CH13-EX02. Volume Profit Calculation Example — Operating Profit and Margin of Safety at 150 Units a Month

Related Chapter: CH13. BEP — Break-Even Point
Related Tool: Volume Profit (core/engine/modes/volume_profit.py, run_volume_profit)
Source: core/schemas/examples/valid/08_volume_profit.json (input) and core/schemas/examples/analysis_results/08_volume_profit.analysis_result.json (result); specified in docs/features/volume_profit/SPEC.md. Hypothetical data for teaching (client_id: sample_co_eta) — not actual company data.

Inputs

Item	Value
Selling price (`actual_price`)	20,000 (VAT-exclusive, `price_includes_vat: false`)
product_service_direct_cost (`material_cost`, `per_unit`)	8,000
variable_selling_delivery (`shipping`, `per_order`)	2,000
fixed_operating_cost (`fixed_ops`, component-scoped, `applies_to_component: "main"`)	1,000,000
fixed_operating_cost.basis	per_month
`sales_plan.planned_quantity`	150
`sales_plan.period_basis`	per_month

It matters that the fixed operating cost is entered at component scope (main). If shared fixed cost were entered as blended_only, FC would be UNKNOWN and this calculation would not hold (see CH13 §4).

Exercise

Using the inputs above, work out the following yourself.

What are the contribution margin per unit (CMu) and the break-even sales quantity (Q_BEP)?
For the plan of selling 150 units a month, what are total net sales, operating profit, and operating profit rate?
What is the margin of safety (quantity and rate), and how should it be read?
Why do the metrics carry the ESTIMATED status?

Show answer and walkthrough

What This Example Illustrates

If BEP answers “how many units must be sold to stop losing money,” this example shows how Volume Profit answers the next question: “if we sell the quantity we planned, how much is left, and how far above break-even is that plan?” The input is the same structure as CH13-EX01 (the normal BEP path) plus a monthly sales plan, sales_plan — the simplest complete-input case.

Calculation

N     = 20,000                          (VAT-exclusive selling price)
CMu   = N − direct_cost − variable_cost
      = 20,000 − 8,000 − 2,000
      = 10,000
FC    = 1,000,000
Q_BEP = FC / CMu = 1,000,000 / 10,000 = 100

total_net_sales_ex_vat    = N × Q        = 20,000 × 150           = 3,000,000
total_contribution_margin = CMu × Q      = 10,000 × 150           = 1,500,000
operating_profit          = CMu × Q − FC = 1,500,000 − 1,000,000  =   500,000
operating_profit_rate     = 500,000 / 3,000,000                   ≈ 16.67%
margin_of_safety_quantity = Q − Q_BEP    = 150 − 100              =        50
margin_of_safety_rate     = 50 / 150                              ≈ 33.33%

Results

total_net_sales_ex_vat = 3,000,000, status: OK
total_contribution_margin = 1,500,000, status: ESTIMATED
operating_profit = 500,000, status: ESTIMATED
operating_profit_rate ≈ 0.1667, status: ESTIMATED
break_even_quantity_exact = 100, status: ESTIMATED
margin_of_safety_quantity = 50, status: ESTIMATED
margin_of_safety_rate ≈ 0.3333, status: ESTIMATED
Warning: ASSUMES_ONE_UNIT_PER_ORDER
module status: OK

For the same input, the BEP module reports break_even_quantity_exact = 100 with status OK — the same value.

Interpretation

At the current price (N = 20,000) and cost structure, the contribution margin per unit is 10,000, and recovering the monthly fixed operating cost of 1,000,000 requires selling 100 units a month (BEP). If the plan is to sell 150 a month, monthly operating profit is 500,000, and the plan sits 50 units (about 33% of the plan) above break-even. That margin of safety can be read as: “even if sales fall about 33% short of the plan — down to 100 units — fixed costs are still recovered.”

Why the status is ESTIMATED. The shipping cost is per_order (2,000 per order). Because Volume Profit calculates CMu × Q, it assumes one unit is sold per order for per_order costs. If customers buy two or more units in one order, shipping is overstated and the true operating profit may be higher than this figure. This does not mean the value is wrong; it marks that the value depends on this assumption. The same Q_BEP is reported as OK by BEP and ESTIMATED by Volume Profit because Volume Profit is the module that makes this assumption visible.

What this example does not show. planned_quantity is simply an input supplied from outside; whether that volume is actually achievable must be verified separately against the basis for determining Qty by transaction type (CH13 §7, KM062). The rules for a plan that falls short of break-even (a negative margin of safety with a BELOW_BREAK_EVEN warning) are described in CH13 §6, but the source material for this example contains no input or result for that case, so no figures are given for it.