Question

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A firm produces a product with the following costs: $1.30 of materials and $0.90 of wages for factory labor. In addition, the firm also pays rent of $483 and insurance of $242 per month. Its past few statements for electricity had the following total costs:

Cost of Electricity

Month	# of units products	Cost ($)
March	325	250
April	280	233
May	355	255

If it pays a sales commission of $0.50 on each unit, which it sells its for $10, what is its breakeven point?

At its breakeven point, about how much should it expect to pay for electricity?

When you make this estimate, what branch of statistics are you using? Why is the estimate that you provided “good?”

You may use Excel or the TI BA II Plus/Professional calculator. You may use your class notes as a guide.

You MUST also use the ideas of differential calculus to show how the coefficients (intercept & slope) are computed. You should set-up the appropriate problem, and then use Wolfram Alpha to help you do the calculations to solve the problem to show that any intercepts and slope coefficients from Excel or the calculator are correct. Be sure to copy-and-paste the significant results from Wolfram Alpha into your Word document.

A “B/B+”-quality response would have all of the correct steps but without any explanation of the steps taken.
A response that also clearly describes the reasoning behind each step will receive full credit.

Answer 1

Answer:

1. Break Even Point is described as that Sales Volume at which there is neither Profit nor Loss.

2. Electricity costs are checked for semi-variable costs

and there is no fixed element in it. Hence considered as Variable costs (vary with Units produced)

Selling Price Per Unit		$ 10
Materials	$ 1.30
Wages	$ 0.90
Sales Commission	$ 0.50
Electricity (WN1)	$ 0.77*
VC		$ 3.47
Contribution (SP-VC)		$ 6.53

Rent	$ 483
Insurance	$ 242
Fixed Costs		$ 725

a) Break Even Point = Fixed Cost/Contribution per unit =725/6.53 = 111 Units (apprx)

b) At its BEP, the firm is expected to pay $85.35 (111uts * $0.77 p.u) as electricity costs.

c) While making the estimate of Electricity cost, the Branch of Descriptive statistics is used, wherein the concept of Arithmetic Mean(Measure of Central tendency) is applied to the units produced and corresponding electricity costs columns.

The AM is chosen because all the items in the either of the columns are independent and equally important, hence, provides a balanced measure of unit products and electricity costs.

Working Note 1:

Month	# of units produced	Electricity Cost ($)
March	325	250
April	280	233
May	355	255
Mean (Average formula)	320	246
Electricity Cost per Unit product	(246/320)	$       0.77*