Comprehensive Management Accounting: CVP Analysis, Differential Decision-Making, Traditional Costing, and Activity-Based Costing

Cost Behavior, Terminology, and Classification

• Cost Behavior Fundamentals:

  • Variable Costs ($\text{VC}$): Costs that vary in direct proportion to changes in the activity level ($Q$). The total variable cost is expressed as:     $\text{VC} = \text{VCu} \times Q$

  • Unit Variable Cost ($\text{VCu}$): Remains constant regardless of changes in the production or sales volume.

  • Fixed Costs ($\text{FC}$): Costs that remain constant in total over a wide range of activity levels within the relevant range.

  • Unit Fixed Cost ($\text{FCu}$): Decreases progressively as the activity level increases, described by the relationship:       $\text{FCu} = \frac{\text{CF}}{Q}$

  • Unit Total Cost Impact: Because unit fixed cost decreases as production volume increases, the total unit cost of any cost object steadily declines as output expands.

• Direct Versus Indirect Costs:

  • Traceability Criterion: A cost is classified based on whether it is practical and economically feasible to trace directly to a specific cost object (such as a product, service, department, or order).

  • Direct Costs: Can be easily and conveniently traced to the specified cost object:

  • Direct Materials ($\text{DM}$ / Matières Premières, $\text{MP}$): Raw materials that become an integral part of the finished product and can be directly linked to individual units produced.

  • Direct Labor ($\text{DL}$ / Main-d'œuvre Directe, $\text{MOD}$): Labor compensation paid to workers who touch or assemble the product directly during manufacturing.

  • Indirect Costs: Cannot be easily or conveniently traced to an individual cost object. They require allocation mechanisms:

  • Manufacturing Overhead ($\text{MOH}$ / Frais Généraux de Fabrication, $\text{FGF}$ / Frais Indirects de Fabrication, $\text{FIF}$): All manufacturing costs except direct materials and direct labor.

    • Indirect Materials: Auxiliary supplies supporting operations (e.g., machine lubricants, cleaning rags, maintenance glue, finishing paper).

    • Indirect Labor: Wages of personnel supporting manufacturing without directly assembling products (e.g., factory supervisors, quality control inspectors, material handlers, maintenance mechanics).

    • Factory Operating Costs: Factory equipment depreciation, factory building rent, property taxes, factory insurance, and plant heating, water, and electricity.

  • Non-Manufacturing Costs (Period Costs): Selling and administrative expenses ($\text{S\&A}$ / Frais de vente et d'administration, $\text{FVA}$).

• Inventoriable (Product) Costs Versus Period Costs:

  • Inventoriable / Product Costs (Coûts incorporables):

  • All costs involved in acquiring or manufacturing products.

  • Composed exclusively of manufacturing costs: $\text{DM} + \text{DL} + \text{MOH}$.

  • Treated as assets in balance sheet inventory accounts ($\text{Raw Materials}$, $\text{Work in Process}$, $\text{Finished Goods}$) until the goods are sold.

  • Flow into the income statement as Cost of Goods Sold ($\text{COGS}$ / Coût des marchandises vendues, $\text{CMV}$) in the exact period when the related revenue is recognized.

  • Period Costs (Coûts non incorporables):

  • Non-manufacturing costs that are expensed on the income statement in the period in which they are incurred.

  • Comprise selling costs (e.g., sales commissions, advertising, shipping, sales representative vehicle depreciation) and administrative costs (e.g., executive salaries, office rent, corporate accounting expenses).

• Manufacturing Cost Versus Full Cost:

  • Manufacturing Cost (Coût de revient de fabrication): Consists solely of production-related resources:     $\text{Manufacturing Cost} = \text{DM} + \text{DL} + \text{MOH}$

  • Full Cost (Coût de revient complet): Comprises all organizational costs attributable to an object over its entire value chain:     $\text{Full Cost} = \text{Manufacturing Cost} + \text{Selling Costs} + \text{Administrative Costs}$

• Worked Example — Cost Classification and Full Cost Calculation (Patin Manufacturing):

  • Operational Data: Production and sales of $3,500$ pairs of skates.

