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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