Question

At an output level of 17,500 units, you have calculated that the degree of operating leverage is 3.40. The operating cash flow is $59,000 in this case. Ignore the effect of taxes. What will be the new degree of operating leverage for 18,500 units and 16,500 units?

Answer 1

new degree of operating leverage = 3.009

new degree of operating leverage = 3.97

Step-by-step explanation:

given data

output level X = 17,500 units

operating leverage = 3.40

operating cash flow = $59,000

solution

we will apply here operating leverage equation that is

operating leverage =
`((P-V)*X)/(((P-V)*X-FC))` ..........1

here we X is output level

and we consider here

(P-V)*X =T ....................2

so equation 1 will as here as

3.4 =
`(T)/(T-FC)`

T = 3.4 T - 3.4 FC

so

2.4 T = 3.4 FC

`(FC)/(T) =(2.4)/(3.4)`

so now put T here from equation 2

`(FC)/((P-V)*X) =(2.4)/(3.4)`

`(FC)/((P-V)) =(2.4*17500)/(3.4)`

`(FC)/((P-V)) =12352.9411`

so

now for operating leverage for X = 18,500 units

new degree of operating leverage

new degree of operating leverage =
`(X)/(X -(FC)/((P-V)))`

put here

new degree of operating leverage =
`(18500)/(18500 -12352.9411)`

new degree of operating leverage = 3.009

and

now for operating leverage for X = 16,500 units

new degree of operating leverage

new degree of operating leverage =
`(X)/(X -(FC)/((P-V)))`

put here

new degree of operating leverage =
`(16500)/(16500 -12352.9411)`

new degree of operating leverage = 3.97