  • Direct materials: 99,750\,\

  • Direct labor: 96,600\,\

  • Production supervisor salary: 5,000\,\ (Factory overhead)

  • Building rent: 2,000\,\ (Factory occupies $80\%$ of surface area, administration occupies $20\%$)

    • Factory portion ($\text{MOH}$): 2,000\,\$ \times 80\% = 1,600\,\

    • Administrative portion ($\text{Admin}$): 2,000\,\$ \times 20\% = 400\,\

  • Finished goods skate storage cost: 6,000\,\ (Selling expense)

  • Factory insurance: 400\,\ (Factory overhead)

  • Administrative salaries: 12,000\,\ (Administrative expense)

  • Total organizational expenses incurred: 221,750\,\

  • Classification and Calculations:

  • Total Manufacturing Costs:       \text{Total Manufacturing Costs} = 99,750 + 96,600 + 5,000 + 1,600 + 400 = 203,350\,\

  • Unit Manufacturing Cost:       \text{Unit Manufacturing Cost} = \frac{203,350}{3,500} = 58.10\,\

  • Total Full Costs:       \text{Total Full Costs} = 203,350 + 6,000 + 400 + 12,000 = 221,750\,\

  • Unit Full Cost:       \text{Unit Full Cost} = \frac{221,750}{3,500} = 63.3571\,\

Cost-Volume-Profit (CVP) Analysis for Single-Product Organizations

• Core Dimensions of CVP Analysis:

  • Evaluates how operating profits react to interactions among five fundamental parameters:

  • Selling price per unit ($P$

  • Sales volume / activity level ($Q$

  • Unit variable cost ($\text{VCu}$

  • Total fixed costs ($\text{FC}$

  • Product mix / sales composition

• Contribution Margin Metrics:

  • Unit Contribution Margin ($\text{MCVu}$, Marge sur coûts variables unitaire):     $\text{MCVu} = P - \text{VCu}$

  • Represents the portion of each sales dollar remaining after variable costs to contribute toward covering fixed costs and generating profit.

  • Total Contribution Margin ($\text{MCV}$):     $\text{MCV} = \text{MCVu} \times Q = \text{Sales} - \text{VC}$

  • Contribution Margin Ratio ($\text{CMR}$, Ratio de MCV / \%MCV):     $\text{CMR} = \frac{\text{MCV}}{\text{Sales}} = \frac{\text{MCVu}}{P}$

  • Expresses the contribution margin as a percentage of revenue, indicating the exact increase in operating profit generated by each additional dollar of sales.

• Contribution Margin Income Statement Versus Traditional Gross Margin:

  • Traditional Income Statement (Absorption Format):     $\text{Sales} - \text{COGS} = \text{Gross Margin (Marge brute)}$     $\text{Gross Margin} - \text{S\&A Expenses} = \text{Operating Income}$

  • Blends fixed and variable costs inside $\text{COGS}$ ($\text{DM} + \text{DL} + \text{Variable MOH} + \text{Fixed MOH}$).

  • Contribution Margin Statement (Variable Costing Format):     $\text{Sales} - \text{Total Variable Costs} = \text{Contribution Margin}$     $\text{Contribution Margin} - \text{Total Fixed Costs} = \text{Operating Income}$

  • Groups costs strictly by behavior, separating variable production and operating expenses from fixed expenses.

• CVP Graphical Representation:

• Key CVP Mathematical Equations:

  • Basic Profit Equation:     $\text{Profit} = (P - \text{VCu}) \times Q - \text{FC} = \text{MCVu} \times Q - \text{FC}$

  • Breakeven Point in Units ($Q^*$):     $Q^* = \frac{\text{FC}}{\text{MCVu}}$

  • Breakeven Point in Sales Dollars ($\text{Sales}^*$):     $\text{Sales}^* = \frac{\text{FC}}{\text{CMR}} = Q^* \times P$

  • Target Profit Sales Volume ($Q_{\text{target}}$):     $Q_{\text{target}} = \frac{\text{FC} + \text{Target Profit}}{\text{MCVu}}$

  • Margin of Safety ($\text{MS}$):

  • In Units:       $\text{MS}_{\text{units}} = Q_{\text{actual}} - Q^*$

  • In Percentage:       $\text{MS}\% = \frac{\text{MS}_{\text{units}}}{Q_{\text{actual}}} = \frac{\text{Actual Sales} - \text{Sales}^*}{\text{Actual Sales}}$

