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Review the following memorandum and provide a response to the information requested.

A smaller 2-year old emerging venture is set to enter a new segment of its original target market, with a modified version of very popular product already being sold by about a half dozen suppliers in that space. The detailed marketing research produced the model: Q = 44,000 – 12.70P.

Her targeted price seems to be around $3,200 +/- (she hopes, subject to many factors). We’ve helped her develop an overhead/operations budget for next year at $965,000. Her labor + materials + related direct cost of production are modeled as: $2,566.59Q + .0811Q2.

Get some analysis completed in time for our meeting with her and hear advisory team before Session 14. We examined a range of possible annual production runs between 400 and 4,000 units manufactured and sold. We need some basic answers to these

1. Demand function and graph
2. Sales function and graph
3. Total cost function and graph
4. Profit function and graph

Please also elaborate on your findings in a narrative response.

Cost-volume-profit analysis involves examining the relationship among revenues, costs, and profits. Performing cost-volume-profit analysis requires an understanding of selling prices and and the behavior of activity cost drivers. cost-volume-profit analysis is widely used in the economic evaluation of existing or proposed products or services. Typically, it is performed before decisions are finalized in the operating budget for a future period. To use the profit formula we need to separate all the company’s costs into variable and fixed components. Specifically, the formulas are as follows:

Profit (Π) of a product, service or event = Total revenues (R) minus total costs (Y).

Revenues (R) are a function of unit sales volume (X) and unit selling price (p).

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Total costs for a time period (Y) are a function of fixed costs per period ( a) and unit variable costs ( b).To illustrate, assume the T-shirt business we referred to in our financial accounting sessions is venturing into designer fashion. Specifically, we sell upscale T-shirts along the lines of Italian designers such as Prada and Gucci. As before our only product is T-shirts. Having done market analysis, a topic you will cover in other classes in your MBA, we derive the following revenue and cost functions. The least-squares regression cost estimation technique we discussed last session might also be used to determine the variable and fixed amounts for the corporation. Let’s assume we have the following information from the cost estimation model, where Q stands for sales quantity (often people use X instead).

Revenue function: 299 Q – 0.03857Q2

Variable cost function: 344.25Q- 0.1152Q2 + 0.000015889Q3

Fixed cost = 46,280


Total cost function: 46,280 + 344.25Q- 0.1152Q2 + 0.000015889Q3

Profit function: 299 Q – 0.03857Q2 – 46,280 + 344.25Q- 0.1152Q2 + 0.000015889Q3

Now the important assumptions that underlie cost-volume-profit analysis are: (i) all costs are classified as fixed or variable with unit-level activity cost drivers, (ii) the total cost function is linear within the relevant range, (iii) the total revenue function is linear within the relevant range, (iv) the analysis is for a single product, or the sales mix of multiple products is constant, and (v) there is only one activity cost driver: unit or dollar sales volume. Therefore, we have to make the functions linear by taking the first derivative. Please refer to the Excel sheet for our example.

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