*SuperFun Toys Inc.*

SuperFun Toys Inc . To ensure product success it is important to conduct a rigorous assessment that includes input from business strategy, market, sales, revenue and cost. A sensitivity analysis allows product managers to utilize a sophisticated approach in recognizing uncertainty in a business case. This objective approach significantly enforces discipline and structure around making data-informed investment decisions.

While this exercise organically triggers a healthy tension between the proselytizing product manager and the skepticism of the finance division, integrating statistics with product management gives stakeholders an unbiased view of opportunities and projections which affords the company realistic, actionable forecast and puts them in a position of control and agility. This analytics-driven strategy constitutes a company’s product management intuition that develops a company’s business sense and robustly justifies their decisions to stakeholders.

SuperFun Toys Inc. represents an organization which sells several new and innovative children’s toys. The best critical time to introduce new toys is during the pre-holiday season. This therefore means that the best opportune moment to introduce the new toy is during the December holiday. To achieve this, it is critical to start in June or July so that they can reach the store shelves by October.

In our case study, the team is tasked with aiding SuperFun Toys who propose to introduce a new plan in the market. The new product’s name is Weather Teddy which is a talking teddy produced by a company based in Taiwan. It will therefore be critical to perform project projections and statistical analysis conducted by the project management group. It is important for the team to provide the management with the results of stock-out probabilities analysis for the estimate of profit potential and various order quantities. This analysis will play an important role in helping make an order quantity recommendation.

The sales forecaster’s prediction can be applied to describe a normal probability distribution which can be applied to approximate the demand distribution. The normal distribution is usually or described by two parameters: the standard deviation *σ *and the mean* μ* (Black, 2017). These two values are used in coming up with a normal distribution. The density distribution function which is mathematically applied in representing a normal distribution is:

*f*(*x*)=1*σ*2*π* √ *e* −1/2[(*x*−*μ*)/*σ*)] 2.

From the dataset, the expected demand is 20,000 with a 95% probability. This kind of dataset will give demand which ranges between 10,000 and 30,000 units. In this case, the demand distribution is normal with a mean of 20,000.

Taking X to represents the demand for the toy.

Then X follows the normal distribution with mean μ = 20000 and standard deviation σ.

P(10000 < X < 30000) = 0.95

P((10000-20000)/σ < (X-20000)/σ < (30000-20000)/σ) = 0.95

From tables of areas under the standard normal curve (30000-20000)/σ = 1.96

σ = (30000-20000)/1.96 =10000/1.96 = 5102.

The sketched distribution shows the calculation of a normal distribution probability in a bell curve with 20,000 being the mean and 10,000 being the standard deviation. To calculate the mean, all the data was added then divided the information. The mean was then subtracted by each data point as follows 10,000-20,000=-10,000, 20,000-20,000=0, and 30,000-10,000.

The mean average is in the center of a bell curve, which has one mean, and is known as the unimodal curve. The bell curve is also known as a normal curve, which means that the provided data will have a predictable standard deviation. A normal curve is also considered to be symmetric, meaning that half of the data points are equally placed on the left and right sides of the curve. The standard deviation enables researchers to determine where the data will fall in the curve.

The Empiral rule is used by researchers to help forecast statistical data. Following the Empiral rule in relation to a normal distribution the sketch shows that the data fall inside three standard deviations of the mean, which is 20,000. And following the Empiral rule also known as the 68,95,99.7 rule researchers will be able to tell what percentage of distribution falls inside one, two and three standard deviations of the mean. The measurements are calculated as distances from the mean. The Empiral rule is best to use with the given data set, due to the fact that the data is considered to be unimodal distribution, which is a distribution with one peak that is easy to interpret (Stephanie, 2013).

**Probability of Stock out **

*Table 1.* Probability stock-out for Weather Teddy.

Order (K) | (K-20000)/5102 | P(X > K) |

15000 | 0.98001 | 0.836458876 |

18000 | 0.392 | 0.652472052 |

24000 | 0.784006 | 0.216518215 |

28000 | 1.568013 | 0.058439102 |

Mean= 20,000 Standard Deviation= 5,102

- Z= (15,000 – 20,000)/5,102= 0.98
- Z= (18,000 – 20,000)/5,102 = 0.39
- Z= (24,000 – 20,000)/5,102 = 0.78
- Z = (28,000 – 20,000)/5,102 = 1.56

*SuperFun Toys Inc.*

*Table 2.* Projected profits for Weather Teddy under three projected scenarios

Sales Quantity (Q) | Cost =$16 per unit | Revenue = Sales price = $24 per unit | Profit = $8 per unit |

10,000 (Pessimistic) | $160,000 in Cost at 10,000 units | $240,000 in revenue | Total profit equals $80,000 |

20,000 (Most Likely) | $320,000 in Cost with 20,000 units | $480,000 in revenue | Total profit equals $160,000 |

30,000 (Optimistic) | $480,000 in Cost with 30,000 units. | $720,000 in revenue | Total profit equals $240,000 |

- Pessimistic 10,000 units = (10,000 * $16 (cost) = $160,000), (10,000 * $24 (revenue) =

$240,000), ($240,000 – $160,000 = $80,000 in profit).

- Most Likely 20,000 units = (20,000 * $16 (cost) = $320,000), (20,000 * $24 (revenue) = $480,000), ($480,000 – $320,000 = $160,000 in profit).
- Optimistic 30,000 units = (30,000 * $16 (cost) = $480,000), (30,000 *$24 (revenue) =

$720,000), ($720,000 – $480,000 = $240,000 in profit).

*SuperFun Toys Inc.*

We understand that Super Fun’s managers felt the profit potential was so great the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock- outs. The quantity that should be ordered under this policy is 12,000. The projected profit under the three sales scenarios are as follows:

Order Quantity: 12,000

Purchase cost per unit: $16.00

*Table 3.* Profit potential with 30% stock-out probability.

Sales Quantity (Q) | Cost =$16 per unit | Revenue = Sales price = $24 per unit | Profit = $8 per unit |

10,000 (Pessimistic) | $192,000 in Cost at 10,000 units | $288,000 in revenue | Total profit equals $96,000 |

20,000 (Most Likely) | $384,000 in Cost with 20,000 units | $576,000 in revenue | Total profit equals $192,000 |

30,000 (Optimistic) | $576,000 in Cost with 30,000 units. | $864,000 in revenue | Total profit equals $288,000 |

*SuperFun Toys Inc.*

In order to ensure the success of the new product Weather Teddy for the holiday season, our team has demonstrated through statistical analysis that this could potentially be a successful investment. We have utilized the sales forecaster’s prediction to describe a normal probability distribution which was used to provide an approximate demand distribution and has been represented in a sketch that reflects its mean and standard deviation.

Throughout this analysis we have also computed the probability of a stock-out and projected profits for the order quantities of three possible outcomes from a negative aspect, more likely, to a desired amount of 30,000 sales, all to include the projected profit of each scenario.

*SuperFun Toys Inc.*

Based on the Empirical Rule, we conclude that Super Fun Toys can lose a significant amount of profits if sales fall below their most likely profit margin of 20,000. Not purchasing enough will only result in the loss of more opportunities to sell their product which could increase its demand and lead to dissatisfied customers, a slight impact of the stock-out. It has been proven that it would be a wise decision to have an order quantity of 70% to have a great chance of meeting the demand and 30% chance of potential stock-outs so that a profit balance can be defined between the two margins.

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