  • Direct Profit Relationship:       $\text{Profit} = Q_{\text{actual}} \times \text{MS}\% \times \text{MCVu}$

  • Potential Profit ($\text{BP}$, Bénéfice potentiel): Operating profit at theoretical or practical plant capacity:     $\text{BP} = \text{Capacity}_{\text{max}} \times \text{MCVu} - \text{FC} = (\text{Capacity}_{\text{max}} - Q^*) \times \text{MCVu}$

  • Indifference Point (Seuil d'indifférence): Production volume where two operating structures or technological alternatives deliver equal profit:     $\text{MCVu}_1 \times Q - \text{FC}_1 = \text{MCVu}_2 \times Q - \text{FC}_2$     $Q_{\text{indifference}} = \frac{\text{FC}_1 - \text{FC}_2}{\text{MCVu}_1 - \text{MCVu}_2}$

• Comprehensive Worked Case Study 1 — Vélos Inc.:

  • Baseline Operating Parameters:

  • Selling price ($P$): 500\,\

  • Unit variable cost ($\text{VCu}$): 300\,\

  • Unit contribution margin ($\text{MCVu}$): 500 - 300 = 200\,\

  • Contribution margin ratio ($\text{CMR}$): $\frac{200}{500} = 40\%$

  • Total monthly fixed costs ($\text{FC}$): 80,000\,\ (Store depreciation 50,000\,\, advertising 10,000\,\, other fixed overhead 20,000\,\)

  • Baseline sales volume ($Q$): $500\text{ bicycles}$

  • Baseline income statement:

    • Sales ($500 \times 500$): 250,000\,\

    • Less variable costs ($500 \times 300$): 150,000\,\

    • Contribution margin: 100,000\,\

    • Less fixed costs: 80,000\,\

    • Net operating income: 20,000\,\

  • Baseline breakeven point:       $Q^* = \frac{80,000}{200} = 400\text{ bicycles}$       \text{Sales}^* = \frac{80,000}{0.40} = 200,000\,\

  • Baseline margin of safety:       $\text{MS}_{\text{units}} = 500 - 400 = 100\text{ bicycles}$       $\text{MS}\% = \frac{100}{500} = 20\%$       \text{Profit} = 500 \times 20\% \times 200 = 20,000\,\

  • Target profit calculation (Target = 100,000\,\):       $Q = \frac{80,000 + 100,000}{200} = \frac{180,000}{200} = 900\text{ bicycles}$

  • Impact of reduced sales to $350\text{ bicycles}$:       \text{Profit} = (350 \times 200) - 80,000 = 70,000 - 80,000 = -10,000\,\ (Operating loss of 10,000\,\)

  • Strategic Scenario Analyses for Vélos Inc.:

  • Scenario 1: Change in Fixed Costs and Sales Volume:

    • Proposal: Increase monthly advertising by 10,000\,\ to increase sales from $500$ to $540\text{ units}$.

    • Differential contribution margin: (540 - 500) \times 200 = 40 \times 200 = +8,000\,\

    • Differential fixed costs: -10,000\,\

    • Net financial effect: 8,000 - 10,000 = -2,000\,\

    • Decision: Reject the proposal, as net profit drops by 2,000\,\.

  • Scenario 2: Change in Variable Costs and Sales Volume:

    • Proposal: Install higher-grade wheels increasing $\text{VCu}$ from 300\,\ to 320\,\ ($\text{MCVu}$ falls from 200\,\ to 180\,\); sales volume increases from $500$ to $550\text{ units}$.

    • Direct income calculation:         \text{Profit} = (550 \times 180) - 80,000 = 99,000 - 80,000 = 19,000\,\

    • Compared to baseline (20,000\,\): Profit declines by 1,000\,\.

    • Differential analysis:

    • Gain on incremental units: 50 \times 180 = +9,000\,\

    • Loss on baseline units: 500 \times (180 - 200) = -10,000\,\

    • Net differential effect: 9,000 - 10,000 = -1,000\,\

    • Decision: Reject the proposal.

