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THE WORLD’S TOP MINDS AT WORK FOR YOU.
OPTIMAL
Josh Daulton, Celine Li, Yuki Abe, Fernando A Del-sol-santa-cruz | October 6, 2015
Investor’s Solution
SOLUTION MANUAL FOR INVESTOR’S DILEMMA
PAGE 1
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
Table of Contents
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 1
Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 2
Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 3 – 7
Why We Are Right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 3
Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4
Optimal Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 5 - 7
PAGE 2
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
Executive Summary
An Optimal Solution from Optimal Consultants
Inventor’s encounter many tough decisions along the road to success. Some of those decisions can
mean the difference between worldwide success and bankruptcy. You have made the right
decisions so far and are on track for future success. By hiring the professionals at Optimal, you
have made another right choice; one that will help ensure your long-term success. Your executives
approached us with a question, “How do we invest?” Our brightest minds analyzed the data and
crafted a personalized solution help you maximize profits.
Investment
Expected
Market Value
1st
Market Research €143,000
2nd
Product Feasibility Testing €296,000
3rd
Full-Scale Production €652,000
Product Success €940,000
Investing in 1) market research, 2) product feasibility, and 3) full-scale production, in that order,
reduces possible losses therefore optimizing expected market value. If the product is successful,
you can expect to make just under a million euros. Even if things go unexpectedly, you are still
expected to profit from your investments. With uncertainty comes risk and our advice is to choose
an investment strategy that minimizes that risk.
PAGE 3
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
SPECIFICS
Why We Are Right
Business solutions without the quantifiable data to support it, in our data driven economy, can be
very risky. At Optimal, we support our intuition and experience by utilizing complex logarithms
and state of the art software to create defendable statistics for the answers we provide our clients.
As an investor, you are faced with three initial decisions. Invest in market research, invest in
product feasibility, or simply postpone your investment until the opportune moment. Our data
shows that now is a good time to invest and we strongly suggest investing in market research
before testing for product feasibility. Accounting for the probabilities of every possible outcome,
we have found that this strategy optimizes predicted profitability. Because market research costs
far less than testing for product feasibility, it is wise to invest in this valuable information first.
Understanding the market demand for your product before making large investments in research
and development reduces the risk of financing a bad project.
Assuming a strong reaction from the market, we suggest investing in product feasibility research
before capitalizing on large scale production to reduce losses if the technology isn’t feasible.
However, if research shows a lack of interest from the market, we advise postponing investment or
possibly pursuing a new venture. Losing the €10,000 invested in market research is far better than
hundreds of thousands you stand to lose investing in an unwilling market.
Using the probabilities given to us, we were able to disentangle underlying values and rearrange
them in new ways to calculate other very important pieces of information (see figure 1.1). Using the
newfound dataset, we constructed a decision tree to determine your optimal investment strategy
(see figure 1.2). By following our suggestions, we can assure that your investment is ideal.
Risk aversion is the key principle behind why we suggest this particular investment strategy.
Investing in market research, then product feasibility research, then full scale production creates
the most opportunities to reevaluate the situation and back out of the investment with minimal
losses if things do not go as planned at each stage.
PAGE 4
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
Probabilities
Optimal Decisions
Probabilities
P(+|S) 0.7
P(-|S) 0.3
P(-|F) 0.8
P(+|F) 0.2
P(S) 0.6
P(F) 0.4
P(+) 0.5
P(-) 0.5
P(S|-) 0.36
P(F|-) 0.64
P(S|+) 0.84
P(F|+) 0.16
+ -
0.42 0.18 0.6
0.08 0.32 0.4
0.5 0.5 1
Product Failure
Product Success
Market Research
Figure 1.2
Figure 1.1
PAGE 5
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
Method
Initial decision tree:
Probability Payoff Cost Type
Investor's Dilemma
¦--Market research decision
¦ ¦--Positive result 50.00 % chance
¦ ¦ ¦--First Investment decision
¦ ¦ ¦ ¦--Feasible 50.00 % chance
¦ ¦ ¦ ¦ ¦--Second investment decision
¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance
¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance
¦ ¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ ¦ °--Unfeasible 50.00 % -60,000 chance
¦ ¦ °--Do nothing -10,000 decision
¦ °--Negative result 50.00 % chance
¦ ¦--First Investment decision
¦ ¦ ¦--Feasible 50.00 % chance
¦ ¦ ¦ ¦--Second investment decision
¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance
¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance
¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ °--Unfeasible 50.00 % -60,000 chance
¦ °--Do nothing -10,000 decision
¦--First investment decision
¦ ¦--Feasible 50.00 % chance
¦ ¦ ¦--Market research decision
¦ ¦ ¦ ¦--Positive result 50.00 % chance
¦ ¦ ¦ ¦ ¦--Second investment decision
¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance
¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance
PAGE 6
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
¦ ¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ ¦ °--Negative result 50.00 % chance
¦ ¦ ¦ ¦--Second investment decision
¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance
¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance
¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ ¦--Second investment decision
¦ ¦ ¦ ¦--Success 60.00 % 950,000 chance
¦ ¦ ¦ °--Failure 40.00 % -850,000 chance
¦ ¦ °--Do nothing -50,000 decision
¦ °--Unfeasible 50.00 % -50,000 chance
°--Do nothing decision
Final decision tree:
Probability Payoff Cost Type
Investor's Dilemma 143,000.00
¦--Market research 143,000.00 decision
¦ ¦--Positive result 50.00 % 296,000.00 chance
¦ ¦ ¦--First Investment 296,000.00 decision
¦ ¦ ¦ ¦--Feasible 50.00 % 652,000.00 chance
¦ ¦ ¦ ¦ ¦--Second investment 652,000.00 decision
¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance
¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance
¦ ¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ ¦ °--Unfeasible 50.00 % -60,000 chance
¦ ¦ °--Do nothing -10,000 decision
¦ °--Negative result 50.00 % -10,000.00 chance
¦ ¦--First Investment -60,000.00 decision
¦ ¦ ¦--Feasible 50.00 % -60,000.00 chance
¦ ¦ ¦ ¦--Second investment -212,000.00 decision
¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance
PAGE 7
OPTIMAL
THE WORLD’S TOP MINDS AT WORK FOR YOU.
¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance
¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ °--Unfeasible 50.00 % -60,000 chance
¦ °--Do nothing -10,000 decision
¦--First investment 123,000.00 decision
¦ ¦--Feasible 50.00 % 296,000.00 chance
¦ ¦ ¦--Market research 296,000.00 decision
¦ ¦ ¦ ¦--Positive result 50.00 % 652,000.00 chance
¦ ¦ ¦ ¦ ¦--Second investment 652,000.00 decision
¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance
¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance
¦ ¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ ¦ °--Negative result 50.00 % -60,000.00 chance
¦ ¦ ¦ ¦--Second investment -212,000.00 decision
¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance
¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance
¦ ¦ ¦ °--Do nothing -60,000 decision
¦ ¦ ¦--Second investment 230,000.00 decision
¦ ¦ ¦ ¦--Success 60.00 % 950,000 chance
¦ ¦ ¦ °--Failure 40.00 % -850,000 chance
¦ ¦ °--Do nothing -50,000 decision
¦ °--Unfeasible 50.00 % -50,000 chance
°--Do nothing decision

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Investor Dilemma Solution

  • 1. THE WORLD’S TOP MINDS AT WORK FOR YOU. OPTIMAL Josh Daulton, Celine Li, Yuki Abe, Fernando A Del-sol-santa-cruz | October 6, 2015 Investor’s Solution SOLUTION MANUAL FOR INVESTOR’S DILEMMA
  • 2. PAGE 1 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. Table of Contents Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 1 Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 2 Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 3 – 7 Why We Are Right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 3 Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4 Optimal Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 5 - 7
  • 3. PAGE 2 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. Executive Summary An Optimal Solution from Optimal Consultants Inventor’s encounter many tough decisions along the road to success. Some of those decisions can mean the difference between worldwide success and bankruptcy. You have made the right decisions so far and are on track for future success. By hiring the professionals at Optimal, you have made another right choice; one that will help ensure your long-term success. Your executives approached us with a question, “How do we invest?” Our brightest minds analyzed the data and crafted a personalized solution help you maximize profits. Investment Expected Market Value 1st Market Research €143,000 2nd Product Feasibility Testing €296,000 3rd Full-Scale Production €652,000 Product Success €940,000 Investing in 1) market research, 2) product feasibility, and 3) full-scale production, in that order, reduces possible losses therefore optimizing expected market value. If the product is successful, you can expect to make just under a million euros. Even if things go unexpectedly, you are still expected to profit from your investments. With uncertainty comes risk and our advice is to choose an investment strategy that minimizes that risk.
  • 4. PAGE 3 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. SPECIFICS Why We Are Right Business solutions without the quantifiable data to support it, in our data driven economy, can be very risky. At Optimal, we support our intuition and experience by utilizing complex logarithms and state of the art software to create defendable statistics for the answers we provide our clients. As an investor, you are faced with three initial decisions. Invest in market research, invest in product feasibility, or simply postpone your investment until the opportune moment. Our data shows that now is a good time to invest and we strongly suggest investing in market research before testing for product feasibility. Accounting for the probabilities of every possible outcome, we have found that this strategy optimizes predicted profitability. Because market research costs far less than testing for product feasibility, it is wise to invest in this valuable information first. Understanding the market demand for your product before making large investments in research and development reduces the risk of financing a bad project. Assuming a strong reaction from the market, we suggest investing in product feasibility research before capitalizing on large scale production to reduce losses if the technology isn’t feasible. However, if research shows a lack of interest from the market, we advise postponing investment or possibly pursuing a new venture. Losing the €10,000 invested in market research is far better than hundreds of thousands you stand to lose investing in an unwilling market. Using the probabilities given to us, we were able to disentangle underlying values and rearrange them in new ways to calculate other very important pieces of information (see figure 1.1). Using the newfound dataset, we constructed a decision tree to determine your optimal investment strategy (see figure 1.2). By following our suggestions, we can assure that your investment is ideal. Risk aversion is the key principle behind why we suggest this particular investment strategy. Investing in market research, then product feasibility research, then full scale production creates the most opportunities to reevaluate the situation and back out of the investment with minimal losses if things do not go as planned at each stage.
