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. Required: 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:

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= $\frac{Contribution margin}{Operating Income}$

= 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= $\frac{190*65}{6175}$

=2.5

Under Option 2,

Contribution Margin per unit= $950-$760-$760-0.10*$950=$95,

Operating income= $95x65-$0= $6175.

$\frac{95*65}{6175}$

=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.

Answer 2

Cover Rugs can determine the requirements as follows:

1. Break-even point in units for:

a) Option 1 = 39 carpets ($7,410/$190)

b) Option 2 = Total cost = Revenue

= 0 units

2. The operating income under Option 1 = $190Q - $7,410 (Contribution - Fixed Costs)

The operating income under Option 2 = $95Q

For Cover Rugs to earn the same operating income under the two options,

$190Q - $7,410 = $95Q

$95Q = $7,410

Sales (Q) = 78 carpets

or in dollars:

The level of revenue = $74,100 $(78 x $950)

a) If the sales level ranges above 77 carpets, Cover Rugs would prefer Option 1.

b) If sales level ranges between 0 to 77, Cover Rugs would prefer Option 2.  Any sales level above 77 makes Option 1 preferable.

3. The degree of operating leverage = Contribution Margin/Operating Income

Option 1:

Sales revenue = $61,750 ($950 x 65)

Variable costs = $49,400 ($760 x 65)

Contribution margin = $12,350 ($61,750 - $49,400)

Operating income = $4,940 ($12,350 - $7,410)

Degree of operating leverage at sales of 65 units = 2.5 ($12,350/$4,940)

Option 2:

Sales revenue = $61,750 ($950 x 65)

Variable costs = $55,575 ($855 x 65)

Contribution margin = $6,175 ($61,750 - $55,575)

Operating income = $6,175 ($6,175 - $0)

Degree of operating leverage at sales of 65 units Option 2 = 1 ($6,175/$6,175).

4. The answer to requirement 3 shows that there is no change in operating income as a result of the change in sales level under option 2 unlike under option 1,where the operating income changes 2.5 times.

Data and Calculations:

Selling price per carpet = $950

Variable cost per carpet = $760

Contribution margin per unit = $190 ($950 - $760)

Fixed Rental Cost of Option 1 = $7,410

Variable Rental Cost of Option 2 = 10% of total revenues or $95

Total variable cost with Option 2  $855

Contribution margin per unit = $95

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