  • Scenario 3: Change in Fixed Costs, Selling Price, and Sales Volume:

    • Proposal: Reduce selling price by 30\,\ (new price 470\,\, new \text{MCVu} = 470 - 300 = 170\,\), increase advertising by 10,000\,\ (\text{FC} = 90,000\,\), causing sales to rise to $600\text{ units}$.

    • Projected profit:         \text{Profit} = (600 \times 170) - 90,000 = 102,000 - 90,000 = 12,000\,\

    • Net change relative to baseline: 12,000 - 20,000 = -8,000\,\

    • Decision: Reject the proposal.

  • Scenario 4: Change in Variable Costs, Fixed Costs, and Sales Volume:

    • Proposal: Eliminate salesperson fixed salaries of 8,000\,\ per month ($\text{FC}$ falls to 72,000\,\) and replace with a 15\,\ commission per bike sold ($\text{VCu}$ rises to 315\,\, $\text{MCVu}$ becomes 500 - 315 = 185\,\). Sales volume projected to increase by $15\%$ (500 \times 1.15 = 575\text{ bicycles}$).\n * Projected profit:\n        \text{Profit} = (575 \times 185) - 72,000 = 106,375 - 72,000 = 34,375\,\\n * Net change relative to baseline: 34,375 - 20,000 = +14,375\,\\n * Differential calculation:\n * Contribution on incremental sales: (575 - 500) \times 185 = 75 \times 185 = +13,875\,\\n * Fixed salary savings: +8,000\,\\n * Commission cost on baseline units: 500 \times (-15) = -7,500\,\\n * Net differential impact: 13,875 + 8,000 - 7,500 = +14,375\,\\n * Decision: Accept the proposal.\n\n* **Worked Case Study 2 — Coffee Klatch Kiosk**:\n * **Operational Data**:\n * Average selling price (P$):$1.49\,\\n * Average monthly volume: 2,100\text{ cups}\n * Variable production costs per cup: 0.26\,\\n * Variable administrative and commercial costs per cup: 0.10\,\\n * Total unit variable cost (\text{VCu}$):$0.26 + 0.10 = 0.36\,\\n * Monthly fixed production costs: 1,100\,\\n * Monthly fixed administrative and commercial costs: 200\,\\n * Total monthly fixed costs (\text{FC}$):$1,100 + 200 = 1,300\,\\n * **Calculations**:\n * Unit contribution margin: \text{MCVu} = 1.49 - 0.36 = 1.13\,\\n * Contribution margin ratio:\n      \text{CMR} = \frac{1.49 - 0.36}{1.49} = \frac{1.13}{1.49} = 75.8389\% \approx 75.84\%\n * Breakeven point in units:\n      Q^* = \frac{1,300}{1.13} = 1,150.44 \rightarrow 1,151\text{ cups}\n * Breakeven point in sales dollars:\n      \text{Sales}^* = \frac{1,300}{0.758389} = 1,714.14\,\$(or using rounded unit breakeven:$1,151 \times 1.49 = 1,714.99\,\)\n * Target profit volume (\text{Target} = 2,500\,\ per month):\n      Q = \frac{1,300 + 2,500}{1.13} = \frac{3,800}{1.13} = 3,362.83 \rightarrow 3,363\text{ cups}\n * Margin of safety at current volume (2,100\text{ cups}):\n      \text{MS}{\text{units}} = 2,100 - 1,151 = 949\text{ cups}\n      \text{MS}\% = \frac{949}{2,100} = 45.19\%\n\n* **Worked Case Study 3 — Technology Indifference Point**:\n * **Parameters**:\n * **Project 1**: Low-fixed-cost process. P = 375\,\$,$\text{VCu} = 275\,\$($\text{MCVu}_1 = 375 - 275 = 100\,\$),$\text{FC}_1 = 150,000\,\.\n * **Project 2**: Automated process. P = 950\,\$,$\text{VCu} = 825\,\$($\text{MCVu}_2 = 950 - 825 = 125\,\$),$\text{FC}_2 = 525,000\,\.\n * **Equating Profit Equations**:\n    100 Q - 150,000 = 125 Q - 525,000\n    525,000 - 150,000 = 125 Q - 100 Q\n    375,000 = 25 Q\n    Q = \frac{375,000}{25} = 15,000\text{ units}\n * **Managerial Interpretation**: Below 15,000\text{ units}$, Project 1 delivers higher profit due to lower fixed cost exposure; above$15,000\text{ units}$, Project 2 is superior due to its higher unit contribution margin ($125\,\$vs.