  • 5. PAGE 4 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. Probabilities Optimal Decisions Probabilities P(+|S) 0.7 P(-|S) 0.3 P(-|F) 0.8 P(+|F) 0.2 P(S) 0.6 P(F) 0.4 P(+) 0.5 P(-) 0.5 P(S|-) 0.36 P(F|-) 0.64 P(S|+) 0.84 P(F|+) 0.16 + - 0.42 0.18 0.6 0.08 0.32 0.4 0.5 0.5 1 Product Failure Product Success Market Research Figure 1.2 Figure 1.1
  • 6. PAGE 5 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. Method Initial decision tree: Probability Payoff Cost Type Investor's Dilemma ¦--Market research decision ¦ ¦--Positive result 50.00 % chance ¦ ¦ ¦--First Investment decision ¦ ¦ ¦ ¦--Feasible 50.00 % chance ¦ ¦ ¦ ¦ ¦--Second investment decision ¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance ¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance ¦ ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ ¦ °--Unfeasible 50.00 % -60,000 chance ¦ ¦ °--Do nothing -10,000 decision ¦ °--Negative result 50.00 % chance ¦ ¦--First Investment decision ¦ ¦ ¦--Feasible 50.00 % chance ¦ ¦ ¦ ¦--Second investment decision ¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance ¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ °--Unfeasible 50.00 % -60,000 chance ¦ °--Do nothing -10,000 decision ¦--First investment decision ¦ ¦--Feasible 50.00 % chance ¦ ¦ ¦--Market research decision ¦ ¦ ¦ ¦--Positive result 50.00 % chance ¦ ¦ ¦ ¦ ¦--Second investment decision ¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance ¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance
  • 7. PAGE 6 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. ¦ ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ ¦ °--Negative result 50.00 % chance ¦ ¦ ¦ ¦--Second investment decision ¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance ¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ ¦--Second investment decision ¦ ¦ ¦ ¦--Success 60.00 % 950,000 chance ¦ ¦ ¦ °--Failure 40.00 % -850,000 chance ¦ ¦ °--Do nothing -50,000 decision ¦ °--Unfeasible 50.00 % -50,000 chance °--Do nothing decision Final decision tree: Probability Payoff Cost Type Investor's Dilemma 143,000.00 ¦--Market research 143,000.00 decision ¦ ¦--Positive result 50.00 % 296,000.00 chance ¦ ¦ ¦--First Investment 296,000.00 decision ¦ ¦ ¦ ¦--Feasible 50.00 % 652,000.00 chance ¦ ¦ ¦ ¦ ¦--Second investment 652,000.00 decision ¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance ¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance ¦ ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ ¦ °--Unfeasible 50.00 % -60,000 chance ¦ ¦ °--Do nothing -10,000 decision ¦ °--Negative result 50.00 % -10,000.00 chance ¦ ¦--First Investment -60,000.00 decision ¦ ¦ ¦--Feasible 50.00 % -60,000.00 chance ¦ ¦ ¦ ¦--Second investment -212,000.00 decision ¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance
  • 8. PAGE 7 OPTIMAL THE WORLD’S TOP MINDS AT WORK FOR YOU. ¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ °--Unfeasible 50.00 % -60,000 chance ¦ °--Do nothing -10,000 decision ¦--First investment 123,000.00 decision ¦ ¦--Feasible 50.00 % 296,000.00 chance ¦ ¦ ¦--Market research 296,000.00 decision ¦ ¦ ¦ ¦--Positive result 50.00 % 652,000.00 chance ¦ ¦ ¦ ¦ ¦--Second investment 652,000.00 decision ¦ ¦ ¦ ¦ ¦ ¦--Success 84.00 % 940,000 chance ¦ ¦ ¦ ¦ ¦ °--Failure 16.00 % -860,000 chance ¦ ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ ¦ °--Negative result 50.00 % -60,000.00 chance ¦ ¦ ¦ ¦--Second investment -212,000.00 decision ¦ ¦ ¦ ¦ ¦--Success 36.00 % 940,000 chance ¦ ¦ ¦ ¦ °--Failure 64.00 % -860,000 chance ¦ ¦ ¦ °--Do nothing -60,000 decision ¦ ¦ ¦--Second investment 230,000.00 decision ¦ ¦ ¦ ¦--Success 60.00 % 950,000 chance ¦ ¦ ¦ °--Failure 40.00 % -850,000 chance ¦ ¦ °--Do nothing -50,000 decision ¦ °--Unfeasible 50.00 % -50,000 chance °--Do nothing decision