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Blackheath Case Study

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Autor:  anton  14 April 2011
Tags:  Blackheath
Words: 2093   |   Pages: 9
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The Case

Blackheath Manufacturing Company, is a company that manufactures a single product named Ў§Great Heath.ЎЁ The company recently hired a new cost accountant, Lee High, who intends to conduct a new cost analysis over a period of three production weeks. Lee wanted to better identify the fixed, variable, and semi-variable costs associated with production of ЎҐGreat Heath.Ў¦ Once these costs were categorized Lee could determine how this would effect the cost of goods sold. Lee could then develop what the break- even volume that could be generated from a changing volume of sales. The case shows the assumptions that Lee High made with respect to variable as versus fixed costs in determining the cost of goods sold per unit . Lee High was able to develop decision rules for use by the companyЎ¦s owner for management decision-making purposes. Based upon Lee HighЎ¦s data, Charlton Blackheath, the owner, dictated a management decision that sales could not be less than a $7.00 per unit order. The case then introduces a series of sales possibilities that are accepted or declined based essentially on these decision rules. However, a young file clerk decided to take an under-bid proposal at $5.50 for an order of 100 units of ЎҐGreat HeathЎ¦ based upon her own assumption that such a volume order would be profitable. A subsequent sales-cost report was developed by Lee High showing cost per unit based upon his predetermined analysis of costs and including profit per unit. Data showed the file clerkЎ¦s order generated a subsequent loss because the price per unit was so low. Based upon this data, Blackheath then fired the clerk for this error and readjusted the per unit price to $8.00 to generate a higher profit.

Executive Summary

Lee High had made calculations based upon a static volume of sales and production. He was also calculating only the cost of goods sold and did not take into consideration the respective amounts of fixed versus variable costs. While the fixed costs remain constant in total, when the volume of goods produced and sold increases, the amount of fixed cost attributed to each individual unit goes down. Following this logic the variable cost per unit will remain constant on a per unit basis, assuming a constant level of efficiency of production. This leads us to the inevitable conclusion that as production increases, the cost of goods sold will increase overall, but will decrease on a per unit basis. Thus Blackheath can maintain a healthy profit margin, charging a lower price, assuming that the volume increases accordingly.

With respect to the situation that has been defined in this case study; we have drawn the following conclusions. Lee HighЎ¦s decision matrix was fundamentally flawed since he had based everything upon an assumption of 500 units per week sales (p.35), not taking into account the cost fluctuation if production deviates. Lee High also calculated fixed costs incorrectly (p.34) grossly understating them. Mr. Blackheath would lose money in the long run by adopting the new sales strategy of 15% commission for the salesmen who sold Great Heath for a price of $8.00 (p.37). Mr. Blackheath should have promoted, or at least congratulated Adelaide Ladywell on her sales to Maze Woolwich as the added volume increased the Net Profit.


The primary mistake that Lee High made was assuming that fixed expenses were $781. While the President had given him this figure, he should have reviewed the available cost information and come up with his own calculation of fixed costs. The miscalculation of the $781 of fixed costs also led to errant calculations in the variable cost per unit. We are unable to determine how this figure of $781 was reached, therefore we can best assume this figure was arbitrary. The chart below shows the original costs provided in the case. In this chart we have surmised which costs should be labeled as variable, mixed and fixed.


Week 1

Week 2

Week 3




600 Direct






Direct Labor*




750.00 Indirect Labor




220.00 Indirect Materials




300.00 Electricity




135.00 Factory Insurance




125.00 Other Overhead




410.00 Total




The correct figuring of costs are essential in determining the correct pricing for goods. We noted that the original data provided did not properly account for Direct Labor. We can see this in the change of production unit between week 2 and week 3, which clearly shows that the direct labor change is $1.25 per unit (or a $125 difference between weeks.) Thus, the correct direct labor figure for week 1 should be $500*. From this raw data Lee High created income statements for these three weeks (p.35).


Cost of Goods Sold

Gross Margin

Less: Other Expns

Net Income Week 1





(91) Week 2





259 Week 3






These income statements were how Lee High fashioned his decision rules to implement in the pricing of ЎҐGreat Heath.Ў¦ Unfortunately for Lee, he did not take into consideration all of the expenses when he figured his per unit cost. As best as we can determine, Lee utilized the ЎҐHigh-LowЎ¦ method when he was calculating his costs. Lee took only the change of cost of goods sold between week 1 and week 3 into consideration when figuring his variable costs. He also relied upon his president for fixed administration costs of $781. Lee omitted the ЎҐother expenses,Ў¦ a crucial error in his overall cost calculations. His cost analysis is below:

Variable cost per unit = Ñ“Ò‘Cost/Ñ“Ò‘Activity or 560/200=2.8


Fixed cost per unit = Total Cost ÐŽV Variable Cost Element


2390 (Week 3 cost of goods sold) ÐŽV (2.8 X 600) = $710/500 Units = 1.42

*500 Units of production was the arbitrary average Lee assigned in calculations.

Fixed admin and selling costs = $781/500 = $1.56

Added commission costs to sales force @ 7.00 X 10% = $.70

Added amount for conflict in figures = $.12

Break even per unit cost = $6.60

The decision rules that Lee created were based upon this $6.60 break even point figure. However, his failure to include the Ў§other expensesЎЁ missed the mixed and fixed costs that were included in that amount. Our model takes all expenses into consideration.

