Clean & Brite Company's New Product: Probability of Success or Failure
Quantitative Management Practice
Clean & Brite Company Case Study
The product Manager of Clean & Brite is under the dilemma if she should introduce a new brand of toothpaste in the market. The new product can be success or a failure. The report analyses the probabilities of success and failure of the new product and its effect on the profitability of Clean & Brite.
Background to the Problem
Clean & Brite determines that if the new product is a success than it will earn $1,800,000 as profits to the company in future form the sale of new product. However if the new product fails, the company will incur the cost of $750,000. On the other hand if C&B does not market the new brand, its profit from existing products will be same and there will be no impact on its profits.
C&B will introduce the new product if considering the probability of its success there is expected profit. The manager estimates that the new toothpaste brand will be successful with the probability p = 0.35. However, the company can buy additional information on market research for $130,000. The market research will predict the success of the product, given that the product would actually be a success, with p = 0.8 and will predict a failure, given that the product would actually be a failure, with p = 0.7.
Strategy To maximize the Profit (QA)
C&B is looking for the strategy to maximize the expected profit to the company. The manager of C&B can take a decision on this only when the probability for success and failure of the new product are determined and evaluated for the expected profit.
Firstly, the expected profit is determined without the additional information. The manager of C&B predicts the success of the product p = 35%.
Secondly, the expected profit is determined with the additional marketing information. Considering that the actual probability of success of the product is 0.35 and using the information provided by the marketing company, it is determined that the probability that they predict success of the new product is 47.50%. This means that their prediction for the failure of the new product is 52.50%. The probabilities are calculated as shown in Table 1 below:
Table 1: Probabilities of predictions
|Event||Calculations||Probability of correct prediction|
|Prediction of Success of the product||(0.35x0.80) + (0.65 x 0.30)||0.475|
|Prediction of failure of product||(0.35 x 0.20) + (0.65 x 0.70)||0.525|
The posterior probabilities are predicted for the decision tree from the above data. The posterior probabilities are shown in table 3 below.
Table 2: Posterior probabilities given predictions
Using the decision tree, all the possible outcomes for the success and failure of the product given the additional information are mapped. Diagram 1 outlines the various options available to Clean & Brite. The detailed analysis is under the tab labeled Q.A in the attached spreadsheet.
Diagram 1: Decision tree on expected profitability with or without additional information
It can be seen in diagram 1, that given the p= 0.35 for the success of the product, if the additional information is purchased the expected profit of the company increases. The expected profit without additional information is $142,000. The expected profit with the additional information is $227,750 after taking into account the additional cost of information.
Thus the Marketing manager of C&B should buy the additional information. It is also seen in the diagram that the Expected profit is maximum if the product is launched on the prediction of success in additional information and not launched on the prediction of failure in the additional information.
The following strategy is recommended to C&B :
|Decision:||Choose to Buy Information|
|If Information Says Product will be a success:||Launch the product|
|If Information Says Product will be a failure:||Don’t launch the product|
EVI for this decision problem with p = 0.35 (QB)
The additional information provided by the marketing company is useful to C&B but only for a certain range of probability of success. The information is worth buying only when the probability of success of product is more than 0.25. Below this probability the cost of gaining information is more than the benefits derived.
The expected value of Information at p = 0.35 is $227,750. This EVI includes the cost of information of $130,000. The EVI for probabilities form 0.05 to 0.70 at intervals of 0.05 is presented in the table below.
Table 3: Expected Value of Information (EVI)
The Chart of EVI vs P is as below:
It can be seen in the above table and chart that the buying of information is useful only when he actual probability of success of the product is more than 25%
EVSI when p = 0.15 (QC)
The EVSI given the p= 0.15 is -$105,250. Since the probability is less than 25%, the expected value of information is negative. Thus the cost of information is more than the benefit derived from it. The EVSI includes the cost of information. Table 4 below shows the EVSI for the given probability.
Table 4: Expected value of s ample information (EVSI)
|Probability (p)||EVI||EV Without information||EVSI|
|5%||$ (130,000)||$ -||$ (130,000)|
|10%||$ (130,000)||$ -||$ (130,000)|
|15%||$ (105,250)||$ -||$ (105,250)|
|20%||$ (22,000)||$ -||$ (22,000)|
|25%||$ 61,250||$ -||$ 61,250|
|30%||$ 144,500||$ 15,000||$ 129,500|
|35%||$ 227,750||$ 142,500||$ 85,250|
|40%||$ 311,000||$ 270,000||$ 41,000|
|45%||$ 394,250||$ 397,500||$ (3,250)|
|50%||$ 477,500||$ 525,000||$ (47,500)|
|55%||$ 560,750||$ 652,500||$ (91,750)|
|60%||$ 650,000||$ 780,000||$ (130,000)|
|65%||$ 777,500||$ 907,500||$ (130,000)|
|70%||$ 905,000||$ 1,035,000||$ (130,000)|
The table shows that the EVSI is positive only the given range of probability from 0.25 to 0.40.
EVPI when p = 0.35 (QD)
The information provided by the marketing company is not perfect. The information is useful only for a given range of probability. However if the information provided by the marketing company was perfect, the information would be more valuable to C&B. Considering that the information provided is perfect and that the success of the product is predicted to be a success and failure 100% correctly for each event. The EVPI at p = 0.35 is $487,500 as follows:
|Note: The EVPI does not include the cost of information of $130,000|
|Perfect Information Expected Profit:||$ 500,000|
|Basic Information Expected Profit:||$ 142,500|
|Comparison of Expected Values:||$ 357,500|
|Expected Value of Perfect Information:||$ 487,500|
IT is concluded that Clean & Brite should purchase the additional information from the marketing company provided that the probability of the Success of the product is more than 25% and less than 45%. If the probability is outside this range the cost of information will not maximize the profits.