Question

Patterson Products Inc. is considering an upgrade to its manufacturing equipment. The two upgrade options under consideration are shown below.

	Option 1		Option 2
Direct material cost per unit	$	50.4	$	33.6
Direct labour cost per unit	$	42	$	35
Variable overhead per unit	$	8.4	$	26.6
Fixed manufacturing costs	$	2,040,000	$	3,552,000

The selling price of the company’s product is $168 per unit with variable selling costs of 10% of sales. Fixed selling and administrative costs are $3,340,000 per year.

There would be no change to the selling price, variable selling costs, or fixed selling and administrative costs as the result of the manufacturing equipment upgrade.

Required:

1. At what annual number of unit sales would Patterson Products Inc. be indifferent between the two upgrade options?

Annual number of unit sales=

2. If demand falls short of the indifference point calculated in part (1), which option would be preferred?

• Option 1

• Option 2

3. Calculate the break-even point in unit sales under each upgrade option. (Round your final answers to the nearest whole number.)

Break-even unit sales for Option1=

Break-even unit sales for Option2=

Answer 1

1) calculation of annual number of unit sales would Patterson Products Inc. be indifferent between the two upgrade options :

indifference point = difference in fixed costs/variable cost per unit

calculation of fixed cost and variale cost per unit

paricular	option 1	option 2
variale cost per unit :-
Direct material cost per unit	$50.4	$33.6
Direct labour cost per unit	42	35
Variable overhead per unit	8.4	26.6
total manufacturing variale cost per unit	$100.8	$95.2
fixed cost :-
Fixed manufacturing costs	$2040000	$3552000

difference in fixed costs = $3552000 - $2040000 = $1512000

difference in total manufacturing variale cost per unit = $100.8 - $95.2 = $5.6

indifference point = difference in fixed costs/variable cost per unit = $1512000/$5.6 = 270000

2) If demand falls short of the indifference point calculated in part (1), option 1 would be preferred which can be understood as under :

let us assume demand falls short of the indifference point calculated in part (1) to 250000 units then net income will be as under :

particular	option 1	option 2
sales in units	250000	250000
selling price per unit (a)	$168	$168
variale cost per unit :-
Direct material cost per unit	$50.4	$33.6
Direct labour cost per unit	42	35
Variable overhead per unit	8.4	26.6
variable selling cost (10% of sales)	$16.8	$16.8
total variable cost per unit (b)	$117.6	$112
contribution per unit (c = a - b)	$50.4	$56
total contribution (d = 250000 units x c )	$12600000	$14000000
fixed cost :-
Fixed manufacturing costs	$2040000	$3552000
Fixed selling and administrative costs are $3,340,000	$3340000	$3340000
total fixed costs (e)	$5380000	$6892000
net income (f = d - e)	$7220000	$7108000

from the above calculation it is clear that net income of option 1 is more than net income of option 2.

3) Calculation of the break-even point in unit sales under each upgrade option :

particular	option 1	option 2
selling price per unit (a)	$168	$168
variale cost per unit :-
Direct material cost per unit	$50.4	$33.6
Direct labour cost per unit	42	35
Variable overhead per unit	8.4	26.6
variable selling cost (10% of sales)	$16.8	$16.8
total variable cost per unit (b)	$117.6	$112
contribution per unit (c = a - b)	$50.4	$56
fixed cost :-
Fixed manufacturing costs	$2040000	$3552000
Fixed selling and administrative costs are $3,340,000	$3340000	$3340000
total fixed costs	$5380000	$6892000

break-even point in unit sales under each upgrade option = fixed costs/contribution per unit

partticular	option 1	option 2
break-even point in unit sales under each upgrade option	$5380000/$50.4 = 106746 units	$6892000/$56 = 123071 units

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