If DOL is defined as DOL=Percentage change in OCF/Percentage Change in Q please derive equation:
DOL=1+FC/OCF?
I need this by tomorrow...please help.
To derive the equation DOL=1+FC/OCF, we can start with the definition of DOL:
DOL = Percentage change in OCF / Percentage Change in Q
Next, let's express the percentage change in OCF in terms of FC and OCF:
Percentage change in OCF = (OCF - OCF0) / OCF0
where OCF0 is the initial operating cash flow and OCF is the final operating cash flow. Substitute this into the DOL equation:
DOL = ((OCF - OCF0) / OCF0) / Percentage Change in Q
Next, let's express the percentage change in Q in terms of Q and Q0:
Percentage Change in Q = (Q - Q0) / Q0
where Q0 is the initial quantity and Q is the final quantity. Substitute this into the DOL equation:
DOL = ((OCF - OCF0) / OCF0) / ((Q - Q0) / Q0)
Multiplying both the numerator and denominator by Q0, we get:
DOL = ((OCF - OCF0) / OCF0) * (Q0 / (Q - Q0))
Using the mathematical properties of fractions, we can write this as:
DOL = (OCF - OCF0) * (Q0 / (OCF0 * (Q - Q0)))
Now, let's rearrange the equation to match the desired form DOL = 1 + FC/OCF. We know that FC (Fixed Costs) is equal to (OCF0 - OCF), so substitute that in:
DOL = (OCF - OCF0) * (Q0 / (OCF0 * (Q - Q0)))
= (OCF - (OCF0 - FC)) * (Q0 / (OCF0 * (Q - Q0)))
Distribute the Q0 term within the parentheses:
DOL = (OCF - OCF0 + FC) * (Q0 / (OCF0 * (Q - Q0)))
Now, divide both the numerator and denominator by OCF0:
DOL = (OCF/OCF0 - 1 + FC/OCF0) * (Q0 / (Q - Q0))
Simplify further by multiplying Q0 to the numerator:
DOL = Q0 * (OCF/OCF0 - 1 + FC/OCF0) / (Q - Q0)
Finally, multiply both the numerator and denominator by OCF0 to obtain the desired form:
DOL = (Q0 * (OCF - OCF0 + FC)) / (OCF0 * (Q - Q0))
Therefore, the derived equation is DOL = (Q0 * (OCF - OCF0 + FC)) / (OCF0 * (Q - Q0)).
Note: Please double-check the steps and formulas to verify the derivation.