- 18th Feb 2024
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The Jogger Shoe Company Case Study is a Business Analytics Assignment that students need help with. Our statistics assignment experts can provide online tutoring sessions to clarify your doubts and provide you with customized solutions (No plagiarism and no AI content). Below is the question and a reference solution that our expert has written to provide you with a direction on how you should go about solving this case study.

**Jogger Shoe Company Case Study Question**

The Jogger Shoe Company is trying to decide whether to make a change in its most popular brand of running shoes. The new style would cost the same to produce and be priced the same, but it would incorporate a new kind of lac-ing system that (according to its marketing research people) would make it more popular. There is a fixed cost of $300,000 for changing over to the new style. The unit contribution to before-tax profit for either style is $8. The tax rate is 35%. Also, because the fixed cost can be depreciated and will therefore affect the after-tax cash flow, a depreciation method is needed. You can assume it is straight-line depreciation. The current demand for these shoes is 190,000 pairs annually. The company assumes this demand will continue for the next three years if the current style is retained. However, there is uncertainty about demand for the new style, if it is introduced. The company models this uncertainty by assuming a normal distribution in year 1, with a mean of 220,000 and a standard deviation of 20,000. The company also assumes that this demand, whatever it is, will remain constant for the next three years. However, if demand in year 1 for the new style is sufficiently low, the company can always switch back to the current style and realize an annual demand of 190,000. The company wants a strategy that will maximize the expected net present value (NPV) of total cash flow for the next three years, where a 10% interest rate is used to calculate NPV. Realizing that the continuous normal demand distribution doesn’t lend itself well to decision trees that require a discrete set of outcomes, the company decides to replace the normal demand distribution with a discrete distribution with five “typical” values. Specifically, it decides to use the 10th, 30th, 50th, 70th, and 90th percentiles of the given normal distribution. Why is it reasonable to assume that these five possibilities are equally likely? With this discrete approxi-mation, how should the company proceed?

**Jogger Shoe Company - Case Study Solution**

# Introduction

The Jogger Shoe Company is facing a critical decision regarding the potential introduction of a new style of running shoes. This report aims to assist the company in making an informed choice by conducting a decision analysis that integrates financial considerations with uncertain demand projections. This report presents a comprehensive decision analysis for the Jogger Shoe Company regarding the introduction of a new style of running shoes. The analysis considers various financial factors, such as fixed costs, unit contribution to profit, tax rates, and depreciation, while also accounting for uncertain demand projections. By using a discrete distribution to model demand, the report formulates a strategy to maximize the expected net present value (NPV) of total cash flow over the next three years. The analysis is supported by scholarly references.

**Problem Statement**

The company aims to maximize the expected net present value (NPV) of total cash flow over the next three years.

## Decision Variables and Assumptions

- Fixed Cost of Style Change: The decision variable is the fixed cost associated with changing to the new style of running shoes. The report assumes a fixed cost of $300,000 for implementing the style change.
- Unit Contribution to Profit: The unit contribution to profit remains constant for both the current and new styles of running shoes. The report assumes a unit contribution of $8 before tax.
- Tax Rate: The tax rate is a significant factor in determining the after-tax cash flow. The report assumes a tax rate of 35% for calculating the tax liability.
- Depreciation Method: To account for the impact of fixed costs on after-tax cash flow, the report assumes straight-line depreciation. This method allows for an equal depreciation expense to be allocated over the useful life of the style change.

**Net Profit Value (NPV) Model for Three Strategies**

To evaluate the three strategies for the Jogger Shoe Company, we will calculate the Net Present Value (NPV) of total cash flow over the next three years. The strategies are as follows:

**Strategy 1: Stick with the Old Style (No Switch)**

Under this strategy, the company continues producing and selling the current style of running shoes for the next three years without making any changes. The demand remains constant at 190,000 pairs annually. To calculate the NPV, we need to consider the revenue, costs, tax implications, and depreciation effects.

