Diet Coke is also considering introduction of a new brand of diet root beer. An
ID: 3259235 • Letter: D
Question
Diet Coke is also considering introduction of a new brand of diet root beer. An internal study by the management estimates that the probability of success for their new diet root beer is 0.60. Of course they have the option of not producing the product. They have estimated the following payoff table for each choice.
Beside “Soft Drink Consultants”, they have asked the help of another consulting firm “Innovative Research Inc.” to help managers of Diet Coke to make an optimum decision. The “Soft Drink Consultants” provides two indicators, either I1 (Soft Drink Consultants recommends introduction of the new product) or I2 (Soft Drink Consultants doesn’t recommend introduction of the new product), for which P( I1 / S1) = 0.70 and P( I1 / S2) = 0.40. The “Innovative Research Inc.” provides two indicators, either J1 (Innovative Research recommends introduction of the new product) or J2 (Innovative Research doesn’t recommend introduction of the new product), for which P( J1 / S1) = 0.60 and P( J1 / S2) = 0.30.
a. After receiving such results, recommend an optimal decision for Diet Coke, assuming that management believes that results of neither consulting firms’ are correct and their study will NOT be used. Over what range of probability of success their decision is optimal?
b. Calculate the EVPI
c. Calculate the EVSI and the efficiency for both consultants.
d. If both consultants charge $5,000, which firm should be hired and why?
e. If Soft Drink Consultants charges $10,000 and the “Innovative Research Inc.” charges $4,000, which consulting firm should be used and why. Explain in details.
Introduction of the newIntroduction of the new product will be a success product will be a Failure S1 Choices S2 Produce the new brand of diet root beer $250,000 -$300,00o -$20,000 Do not produce the 50,000 new brand of diet root beerExplanation / Answer
c.
Expected value without sample information = Max(Expected value of producing root beer, Expected value of not producing root beer)
Expected value of producing root beer = 0.6 * $250,000 - 0.4 * $300,000 = $30,000
Expected value of not producing root beer = 0.6 * -$50,000 - 0.4 * $20,000 = -$38,000
Expected value without sample information = Max($30,000, -$38,000) = $30,000
Given, P( I1 / S1) = 0.70 and P( I1 / S2) = 0.40.
P( I2 / S1) = 0.30 and P( I2 / S2) = 0.60.
P(I1) = P(S1) P( I1 / S1) + P(S2) P( I1 / S2) = 0.6*0.7 + 0.4*0.4 = 0.58
P(I2) = 1 - P(I1) = 1 - 0.58 = 0.42
P(S1/I1) = P(S1) P( I1 / S1)/P(I1) = 0.6*0.7/0.58 = 0.72
P(S2/I1) = 1 - 0.72 = 0.28
P(S1/I2) = P(S1) P( I2 / S1)/P(I2) = 0.6*0.3/0.42 = 0.43
P(S2/I2) = 1 - 0.43 = 0.57
Expected value when Soft Drink Consultants recommends introduction of the new product = P(S1/I1) * $250,000 - P(S2/I1) * $300,000 = 0.72 * $250,000 - 0.28 * $300,000 = $96,000
Expected value when Soft Drink Consultants does not recommends introduction of the new product = P(S1/I2) * -$50,000 - P(S2/I2) * $20,000 = -0.43 * $50,000 - 0.57 * $20,000 = -$32900
Expected value with sample information = P(I1) * $96,000 - P(I2) * $32900 = 0.58 * $96,000 - 0.42 * $32900 = $41862
EVSI for Soft Drink Consultants = $41862 - $30000 = $11862
Efficiency of Soft Drink Consultants = P(S1/I1) = 0.72
Given, P( J1 / S1) = 0.60 and P( J1 / S2) = 0.30.
P( J2 / S1) = 0.40 and P( J2 / S2) = 0.70.
P(J1) = P(S1) P( J1 / S1) + P(S2) P( J1 / S2) = 0.6*0.6 + 0.4*0.3 = 0.48
P(J2) = 1 - P(J1) = 1 - 0.48 = 0.52
P(S1/J1) = P(S1) P( J1 / S1)/P(J1) = 0.6*0.6/0.48 = 0.75
P(S2/J1) = 1 - 0.75 = 0.25
P(S1/J2) = P(S1) P( J2 / S1)/P(J2) = 0.6*0.4/0.52 = 0.46
P(S2/J2) = 1 - 0.46 = 0.54
Expected value when Innovative Research Inc recommends introduction of the new product = P(S1/J1) * $250,000 - P(S2/J1) * $300,000 = 0.75 * $250,000 - 0.25 * $300,000 = $112500
Expected value when Innovative Research Inc does not recommends introduction of the new product = P(S1/J2) * -$50,000 - P(S2/J2) * $20,000 = -0.46 * $50,000 - 0.54 * $20,000 = -$33800
Expected value with sample information = P(I1) * $112500 - P(I2) * $33800 = 0.48 * $112500 - 0.52 * $33800 = $36424
EVSI for Innovative Research Inc = $36424 - $30000 = $6424
Efficiency of Innovative Research Inc = P(S1/J1) = 0.75
d.
If both consultants charge $5,000, we should hire Soft Drink Consultants, as EVSI of Soft Drink Consultants is larger than Innovative Research Inc.
e.
If Soft Drink Consultants charges $10,000 and the “Innovative Research Inc.” charges $4,000, then
Net EVSI for Soft Drink Consultants = $11862 - $10,000 = $1862
Net EVSI for Innovative Research Inc = $6424 - $4000 = $2424
As, Net EVSI for Innovative Research Inc is larger than that of Soft Drink Consultants, we should hire Innovative Research Inc.
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