This topic covers the relationship between costs, volume of activity, and profit. Students will learn how to calculate break-even points, analyze profit margins, and make decisions based on cost-volume-profit relationships.
Cost‑Volume‑Profit (CVP) Analysis – Quick Reference Notes
| Assumption | Meaning |
|---|---|
| Linear cost behavior | Total cost = Fixed Cost + (Variable Cost per unit × Quantity). |
| Constant selling price | Unit selling price does not vary with volume. |
| Single product (or constant product mix) | When multiple products are sold, the sales‑price‑weighted average contribution margin stays constant. |
| All costs are either fixed or variable | No mixed or step costs are considered in the basic model. |
| Production = sales | No inventory buildup or depletion during the period. |
| Short‑run horizon | Fixed costs are truly fixed for the period under analysis. |
| Term | Definition |
|---|---|
| Fixed Costs (FC) | Costs that do not change with output (e.g., rent, salaries). |
| Variable Costs (VC) | Costs that vary directly with output (e.g., direct materials). |
| Total Cost (TC) | FC + VC. |
| Selling Price per Unit (P) | Revenue earned for each unit sold. |
| Variable Cost per Unit (V) | VC divided by quantity. |
| Contribution Margin (CM) | Per‑unit: ( CM_u = P – V ) Total: ( CM_T = (P – V) × Q ). |
| Contribution Margin Ratio (CMR) | ( CMR = \frac{CM_u}{P} = \frac{P – V}{P} ). |
| Break‑Even Point (BEP) | Output level where profit = 0. |
| Target Profit Analysis | Determines required sales to achieve a specified profit. |
[ \text{Profit} = \text{Total Revenue} – \text{Total Cost} ] [ \Pi = (P \times Q) – [FC + (V \times Q)] ]
[ \Pi = (P – V) \times Q – FC ] [ \Pi = CM_u \times Q – FC ]
[ Q_{BE} = \frac{FC}{P – V} = \frac{FC}{CM_u} ]
[ \text{Sales}_{BE} = \frac{FC}{CMR} ]
[ Q_{TP} = \frac{FC + \text{Target Profit}}{CM_u} ]
[ \text{Sales}_{TP} = \frac{FC + \text{Target Profit}}{CMR} ]