$100\,\).\n\n# Multi-Product CVP and Resource Constraint Optimization\n\n* **Multi-Product Breakeven Formulation**:\n * When an organization sells multiple distinct product lines, breakeven is governed by the sales mix ratio.\n * **Weighted Average Unit Contribution Margin (\text{MCVu}{\text{pondérée}})**:\n    \text{MCVu}{\text{pondérée}} = \sum \left(\text{MCVu}_i \times \frac{Q_i}{Q{\text{total}}}\right) = \frac{\text{Total MCV}}{Q_{\text{total}}}\n * **Total Breakeven Output in Units (Q^)**:\n    Q^ = \frac{\text{FC}}{\text{MCVu}{\text{pondérée}}}\n * **Individual Product Breakeven Sales Quantities (Q^_i)**:\n    Q^_i = Q^* \times \frac{Q_i}{Q{\text{total}}}\n * **Total Breakeven Dollar Sales (\text{Sales}^)**:\n    \text{Sales}^ = \frac{\text{FC}}{\text{CMR}{\text{global}}} = \frac{\text{FC}}{\frac{\text{Total MCV}}{\text{Total Sales}}}\n * **Individual Product Breakeven Dollar Allocations (\text{Sales}^_i)**:\n    \text{Sales}^_i = \text{Sales}^* \times \frac{\text{Sales}_i}{\text{Total Sales}}\n\n* **Underlying Assumptions of Multi-Product CVP Analysis**:\n * Unit selling prices remain constant across all volume ranges.\n * Cost behavior is accurately bifurcated into strictly linear variable and fixed components.\n * The sales mix proportions remain perfectly stable across total volume changes.\n\n* **Multi-Product Breakeven Case 1 — Enterprise AB**:\n * **Data**: Product A sold at 8\,\$($\text{VCu} = 4\,\$,$\text{MCVu} = 4\,\$, sales$50,000\text{ units}$, revenue$400,000\,\$). Product B sold at$5\,\$($\text{VCu} = 3\,\$,$\text{MCVu} = 2\,\$, sales$20,000\text{ units}$, revenue$100,000\,\$). Total volume =$70,000\text{ units}$. Total revenue =$500,000\,\$. Total$\text{VC} = 260,000\,\$. Total$\text{MCV} = 240,000\,\$. Fixed costs =$168,000\,\$. Current profit =$72,000\,\.\n * **Computations**:\n * Product mix weights: A = \frac{50,000}{70,000} = 71.43\%$, B =$\frac{20,000}{70,000} = 28.57\%\n * Weighted contribution margin per unit:\n      \text{MCVu}{\text{pondérée}} = \left(4 \times \frac{50,000}{70,000}\right) + \left(2 \times \frac{20,000}{70,000}\right) = \frac{240,000}{70,000} = 3.42857\,\\n * Total unit breakeven:\n      Q^* = \frac{168,000}{3.42857} = 49,000\text{ units}\n * Individual product breakeven units:\n      Q^A = 49,000 \times \frac{50,000}{70,000} = 35,000\text{ units}\n      Q^_B = 49,000 \times \frac{20,000}{70,000} = 14,000\text{ units}\n * Global contribution margin ratio:\n      \text{CMR}{\text{global}} = \frac{240,000}{500,000} = 48\%\n * Total dollar breakeven sales:\n      \text{Sales}^* = \frac{168,000}{0.48} = 350,000\,\\n * Dollar allocation by sales mix weighting (A = 80\%$, B =$20\% of revenue):\n      \text{Sales}^A = 350,000 \times \frac{400,000}{500,000} = 280,000\,\\n      \text{Sales}^_B = 350,000 \times \frac{100,000}{500,000} = 70,000\,\\n * Cross-verification: (35,000 \times 8) + (14,000 \times 5) = 280,000 + 70,000 = 350,000\,\.\n\n* **Multi-Product Breakeven Case 2 — Products AM and PM**:\n * **Data**: Product AM (P = 12\,\$,$\text{VCu} = 10\,\$,$\text{MCVu} = 2\,\$,$Q = 1,000\text{ units}$, Sales$12,000\,\$). Product PM ($P = 20\,\$,$\text{VCu} = 14\,\$,$\text{MCVu} = 6\,\$,$Q = 2,000\text{ units}$, Sales$40,000\,\$). Total volume =$3,000\text{ units}$. Total revenue =$52,000\,\$. Fixed costs =$10,000\,\.