The NPV value for strategy 1 is $2457,010

**Strategy 2: Switch to New Style and Stick with It**

Under this strategy, the company transitions to the new style of running shoes and produces and sells the new style for the next three years. The demand for the new style is uncertain, following a normal distribution with a mean of 220,000 pairs and a standard deviation of 20,000 pairs in the first year.

Assume the demand for new style is $212,000

The NPV value for strategy 2 is $2528,545

**Strategy 3: Switch to New Style and Switch Back After One Year**

Under this strategy, the company switches to the new style for the first year and evaluates the demand. If the demand in the first year is sufficiently low, the company switches back to the old style for the remaining two years.

The NPV value for strategy 3 is $2,348,050

**New decision: Use discrete distribution**

**Why is it reasonable to assume that these five possibilities are equally likely? **

Assuming that the five possibilities in the discrete distribution are equally likely may be a simplifying assumption made by the Jogger Shoe Company due to various reasons:

- Lack of Precise Data: The company may not have access to comprehensive historical data or market research that provides precise probabilities for each demand scenario. In the absence of specific information, assuming equal likelihood allows for a fair representation of the potential outcomes. (Käki et al., 2013)
- Balanced Representation: By selecting the 10th, 30th, 50th, 70th, and 90th percentiles, the company aims to capture a range of demand scenarios that span from relatively low to high levels. This approach ensures a balanced representation of possibilities and avoids overemphasizing any particular scenario.
- Mitigating Bias: Assuming equal likelihood helps mitigate any subjective biases or assumptions that may influence the analysis. It ensures a more objective approach by treating all possibilities as equally probable.
- Simplification for Decision-Making: Employing equal likelihood simplifies the analysis and facilitates decision-making processes. It allows the company to focus on evaluating the financial implications and expected net present value (NPV) of each strategy without needing to assign subjective probabilities to discrete scenarios.

While assuming equal likelihood is a reasonable approximation, it is essential to acknowledge that the actual probabilities of each demand scenario may differ. Factors such as market conditions, consumer behavior, and other external influences can impact the likelihood of specific demand levels. The company should strive to gather more accurate data and refine their models over time to improve the estimation of probabilities and enhance decision-making precision.

**With this discrete approximation, how should the company proceed? **

The Jogger Shoe Company has decided to replace the continuous normal demand distribution with a discrete distribution comprising five "typical" values. Specifically, they have chosen to use the 10th, 30th, 50th, 70th, and 90th percentiles of the original normal distribution to approximate the demand scenarios.

The net profit value for each year 1 demand (1^{st} strategy) in these five typical point discrete distributions is

Now use What-If-Analysis within excel to find out the net profit value for other two strategies.

**Recommendation:**

After evaluating the three strategies for the Jogger Shoe Company, it is recommended to adopt the strategy of switching to the new style shoes in year 1 and then sticking with that decision for at least the next five demands. This strategy has the potential to yield the highest expected net profit value (NPV) over the next three years, considering the discrete demand scenarios and associated financial implications.

The company's decision to switch to the new style in year 1 allows them to take advantage of the potential benefits associated with the new lacing system, which marketing research suggests would make the shoes more popular. By introducing the new style, the company opens up the opportunity for increased demand and potentially higher profits.

The discrete approximation of the demand distribution using the 10th, 30th, 50th, 70th, and 90th percentiles of the normal distribution allows the company to assess the financial outcomes across a range of demand scenarios. By considering these discrete demand scenarios, the company can calculate the expected NPV by weighting the NPVs of each scenario by their assumed equal likelihood.

Based on the analysis of the expected NPVs, it can be concluded that the strategy of switching to the new style in year 1 and sticking with that decision for at least the next five demands is the most favorable.

**Reference:**

Käki, A., Salo, A., & Talluri, S. (2013). Impact of the shape of demand distribution in decision models for operations management. *Computers in Industry*, *64*(7), 765–775. https://doi.org/10.1016/j.compind.2013.04.010

Chien, C., Dou, R., & Fu, W. (2018). Strategic capacity planning for smart production: Decision modeling under demand uncertainty. *Applied Soft Computing*, *68*, 900–909. https://doi.org/10.1016/j.asoc.2017.06.001