Question

Exercise 1: Variable Costing (cost behavior): Remember that variable cost per unit remains constant and fixed cost in total remains constant. Spot Woman Cleaners Inc., operates a dry cleaning service. The table below shows the cost incurred at various levels of activity. Number of Dresses Cleaned 100 300 700 Total costs: Fixed costs Variable costs A 3000 D 2.000 F3000 B_SODO $ 15,000 G 3500D c_821 E_18000 $38,000 Total costs Cost (unit) per dress cleaned: Fixed cost Variable cost Total cost (unit) per dress dry cleaned $ 30 J10 M_4.28 H_SDK_50N_50 LXD L_600_54.28 1. Fill in the missing amounts labeled A through o, in the table. 2. Based on your answers above, write the company's mixed cost formula equation. 3.Solve the equation above for 1,000 units. Assume fixed costs are in the relevant range,

Answer 1

Answer 1

Following information is given in the question -

Particulars	100 dresses	300 dresses	700 dresses
Fixed cost	A. ____________	D. __________	F. _________
Variable cost	B. ___________	$ 15,000	G. ________
Total cost	C. ___________	E. _______	$ 38,000
Per unit cost
Fixed cost	$ 30	J. ________	M. _______
Variable cost	H. __________	K. _________	N. ________
Total cost per dress	I. __________	L. ___________	O. ________

You have correctly answered the question. Let me reiterate the answer with reasoning -

(a) Fixed cost per dress is given as $ 30, in case of 100 dresses dry cleaned. Hence, total fixed cost comes out to be $ 3,000 [fixed cost per dress ($30) x Number of dresses dry cleaned (100)]. Hence, "A" is $3,000. Total fixed cost remains same irrespective of the number of units (dresses dry cleaned in this case). Hence, "D" and "F" is also $3,000.

Consequently, fixed cost per unit can be computed by dividing the total fixed cost with the number of units. Hence, "J" and "M" can be computed as under -

"J" = $3,000/300 = $10

"M" = $3,000/700 = $4.2857

You may observe that total fixed cost remains same irrespective of the number of units. However, fixed cost per unit decreases as the number of units increase. As in above question, fixed cost per unit is $30 for 100 dresses, $10 for 300 dresses and $4.2857 for 700 dresses.

(b) Total Fixed cost + Total Variable cost = Total cost

Total cost for 700 dresses is given as $38,000. Fixed cost for 700 dresses as computed above ("F") is $3,000. Hence, variable cost (as per the above formula) is computed as $35,000 [Total cost ($38,000) - Fixed cost ($3,000)]. Hence, "G" is $35,000.

Further, Variable cost per unit = Total variable cost / Total units.

Hence, in case of 700 dresses, variable cost per dress comes out at $50 [Total variable cost as computed above($35,000)/Number of dresses(700)]. Hence, "N" is $50. Variable cost per unit remains same. Hence, "H" and "K" shall also be $50. Consequently, total variable cost for 100 dresses shall be $5,000 [variable cost per unit ($50) x Total units (100)]. Hence, "B" is $5000. Similarly, total variable cost for 300 dresses is $15,000 [variable cost per unit ($50) x Total units (300)]. This is already given in the question. Hence, it confirms that our answer is correct.

(c) Using the formula given at point (b) above [Total Fixed cost + Total Variable cost = Total cost], we can calculate the total cost in each case. Hence, total cost for 100 dresses ("C") shall be $8,000 [Fixed cost ($3,000) + Variable cost($5,000)] and for 300 dresses shall be ("E") $18,000 [Fixed cost ($3,000) + Variable cost($15,000)]. Total cost per dress shall consequently be computed as under -

Total cost per dress (in case of 100 dresses), "I" = $80 [Total cost ($8000) / Number of dresses (100)]

Total cost per dress (in case of 300 dresses), "L" = $60 [Total cost ($18000) / Number of dresses (300)]

Total cost per dress (in case of 700 dresses), "O" = $54.2857 [Total cost ($38000) / Number of dresses (700)]

This solves all the variables. You may observe that total fixed cost remains constant irrespective of the number of units but fixed cost per unit changes with change in number of units and variable cost per unit remains constant and total variable cost changes with change in number of units.

This is just reiteration of what you already know since you had calculated the answer correctly.

Answer 2

Total cost can also be said as 'mixed cost'. Total cost is a mix of variable and fixed cost and hence, it is also known as 'mixed cost'.

Total cost = Variable cost + Fixed cost

Hence, mixed cost formula is

Mixed cost = a + bx

where,

a = Total fixed cost

b = Variable cost per unit

x = Number of units

If you observe, "b*x" in the above formula gives total variable cost, which when is added to fixed cost ('a' in above formula) gives total cost or mixed cost.

In this question, 'a' being the total fixed cost is $ 3,000. 'b' being variable cost per unit is $50. Hence, mixed cost formula equation for this company is -

Total mixed cost = $3,000 + $50x, where 'x' is the number of units.

Answer 3

Question requires the mixed for 1000 units. Hence, in the above equation (as provided in Answer 2 above), 'x' is given as 1000 dresses. Hence, total mixed cost can be computed as under -

Total mixed cost = $3,000 + $50x

= $3,000 + $50 * 1000

= $3,000 + $50,000

= $53,000.