## Perform a cost-volume-price analysis

STEP 1:  Description

In this case study, you will act as a consultant for a company that crushes sunflower seeds to produce high quality refined sunflower oil for sale in the wholesale market. The company is looking for you to make a recommendation on the optimal blend of raw materials required for its next production cycle. You will use a number of decision analysis tools including time series forecasting, linear programming, and cost-profit-volume analysis to make the recommendation and provide analysis on the profitability of the company.

You will be required to submit a written report to management, and to include the spreadsheet models you used to generate price forecasts, optimize the raw material, and a perform the break-even analysis. All analysis should be done using Excel and the various models should be implemented on separate worksheets or in separate workbooks.

STEP 2 :  Scenario:

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STEP 3:  Suggested Approach

This is a fairly complex problem. The following approach is suggested:

1. Use the historical price data set as input to a time series forecast model in order to generate forecasted prices for the average price of sunflower seeds, oil, and mash in the next production period. Use standard measures of error to decide between a three-period moving average model or an exponential smoothing model (with α = 0.2). Use the type of model for all three time series forecasts. That is, if you decide to use the moving average model, use a three-period moving average model to fit the relevant data for all three series. Don’t use the moving average for one time series and the exponential smoothing model for another time series.
2. Formulate a linear program to minimize the cost of raw sunflower seeds.  Use the average price of seeds forecasted from the previous step in order to determine supplier prices.
3. Perform a cost-volume-price analysis (review the handout entitled Cost-Volume-Profit Analysis for details) using the average cost per short ton average selling price per short ton.
• a)  You can generate an effective cost per short ton by dividing the total cost of supply (from the linear program) by the total volume (that you assumed in the linear program).
• b)  You can generate an effective selling price per short ton from the expected percentage yields and the forecasted average price of sunflower oil and mash.
• c)  Because of the way that the contract is written, you can assume that the purchase of raw sunflower seeds is a variable cost (you only purchase what you require).

Recall that the cost-volume-price analysis requires you to provide

• d)  an algebraic statement of the revenue function and the cost function,
• e)  a detailed break-even chart that includes lines for the revenue and for the total cost, fixed cost, and variable cost (a total of four lines), and
• f)  a calculation break-even point expressed in number of short tons and percent of capacity.

STEP 4 : Management Report

Prepare a written management report that includes, the following sections:

• 1-Purpose of the Report
• 2-Description of the Problem
• 3-Methodology (which would include the model formulation)
• 4-Findings or Results
• 5-Recommendations
• 6- Conclusions

STEP 5:  Be sure to address all relevant points, discuss any assumptions you are making, justify any modeling choices you have made (for example, the choice of time series forecast model), and highlight the following items in your report:

• – a forecast of the next production period’s average price index for raw sunflower seeds, sunflower oil, and sunflower mash,
• – a recommendation for the optimal purchasing strategy from the various suppliers,
• – a cost-volume-profit analysis using for the recommended purchase strategy and the forecast  sunflower oil and mash
•   sales price,
• – a discussion of the risks and uncertainties that are faced by the company, and
• – an analysis and opinion on the profitability of the company in the next production period (accounting for the expected
•   profit or loss and the inherent risks/uncertainties.