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