Example 2.1: Breakeven Analysis at Great Threads:

Problem Definition:

Great Threads needs to decide if and when it is profitable to launch a Direct Mail Campaign.

Assumptions:

• Fixed Batch Cost of printing a brochure is $20,000
• Variable cost to print a brochure is $0.20/brochure
• Cost of mailing a single brochure is $0.15
• Return reply envelopes cost $0.20 on each customer response
• Average Customer order is $40.00
• Average cost per customer order is $80%
• Company plans to mail 100K catalogs

Unknowns:

• How a change in response rate will affect profit
• For what response rate will Great Threads break-even
• Given a predicted response rate of 3% should they proceed with the campaign
• How does the presence of uncertainty affect the model.

Model Formulation:

Influence Diagram:

Mathematical Model Formulation using EXCEL worksheets:

Sensitivity analysis may be performed using by varying the above Model Response Rate against the calculated profit.

Sensitivity Analysis shows us for every percentage in response rate, profit changes $7800. Moreover, this analysis tells us the breakeven occurs somewhere between a five and six percent response rate. Using Microsoft Excel’s Goal Seek function, we can determine the actual breakeven point at a response rate of 5.77%. This is demonstrated above. Based on this analysis, any response rate less than 5.77% will cause negative profits to be generated. Therefore, if the company expected a 3% response rate, the project is not worth the effort given the assumed conditions.

Uncertainty affects the model in many ways. Market conditions may affect the demand or average order size. Supply conditions may affect raw materials costs, Mailing costs have changed dramatically over the past few years as well. These uncertain inputs may be modeled to determine the worst case scenario. Then the company must determine how averse it is to risk and weigh these risks against other alternatives. It is in these ways uncertainty affects the model.