Question

3-30 Operating leverage. Cover Rugs is holding a 2-week carpet sale at Josh’s Club, a local warehouse store. Cover Rugs plans to sell carpets for $950 each. The company will purchase the carpets from a local distributor for $760 each, with the privilege of returning any unsold units for a full refund. Josh’s Club has offered Cover Rugs two payment alternatives for the use of space. ? ? Option 1: A fixed payment of $7,410 for the sale period Option 2: 10% of total revenues earned during the sale period

Assume Cover Rugs will incur no other costs. 1. Calculate the breakeven point in units for (a) Option 1 and (b) Option 2. 2. At what level of revenues will Cover Rugs earn the same operating income under either option? a. For what range of unit sales will Cover Rugs prefer Option 1? b. For what range of unit sales will Cover Rugs prefer Option 2?

3. Calculate the degree of operating leverage at sales of 65 units for the two rental options. 4. Briefly explain and interpret your answer to requirement 3.

Answer 1

Answer 1.
BEP (In Units) = Fixed Costs / Contribution per Unit
Option 1.
Contribution per Unit = $950 (Sales) - $760 (Variable Costs)
Contribution per Unit = $190
BEP (In Units) = $7,410 / $190
BEP (In Units) = 39 carpets
Option 2.
Contribution per Unit = $950 (Sales) - $760 (Variable Costs) - ($950 X 10%) (Comm.)
Contribution per Unit = $95
BEP (In Units) = $0 / $95
BEP (In Units) = 0 carpets
Answer 2-a.
Let the number of Carpets sold = q
Therefore,
$950 q - $760q - $7,410 = $950 q - $760q - $95q
$190q - $7,410 = $95q
q = $7,410 / ($190 - $95)
q = 78 carpets
Operating incone is equal in both options, when no. of carpets sold is 78.
Answer 2-b.
			Proof
			Option 1	Option 2
Range		Preferred Option	Units	Units
From	To		1 or 200	1 or 200
0	78	Option 2	(7,220.00)	95.00	1 Unit falls in range of 0-78 Units
78	78+	Option 1	30,590.00	19,000.00	200 Units falls in range of more than 78 units
Answer 3.
Operating Leverage = Contribution Income / Operating Income
			Option 1	Option 2
			67 Units	67 Units
Contribution Margin			12,730.00	6,365.00
Operating Income			5,320.00	6,365.00
Operating Leverage			2.39	1.00
Answer 4.
DOL helps managers to calculate the effect of fluctuations on sales on operating income.
or say,
% Change in Operating Income = % Change in Sales X DOL
For example,
Option No.	% Change in Sales	Operating Leverage	% Change in OI
1	10%	2.39	23.93%
2	10%	1.00	10.00%