Costs are classified into three broad categories, that is fixed costs, variable costs and mixed costs. Fixed costs remain unchanged no matter how many units are produced. I our case rent is a fixed cost as it remain at a constant figure of 10,000 all along. Variable costs vary with the number of units being produced, that is to say if more units are produced the cost increase and it decrease if lesser units are produced. In this case the labour and the material costs are variable since they vary directly with the units of production and have a constant rate per unit. For the mixed costs, they have both a fixed cost element and a variable cost element. Mixed costs are also called semi-variable costs. In our case electricity costs are mixed costs since there is one element where the cost vary with the number of units produced and there is also the part of the cost which remains unchanged no matter the level of production. Other expenses also fall under the mixed cost classification since they neither fixed nor do they have a constant rate per unit.Scatter diagram for electricity costs
Scatter diagram for rent
Scatter plot for other expenses
Scatter plot for raw material costs
Scatter plot for labour cost
Total cost estimation formula using the high low method
Units Costs
Low 5000 83378
High 9500 158516
We find out the slope; (158516-83378)/(9500-5000) = 16.70
To find out the total cost equation we use either the low or the high as follows
Total cost= Variable Cost x + fixed cost
158516 = 16.70 (9500) + FC
Thus FC = -134
So the total cost equation is TC = 16.7x-134
Total cost formula using the regression method
The regression line formula is y=a+bxx y xyx squared
5000 83378 416890000 25000000
6000 100653 603918000 36000000
8000 132069 1056552000 64000000
9500 158516 1505902000 90250000
28500 474616 3583262000 215250000
b = (nxy-(x)(y)/nxsqd- (x)squared
b =( 4*3583262000-(28500*474616)/(4*215250000-(28500*28500)
b= 806492000/48750000
b = 16.54
a = y-bx/n
a = 449540-(16.54*28500)/4
a= 3226
Thus the total cost equation the regression method is y=16.54x + 3226
Cost of producing 4500 tables
Using the high low method:
TC = 16.7(4500)-134
TC= 75016
Using the regression equation method
Y= 16.54x + 3226
Y=77656
Cost of producing 8000 tables
Using high low method
TC= 16.7(8000) 134
TC= 133466
Using the regression method
Y = 16.54(8000)+3226
Y = 135546
Cost of producing 10500 tables
Using high low method
TC= 16.7(10500) 134
TC = 175216
Using the regression method
Y = 16.4(10500) +3226
Y = 175426
Explanation: The low high method gives results of a relatively lower cost in all the scenario when compared with the regression method. This is why the regression method is considered more accurate as it eliminates the sum of errors thus more reliable.
Break even point
Break even in unit= fixed costs/contribution margin
Contribution margin = selling price variable costs
For table 1
Y = 16.4(70640) + 3226
Total costs = 1,161,722
Variable costs per unit = 16.4
Contribution margin =58 16.4 = 41.6
Table 1 B.E.P = 3226 * 12/41.6 = 931
To break even on Table model 1 we require to produce 931 tables.
Table 1 break even point in dollars
B.E.P in dollars = Selling price per unit * Break even unit
Table 1 B.E.P in dollars = 58*931 = 54, 404 dollars
Table 2 break even unit =
Margin of safety shows how much sales can fall before attaining the breakeven point
Margin of safety = actual/budgeted sales breakeven sales
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