# Two-Period Questions in Marginal Costing
## Concept
When the question gives data for two periods (or two situations) and asks you to back-calculate the P/V Ratio, contribution per unit, or variable cost per unit, use the change (Δ) method.
The logic: Fixed cost stays constant between two periods, so any change in profit must be due to change in contribution. By relating the change in profit to the change in sales / units / cost, we isolate the variable element.
## The Three Scenarios
| Given Data | What to Find | Formula |
|---|---|---|
| 2 Sales + 2 Profit figures | P/V Ratio | $\dfrac{\Delta \text{Profit}}{\Delta \text{Sales}}$ |
| 2 Units + 2 Profit figures | Contribution per unit | $\dfrac{\Delta \text{Profit}}{\Delta \text{Units}}$ |
| 2 Costs + 2 Profit figures | Variable cost per unit | $\dfrac{\Delta \text{Profit}}{\Delta \text{Cost}}$ (with appropriate interpretation) |
## Why This Works
Profit = Contribution − Fixed Cost. Since Fixed Cost is the same in both periods, it cancels when we take the difference:
$$\Delta \text{Profit} = \Delta \text{Contribution} = \Delta \text{Sales} \times \text{P/V Ratio}$$
Hence rearranging gives the P/V Ratio (or contribution per unit, depending on what the denominator is).
## After Finding the Ratio
Once P/V Ratio or contribution/unit is known, use any single period's data to back out Fixed Cost:
$$\text{Fixed Cost} = \text{Contribution} - \text{Profit}$$