Question

Assume only the specified parameters change in a sensitivity analysis. If the contribution margin increases by $10 per unit then operating profits will: Select one: a. also increase by $10 per unit. b. increase by less than $10 per unit. c. decrease by $10 per unit. d. be indeterminable.

Answer 1

• Contribution per unit equals to Selling Price per unit (-) Variable cost per unit.
• Operating profits are found by deriving Total Contribution Margin (per unit x no of units) and then deducting amount of Fixed Cost from it.
• Now, as the question states, only specified parameters is changing and contribution increasing by $10 per unit.
• As a result of this $10 per unit increase, other things remaining same, the operating profit will also increase by $10 per unit.
• Hence, correct answer is OPTION-A : Also increases by $10 per unit.
• Following are the verifications that when contribution per unit is increased by $10, operating profit will also increase by $10 per unit (other parameters remaining same)

	Assumed cases	1	2	3	4	5
A	Units	10000	15000	5000	20000	25000
B	Original contribution per unit	10	15	20	18	16
C=AxB	Total original contribution margin	100000	225000	100000	360000	400000
D	Assumed fixed cost	5000	5000	5000	5000	5000
E=C-D	Operating profit	95000	220000	95000	355000	395000
F=E/A	Operating profit per unit $	9.5	14.66667	19	17.75	15.8
G=B+$10	New contribution margin (increased y $10 per unit)	20	25	30	28	26
H=GxA	Total NEW contribution margin	200000	375000	150000	560000	650000
I=D	Assumed Fixed Cost	5000	5000	5000	5000	5000
J=H-I	New operating profit	195000	370000	145000	555000	645000
K=A	Units	10000	15000	5000	20000	25000
L=J/K	New operating profit per unit $	19.5	24.66667	29	27.75	25.8
M=F	Old Operating profit	9.5	14.66667	19	17.75	15.8
N=L-M	Increase in operating per unit $	10	10	10	10	10