoff to a
given player nogiven player no
matter what actionmatter what action
or choice the otheror choice the other
player makes.player makes.
27

28. Nash EquilibriumNash Equilibrium
Nash equilibriumNash equilibrium
is a set ofis a set of
strategies fromstrategies from
which all playerswhich all players
are choosing theirare choosing their
best strategy,best strategy,
given the actionsgiven the actions
of the otherof the other
players.players.
28

29. 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

30. Example : Duopoly of 2 StoresExample : Duopoly of 2 Stores
 There are only 2 lightingThere are only 2 lighting
fixture stores, X and Y.fixture stores, X and Y.
 Owner of store X has 2Owner of store X has 2
advertising strategies –advertising strategies –
radio spots and newspaperradio spots and newspaper
ads.ads.
 Owner of store Y preparesOwner of store Y prepares
to respond with radio spotsto respond with radio spots
and newspaper ads.and newspaper ads.
 The 2x2 payoff matrixThe 2x2 payoff matrix
shows the effect on marketshows the effect on market
shares when both storesshares when both stores
advertise.advertise.
30

31. Example : Duopoly Game OutcomesExample : Duopoly Game Outcomes
Store XStore X
StrategyStrategy
Store YStore Y
StrategyStrategy
OutcomeOutcome
(% Change in Market(% Change in Market
Share)Share)
X1X1
(Use Radio)(Use Radio)
Y1Y1
(Use Radio)(Use Radio)
X wins 3X wins 3
And Y loses 3And Y loses 3
X1X1
(Use Radio)(Use Radio)
Y2Y2
(Use Newspaper)(Use Newspaper)
X wins 5X wins 5
And Y loses 5And Y loses 5
X2X2
(Use Newspaper)(Use Newspaper)
Y1Y1
(Use Radio)(Use Radio)
X wins 1X wins 1
And Y loses 1And Y loses 1
X2X2
(Use Newspaper)(Use Newspaper)
Y2Y2
(Use Newspaper)(Use Newspaper)
X loses 2X loses 2
And Y wins 2And Y wins 2
1- 31

32. 3-32
Minimax Criterion
Used 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.

33. 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 ifAn equilibrium or saddle point condition exists if
the upper value of the game is equal to the lowerthe upper value of the game is equal to the lower
value of the game. This is called the value of thevalue of the game. This is called the value of the
game.game.
Minimum of maximumsMinimum of maximums Maximum of minimumsMaximum of minimums

34. 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 eachWhen a saddle point is present, the strategy each
player should follow will always be the sameplayer 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

35. 3-35
Mixed Strategy Game
STRATEGIESSTRATEGIES
Y1Y1
(P)(P)
Y2Y2
(1 - P)(1 - P)
ExpectedExpected
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)
ExpectedExpected
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 playWhen there is no saddle point, players will play
each strategy for a certain percentage of the timeeach 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.

36. 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

37. 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

38. Example : DominanceExample : Dominance
1- 38
Y1Y1 Y2Y2 Y3Y3 Y4Y4
X1X1 -5-5 44 66 -3-3
X2X2 -2-2 66 22 -20-20

39. 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”

40. Example: Advertising Arms Race
Drugco and Pharmco produce the two leading drugs toDrugco and Pharmco produce the two leading drugs to
treat severe flu symptoms. These are strong medicationstreat severe flu symptoms. These are strong medications
available only by prescription, and both firms market theiravailable only by prescription, and both firms market their
medicines heavily to physicians. Both firms aremedicines 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 awarenessAdvertising 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 inEach firm can independently choose to be aggressive in
the direct-to-consumer market by choosingthe direct-to-consumer market by choosing highhigh
advertisingadvertising or to be less aggressive by choosingor to be less aggressive by choosing lowlow
advertisingadvertising. If only one of the two firms chooses. If only one of the two firms chooses highhigh
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 thethe NPV of the low advertisinglow advertising firm would be $100M. Iffirm would be $100M. If
both firms chooseboth firms choose high advertisinghigh advertising, then the NPV of each, then the NPV of each
product would be $200M. If both firms chooseproduct would be $200M. If both firms choose lowlow
advertisingadvertising, then the NPV of each product would be, then the NPV of each product would be
$400M.$400M.

