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Answer:
The step by step answer to your problem is given below:
Explanation:
1A) Break even point for option 1:
Sales- Variable cost= Fixed cost
Q* $950-Q*$760= $7410
Q*$190= $7410
Q=$7410/$190
Q= 39 carpets
1B) Breakeven point for Option 2
Sales- variable cost-rent cost= 0
Q*$950- $760*Q- (Q*950*10%)= 0
95Q= 0
Q= 0
2. At what level of revenues will Cover Rugs earn the same operating income under either option?
Operating income under Option 1 = $190Q - $7140
Operating income under Option 2 = $95Q
We have to find Q such that $190Q - $7140 = $95Q
Q=$7410/$95= 78 Carpets
Revenue= $950 x 78 = $74,100
For Q = 78 Carpets, operating income under both option 1 and 2 will be = $7410
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?
For Q > 78, say 79 carpets:
Option 1 gives operating income= (190*79) - 7410= $7600
Option 2 gives operating income= 95*79= $7505
So color rugs will prefer Option 1.
For Q < 78, say 77 carpets:
Option 1 gives operating income= (190*77) - 7410= $7220
Option 2 gives operating income= 95*77= $7315
So color rugs will prefer Option 2.
3. Calculate the degree of operating leverage at sales of 65 units for the two rental options.
Operating Leverage=
= Contribution margin per unit x Numbers of Carpet Sold= Contribution Margin
Under Option 1,
Contribution Margin per unit= $950-$760=$190,
Operating income= $190*65-$7410= $4940.
Degree of Operating Leverage=
=2.5
Under Option 2,
Contribution Margin per unit= $950-$760-$760-0.10*$950=$95,
Operating income= $95x65-$0= $6175.
=1.0
4. Briefly explain and interpret your answer to requirement 3.
The degree of operating leverage helps managers calculate and anticipate the effects of fluctuations in sales on operating income. The calculation in requirement 3 show that when sales are 65 units, a % change in sales and contribution margin will result in 2.5 times that % change in operating income for option 1. But the same % change in Option 2 because there are no fix costs attached in option 2.