# Explanation of operating leverage

when operating leverage ratio is 2, when contribution margin increase 50%, according to DOL formula, operating income will increase 50%X2=100%, but i cant found any formula,explanation to interpret the relationship 50%X2=100% excetp for the formula that percentage change in operating income on percentage change in units sold.

or who can tell why DOL=percentage change in operating income on percentage change in units sold.

what’s else body thinking ?

If you like to see it from a mathematical perspective:

DOL = \frac { \% Change \ In \ Operating \ Income}{\%Change \ In \ Units \ sold} = \frac {(SP - VC) \times Q_0}{(SP - VC) \times Q_0 - FC}

Contribution \ margin_0 = (SP - VC)

Operating \ income_0 = (SP - VC) \times Q_0 - FC

If contribution margin increases by 50%, then:

Contribution \ margin_1 = 1.5 \times (SP - VC)

Operating \ Income_1 = 1.5 \times (SP - VC) \times Q_0 - FC

So:

\% Change \ in \ Operating \ Income = \frac {Operating \ Income_1 - Operating \ Income_0}{Operating \ Income_0}

\% Change \ in \ Operating \ Income = \frac {[1.5 \times (SP - VC) \times Q_0 - FC] - [(SP - VC) \times Q_0 - FC]}{(SP - VC) \times Q_0 - FC}

\% Change \ in \ Operating \ Income = \frac {(1.5 \times Q_0 - Q_0) (SP - VC)}{(SP - VC) \times Q_0 - FC}

\% Change \ in \ Operating \ Income = \frac {(0.5Q_0) (SP - VC)}{(SP - VC) \times Q_0 - FC}

\% Change \ in \ Operating \ Income = 0.5 \times \frac { (SP - VC) Q_0}{(SP - VC) \times Q_0 - FC}

\% Change \ in \ Operating \ Income = 0.5 \times DOL = 0.5 \times 2 = 100\%

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Thank you so so much!! Its very clear to understand.

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