Answer:
the new degree of operating leverage for output levels of 16,400 units and 14,400 units will be -0.0858 and - 0.0745 respectively.
Explanation:
From the given information:
the degree of operating the leverage at 415,400 units = [tex]\mathtt{\dfrac{contribution \ \ margin}{operating \ \ income}}[/tex]
where contribution margin = 2 × 58000 =116000
If we assume that the sales price should be p and the variable cost be q per unit .
Then, 415,400p - 415,400q = 116000
p - q = [tex]\mathtt{\dfrac{116000}{415400}}[/tex]
p - q = 0.279 at 415400 unit
Contribution margin = 415400 × 0.279
Contribution margin = 115896.6
The operating income = contribution margin - fixed expense
58000 = 115896.6 - fixed expense
fixed expense = 115896.6 - 58000
fixed expense = 57896.6
However, when the output level is 16400 unit,
the contribution margin = 16400(p-q)
the contribution margin = 16400(0.279)
the contribution margin = 4575.6
The operating leverage = [tex]\mathtt{\dfrac{contribution \ \ margin}{contribution \ \ margin - fixed \ \ costs}}[/tex]
The operating leverage = [tex]\mathtt{\dfrac{4575.6}{4575.6 - 57896.6}}[/tex]
The operating leverage = [tex]\mathtt{\dfrac{4575.6}{-53321}}[/tex]
The operating leverage = -0.0858
when the output level is 14400 unit,
the contribution margin = 14400(p-q)
the contribution margin = 14400(0.279)
the contribution margin = 4017.6
The operating leverage = [tex]\mathtt{\dfrac{contribution \ \ margin}{contribution \ \ margin - fixed \ \ costs}}[/tex]
The operating leverage = [tex]\mathtt{\dfrac{4017.6}{4017.6 - 57896.6}}[/tex]
The operating leverage = [tex]\mathtt{\dfrac{4017.6}{-53879}}[/tex]
The operating leverage = - 0.0745
