DA Corp's Investment Decision: A Comprehensive Analysis

This report analyzes DA Corp's decision-making process concerning a potential investment in a new smart audio equipment product. The company faces a decision of investing either $1 million or $2 million in January 2019, with uncertainties surrounding the product's completion by June 2019. The analysis employs a decision tree method to evaluate the alternatives, considering probabilities of completion and potential returns. It also explores the concept of stochastic dominance between the investment options and evaluates the value of clairvoyance and expert assessment in predicting competitor actions, providing insights into optimal decision-making strategies for DA Corp.

DECISION MAKING 1
Decision Making
Name
Institution
Course
Date

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a. Optimal decision making using the decision tree method
The decision making process using the decision tree method is used in the evaluation of
alternatives of decision that have decision branching as well as the event branching (Greco,
Figueira, Ehrgott, 2016). According to the information available concerning the DA Corp, there
are two decisions to be made concerning investment in the development of a new product. The
first branch of decision involves either making an initial investment of $ 1 million or $2 million
in January 2019. The following decision tree follows the situations leading the decision that was
made;
Pro o to e completed neb f 0.6 b by Ju
pro to e completed ne0.8 b b by Ju
The probabilities for the investment in the first stage are given, indicating that the company
believes that, if it invests $1 million in January 2019, the product will be completed in June 2019
eci ionD s
nitialI
n e t mI v s $1
nitialI
n e t mI v s $2
otN
complet
ed by
neJu
ot completedN
neby Ju
n e t anot erI v s h $2
million to complete t eh
pro ectj
Terminate t e pro ecth j
n e t anot erI v s h $2
million to complete t eh
pro ectj
Terminate t e Pro ecth j

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with probability 0.6; if it invests $2 million instead, the product will be completed in June 2019
with probability 0.8.
This suggest that in the event that the investment is revalued based on the two steps, the
probability of an initial high demand is 0.6*$1million=6000 as the expected return. On the other
hand the probability of an initial high possibility is 0.8*$2 million= $1.6 million as the expected
return. It follows from this that the probability of a low return is 0.6*$1million=600,000 as the
expected return. The question that emerges here is what is the probability ratio of the initially
high return remaining in the second period so that the project can be completed? The probability
of two independent events occurring simultaneously is the product of the individual occurrences
of the events. Thus the probability of a high return all through the period is 80%. So the
company’s optimal decision policy and certainty equivalent to make the initial investment of $
2million that has a completion rate of 80% by June.
b. Plot the risk profiles for the company’s two initial decision alternatives on a common graph paper
The graph below shows the interaction between the initial investment choices that are to be made
subject to the probabilities given of return on investment upon the completion of the project
within the stipulated time.

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c. Is there any first or second order stochastic dominance among the two initial alternatives?
Explain your answers.
The stochastic dominance involves a partial order among the existing variables through the
decision concepts and analysis in situations involving probabilities (Torra, Xu, Xu, Herrera, pp.
89-96). However, it is important to note that the probability has possible outcomes as well as
their associated probabilities. Technically, a decision A has first-order stochastic dominance over
decision B if for any outcome x, A gives at least as high a probability of receiving at least x as
does B, and for some x, A gives a higher probability of receiving at least x.
On the other hand, for two decisions, A and B, decision A has second-order stochastic
dominance over decision B if the former is more predictable with lower risk level and has at
least as high a mean.
Therefore, based on the decision situation above, there are both the first and the second order
stochastic dominance among the two initial alternatives. The second order stochastic dominance
is more likely.
d. What is the value of clairvoyance to DA Corp on whether Cyber Inc. will finish its
product by the end of June 2019 or not? Show your computations.
As a direct competitor, DA Corp has information in the market about the competitor, Cyber Inc.
that Cyber Inc. is working on another competing product to be completed by June or October
around the same time as DA Corp, but everything is dependent on June target. Based on the
given probabilities, the optimal solutions for DA Corp involve:

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Companies Month Marketing and sales profit
DA Corps June $4 million
Cyber Inc. June $4 million
DA Corps October $4 million
Cyber Inc. October $4 million
DA Corps June/October $4 million/ $1 million
Cyber Inc. October/June $ 1 million/ $4 million
Based on the analysis table above, marketing and sales gives both the companies a profit of $ 4
million if they complete the projects at the same time and a profit of $ 4 million for the one that
completes first before the other. The last to complete the project makes $1 million from
marketing and sales. Therefore, it is upon each company to make the optimal decision within the
optimal timeline.
e. John, an ex-employee of Cyber offers to help DA assess whether Cyber would complete
the product by June or October 2019. However, as John had left the company months ago, his
assessment will not be perfect. If Cyber can complete by June 2019, John will predict it correctly
with probability 0.75. On the other hand, if Cyber completes the product in October 2019
instead, John will predict it correctly with probability of 0.9. How much is John’s assessment
worth to DA?
Basing DA Corps completion of the project based on John’s prediction, then;
If Cyber complete by June before DA corps, then DA Corps makes
0.75*1,000,000 (if DA Corps complete later in October) = $750,000
0.75*4,000,000 (if DA Corps complete in June) = $ 3,000,000
However, if Cyber completes the product in October, the based on John’s prediction, DA Corps
makes; 0.9*4,000,000 = $3,600,000 (either way).

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Bibliography
Greco S, Figueira J, Ehrgott M. Multiple criteria decision analysis. New York: Springer; 2016.
Rodríguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Martínez L,
Torra V, Xu YJ, Xu ZS, Herrera F. A position and perspective analysis of hesitant fuzzy sets on
information fusion in decision making. Towards high quality progress. Information Fusion. 2016
May 1;29:89-97.