41. Advertising Game, Extensive FormAdvertising Game, Extensive Form

42. Example: Standards GameExample: Standards Game
Gameco 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 identicalIn the past, these two companies were able to agree on identical
technical standards, but they are now embroiled in a fierce debatetechnical standards, but they are now embroiled in a fierce debate
about the next generation of technology. Gameco believes that theabout the next generation of technology. Gameco believes that the
time is ripe for a revolutionary change in DVD technology that wouldtime is ripe for a revolutionary change in DVD technology that would
provide much larger storage capacity and allow for highly complexprovide much larger storage capacity and allow for highly complex
interactive games. Movieco, on the other hand, favours a moreinteractive games. Movieco, on the other hand, favours a more
evolutionary change that would maintain a higher degree of backwardevolutionary 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. Otherthey have continued with separate development projects. Other
content providers are reluctant to choose sides, fearing that they maycontent 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 areterm sales potential of both technologies. If the two companies are
unable to settle on a single technology, then each project would beunable to settle on a single technology, then each project would be
worth $2B. Both companies would do better if they could agree on aworth $2B. Both companies would do better if they could agree on a
single standard—but which one? The revolutionary standard wouldsingle standard—but which one? The revolutionary standard would
favour Gameco, with an expected NPV of $10B versus only $4B forfavour Gameco, with an expected NPV of $10B versus only $4B for
Movieco. The evolutionary standard would favour Movieco, with anMovieco. The evolutionary standard would favour Movieco, with an
expected NPV of $10B versus only $4B for Gameco. Although this isexpected NPV of $10B versus only $4B for Gameco. Although this is
an ongoing battle with no clear endpoint, we choose to model it as aan ongoing battle with no clear endpoint, we choose to model it as a
single-stage simultaneous game, where each company must decide onsingle-stage simultaneous game, where each company must decide on
a standard.a standard.

43. Standards Game, Extensive FormStandards Game, Extensive Form

44. Example: Entry GameExample: Entry Game
Drugco sellsDrugco 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 theGenerico, a maker of generic drugs, is considering entry into the
hypertension market with the chemical equivalent ofhypertension market with the chemical equivalent of LeaufleauLeaufleau..
Under law, if Generico is the first company to gain approval for aUnder law, if Generico is the first company to gain approval for a
generic version ofgeneric 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, otheras the only generic competitor. After this six months is over, other
companies can enter the market with their own versions. As soon ascompanies can enter the market with their own versions. As soon as
generic competition intensifies, the profits for both the incumbentgeneric 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 byDrugco 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 claimingintroduce their drug, Drugco files expensive lawsuits claiming
infringement of patents related to the manufacturing ofinfringement of patents related to the manufacturing of LeaufleauLeaufleau
and prepares to drop the price ofand prepares to drop the price of LeaufleauLeaufleau to keep consumers fromto keep consumers from
switching to the generic form during Generico’s six-monthswitching to the generic form during Generico’s six-month
exclusivity period. If Drugco succeeds in scaring Generico awayexclusivity period. If Drugco succeeds in scaring Generico away
from entry, then Drugco will increase their NPV by $1B, andfrom entry, then Drugco will increase their NPV by $1B, and
Generico will have an NPV of 0. If Generico enters the market andGenerico will have an NPV of 0. If Generico enters the market and
Drugco chooses to fight with these measures, then both companiesDrugco 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.

45. Entry Game, Extensive FormEntry Game, Extensive Form

46. Subgame-Perfect Nash EquilibriumSubgame-Perfect Nash Equilibrium
Step 1) Identify all “subgames” inStep 1) Identify all “subgames” in
the extensive form.the extensive form.
Step 2) Solve backwards, using NEStep 2) Solve backwards, using NE
in each subgame.in each subgame.

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

48. Entry Game, with CommitmentEntry Game, with Commitment
Extensive FormExtensive Form

49. 3. R&D Valuation

50. Evaluating R&D projectsEvaluating R&D projects
60 ideas are evaluated for:60 ideas are evaluated for:
Technical feasibilityTechnical feasibility
Financial feasibilityFinancial feasibility
SuitabilitySuitability
12 ideas worthy of evaluation12 ideas worthy of evaluation
through: Technical evaluation andthrough: Technical evaluation and
market research analysismarket research analysis
6 potential products worthy of6 potential products worthy of
further development andfurther development and
analysisanalysis
3 prototypes for technical and3 prototypes for technical and
market testingmarket testing
2 products2 products
launchedlaunched
11
successfulsuccessful
productproduct
Evaluation of research project ideasEvaluation of research project ideas
NumberNumber
ofof
researchresearch
ideasideas

51. IntroductionIntroduction
GrowthGrowth
MaturityMaturity
DeclineDecline
Development:Development:
demonstration ofdemonstration of
application andapplication and
product engineeringproduct engineering
Applied research:Applied research:
laboratorylaboratory
verificationverification
BasicBasic
research:research:
scientificscientific
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

52. Example: Real Options and Competition
Fuelco is considering a consumer application for their patented fuel-cellFuelco is considering a consumer application for their patented fuel-cell
technology. They have already completed several R&D projects with thistechnology. They have already completed several R&D projects with this
technology, so they have eliminated the technical risk for this new project. Totechnology, so they have eliminated the technical risk for this new project. To
begin producing and marketing to the consumer market would require a newbegin 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 oninvestment 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 entersconsumer demand and also depends on whether a competitor, Cellco, also enters
this market. To keep things (relatively) simple, we assume that the beta for thethis 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 zeroproject 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 firmAt 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 andinvests 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. Ifhave 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 towhich 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 decidesobserve 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 onewhether 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 otherfirm 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 anfirm 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. IfNPV 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, thendemand 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 anthat 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 bothNPV 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.

53. Fuelco’s Project C, with competition

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

55. 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.

56. 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 6Marketing costs of $300M in first year, increase with 6
percent market growth rate.percent market growth rate.

60. 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'
BigcoNPV
NPV = 0

61. 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'

62. 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

63. 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

64. 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

65. QUESTIONS?