Methods of Estimating Costs—Cost of Prediction Error: (Computer required.) The manager of the chemical processing division of Diamond Products Corporation, a small petrochemical company, is preparing a fixed price bid to process up to 800 units per month of certain feedstocks for a large farm cooperative. All of Diamond's customers have processing agreements that specify the allowed production and processing fee Diamond can charge. Diamond receives the feedstocks, processes them, and then delivers the finished products to the contracting company. Diamond incurs conversion costs in the process. Diamond's plant has a maximumcapacity of 9,000 units per month. In a typical month, usage is less than the full capacity and is expected to run at 7,300 units per month over the period of the contract with the cooperative. The manager knows that the cooperative can obtain similar processing elsewhere for a fee of $3.51 per unit. Any bid of $3.50 per unit or less will be accepted by the cooperative. A schedule of past production and processing costs is:

The manager turns to the computer terminal and enters these data to obtain regres- sion estimates of fixed and variable costs. The following results appear on the screen:

After looking at the results, the manager prepares a bid of $3.50 for the process- ing. The manager's bid is forwarded to the controller's office for review and approval. The controller notes the bid and cost estimates. The controller expresses concern with the regression results because fixed costs are lower than expected. The control- ler pulls out the cost report for the division and notes the following items, which are believed to be fixed costs:

In addition, the controller notes that there are a number of "mixed" costs in the chemical processing operation. Since the controller's estimate of fixed costs substan- tially exceeds the fixed cost estimate in the manager's regression equation, the controller asks the manager to explain the difference in the estimates.

The manager states that because the fixed costs will not change as a result of the contract, they can be excluded from consideration.

Required:

a. Without the use of a computer. prepare an estimate of the fixed and variable costs that can be used to confirm or reject the manager's regression results.

b. (Computer required.) Prepare your own regression estimate of fixed and variable costs.

c. Assuming the manager submits a bid of $3.50 per unit for the 800 units per month, how much better or worse off would the company be each month compared to not submitting a bid? (That is, what is the cost of prediction error?

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Conversion Production (units per Month Costs month) 12345. $23,840 7,300 25,714 7,615 21,375 6,410 24,163 7,130 27,332 8,120 6 21,163 6,110 7 23,143 7,040 8 27,582 8,340 9 23,913 7,280 10 23,708 7,045 11 25,315 7,610 12 26,862 8,030 13 27,439 8,150 14 23,840 7,115 15 24,988 7,580 16 23,100 6,960 17 24,189 7,320 18 24,631 7,540 19 25,917 7,880 21 222222 20 23,711 7,210 22,324 6,510 23,684 7,130 23 28,790 8,410 24 25,446 7,830