Question

At an output level of 415,400 units, you have calculated that the degree of operating leverage is 2.00. The operating cash flow is $58,000 in this case. Ignore the essect of taxes. What will be the new degree of operating leverage for output levels of 16,400 units and 14,400 units

Answer 1

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.

Step-by-step explanation:

From the given information:

the degree of operating the leverage at 415,400 units =
`\mathtt{(contribution \ \ margin)/(operating \ \ income)}`

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 =
`\mathtt{(116000)/(415400)}`

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 =
`\mathtt{(contribution \ \ margin)/(contribution \ \ margin - fixed \ \ costs)}`

The operating leverage =
`\mathtt{(4575.6)/(4575.6 - 57896.6)}`

The operating leverage =
`\mathtt{(4575.6)/(-53321)}`

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 =
`\mathtt{(contribution \ \ margin)/(contribution \ \ margin - fixed \ \ costs)}`

The operating leverage =
`\mathtt{(4017.6)/(4017.6 - 57896.6)}`

The operating leverage =
`\mathtt{(4017.6)/(-53879)}`

The operating leverage = - 0.0745