Total expenses for the 3 weeks can be determined as follow, Week 1= $2891, Week 2=$3241, and Week 3=$3591. All of the expenses help us to see what were the actual costs utilized in production. The difference in net income helped us to determine, that as income rose each week, there was a difference of $350. This assists us in determining what the variable costs per unit were. Because production rose each week 100 units between weeks 1 to 2 and 2 to 3, we can determine from this that variable cost will increase on a per unit basis of $3.50. The cost analysis method through which we determined our results utilized the ЎҐleast-squares regression method.Ў¦ Through linear regression we have determined that the fixed costs are $1,491.00, and confirmed variable costs are $3.50 per unit. We plotted our regression points for our graph by determining the total expenses for # of units produced by week in the income statement produced by Lee High:

Week 1= 400 units/$2891 total expenses

Week 2= 500 units/$3241 total expenses

Week 3= 600 units/$3591 total expenses

At zero units produced we can determine through linear regression that our fixed costs are $1491.

Y=3.5x+1491, R2 = 1.00

Ў§The R2 varies from 0% to 100%, and the higher the percentage, the better,ЎЁ according to our text (Garrison/Noreen p. 211.) The R2 in our graph is a perfect 1.0, thus we believe the cost structure and method of cost analysis is the more accurate then Lee HighЎ¦s analysis (High-Low Method.) Once the variable and fixed costs have been accurately defined, this helps us to determine accurate break-even points.

Ў§Once break-even point has been reached, net income will increase by the unit contribution margin for each additional unit sold.ЎЁ (Garrison/Noreen p.236) Finding what the break-even points are in relation to volume produced versus pricing, permit us to have a more aggressive sales decision rule. Assuming production capacity costs remain constant we can create a competitive sales decision rule that will allow us to accept sales orders for a lower contribution margin, of course, within reason. It should also be noted, that as the numbers of units are increased, the fixed cost will go down as this cost is spread across more units.

Using the new calculations we have calculated the break-even price as well as the price to achieve a desired profit of $1,000.

Break Even Sales Price by Unit Sales Desired Profit Sales

100 $18.41 $28.41

200 $10.96 $15.96

300 $8.47 $11.80

400 $7.23 $9.73

500 $6.48 $8.48

600 $5.99 $7.65

700 $5.63 $7.06

800 $5.36 $6.61

In the following-cost profit volume analysis graph or break-even chart, the volume unit/price shows the range of break even-points.

There are a couple of break-even computations that the text utilizes in calculation. This can be calculated either by the Equation Method or the Contribution Margin Method (Garrison/Noreen p. 244-46.)

The Equation Method:

Sales = Variable expenses + Fixed expenses + Profits

$8.00Q = $3.50Q + $1491 + 0

$4.50Q = $1491

Q = 331.33 Units of ЎҐGreat HealthЎ¦

Or 331.33 Bottles X $8.00 = $2650.66

The Contribution Margin Method, like the equation method can be defined in units sold or as in total sales dollars:

Fixed Expenses = $ 1491 = 331.33 Break-even Units

Unit Contribution Margin $4.50


Fixed Expenses = $ 1491 = $2650.66 Break-even total sales

CM Ratio .5625

Break-Even Points

Price Per Unit

$8 Per Unit

$7 Per Unit

$6 Per Unit

$5 Per Unit Break-Even Units




994 Break-Even Sales





These calculations are based upon the assumption that the ratio of sales made by the salesmen on the road and those made by the office sales staff remain constant. If the ratio fluctuates then the numbers would need to be adjusted to compensate for the added or reduced commissions paid.

The sales that were accepted as a result of LeeЎ¦s decision matrix actually caused Blackheath to lose money. There was a loss of $26.00, which he had blamed on Ms. LadywellЎ¦s sale. In fact, had they not used LeeЎ¦s matrix and accepted all of the sales, Blackheath would have show a profit of $812 rather than a loss of $26 as explained in the summary below.

** Insert Chart Here **

This leads us to Mr. BlackheathЎ¦s idea of a new commission structure for the salesmen that would offer a 15% commission on sales at a price of $8.00. While on the surface this would seem logical, that you would make a higher profit margin by raising the price and producing fewer units, this doesnЎ¦t take into account the increased costs generated by the lower volume. Since there are fewer units being produced and sold, fixed costs will increase on a per unit basis, which would eat into any added revenue gained by the higher price. If we assume that Mr. BlackheathЎ¦s volume predictions are correct then we have the following result:

350 Units at a price of $8.00 per unit, with 15% commission

Sales = $2,800.00

Costs = $2,891.00

Net = -$91.00

450 units at a price of $7.00 per unit, with a 10% commission

Sales = $3,150.00

Costs = $3,066.00

Net = $84.00

When the commission is increased to 15% the variable cost is increased by $0.50 ($0.70 to $1.20). The new rules would end up costing the company $175.


Lee HighЎ¦s decision matrix was flawed and should never have been adopted. In the end Blackheath lost out on valuable sales that could have increased the overall volume and profit. Mr. BlackheathЎ¦s new commission structure, giving the salesmen a 15% commission on sales of $8.00 per unit at a lower volume would end up costing the company an average of $175 and should not be implemented. And finally, Adelaide Ladywell did the right thing by accepting the order of 100 units for a price of $5.50. The added volume reduced the fixed costs per unit and generated added revenue. She should have been commended and not fired.


Garrrison, R., and Noreen, E., (2003). Managerial Accounting. McGraw-Hill/Irwin.

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