\n * **Computations**:\n * Total contribution margin: (1,000 \times 2) + (2,000 \times 6) = 2,000 + 12,000 = 14,000\,\\n * Weighted average unit contribution margin:\n      \text{MCVu}{\text{pondérée}} = \frac{14,000}{3,000} = 4.6667\,\\n * Total breakeven units:\n      Q^* = \frac{10,000}{4.6667} = 2,142.86 \rightarrow 2,143\text{ units}\n * Individual product breakeven:\n      Q^{\text{AM}} = 2,143 \times \frac{1,000}{3,000} = 714.33 \rightarrow 714\text{ units}\n      Q^{\text{PM}} = 2,143 \times \frac{2,000}{3,000} = 1,428.67 \rightarrow 1,429\text{ units}\n * Revenue breakeven:\n      \text{CMR} = \frac{14,000}{52,000} = 26.9231\%\n      \text{Sales}^* = \frac{10,000}{0.269231} = 37,142.86 \approx 37,143\,\\n * Individual revenue: \text{Sales}^{\text{AM}} = 714 \times 12 = 8,568\,\$;$\text{Sales}^{\text{PM}} = 1,429 \times 20 = 28,580\,\$(Sum =$37,148\,\ due to unit rounding).\n\n* **Production Optimization Under Constrained Resources**:\n * **The Bottleneck Principle**: When an operational capacity limitation (labor hours, machine hours, floor space, raw materials) constrains the ability to satisfy total demand, maximizing total profit requires prioritizing products that generate the highest contribution margin per unit of the constrained resource.\n * **Governing Decision Rule**:\n    \text{Contribution Margin per Unit of Constraint} = \frac{\text{MCVu}}{\text{Quantity of Constraint Consumed per Unit}}\n * **Three-Step Optimization Algorithm**:\n 1. Quantify total available constrained resource and prove that total unconstrained demand exceeds total resource capacity.\n 2. Calculate contribution margin per unit of constraint for every product and rank products in descending order.\n 3. Allocate available constraint capacity to fully satisfy the market demand of the highest-ranked product first, proceeding sequentially down the hierarchy until resources are exhausted.\n\n* **Worked Constraint Case 1 — Food Truck at Festival d'été de Québec (FEQ)**:\n * **Operating Parameters**: 60\text{ minutes} remaining before closure. Long line of customers.\n * Poutine: Price 20\,\$,$\text{VCu} = 6\,\$,$\text{MCVu} = 14\,\$, Prep time =$4\text{ min}$, Stock available =$50\text{ units}.\n      \text{Margin per minute} = \frac{14}{4} = 3.50\,\$/\text{min}\n * Tacos: Price 15\,\$,$\text{VCu} = 4\,\$,$\text{MCVu} = 11\,\$, Prep time =$2\text{ min}$, Stock available =$5\text{ units}.\n      \text{Margin per minute} = \frac{11}{2} = 5.50\,\$/\text{min}\n * Hot-dog: Price 10\,\$,$\text{VCu} = 2\,\$,$\text{MCVu} = 8\,\$, Prep time =$1\text{ min}$, Stock available =$40\text{ units}.\n      \text{Margin per minute} = \frac{8}{1} = 8.00\,\$/\text{min}\n * **Priority Ranking**: 1. Hot-dogs (8.00\,\$/\text{min}$), 2. Tacos ($5.50\,\$/\text{min}$), 3. Poutine ($3.50\,\$/\text{min}).\n * **Execution Plan**:\n * Step 1: Cook 40\text{ hot-dogs}$: consumes$40 \times 1 = 40\text{ min}$. Remaining time:$60 - 40 = 20\text{ min}.\n * Step 2: Cook 5\text{ tacos}$: consumes$5 \times 2 = 10\text{ min}$. Remaining time:$20 - 10 = 10\text{ min}.\n * Step 3: Cook Poutines with remaining time: \frac{10\text{ min}}{4\text{ min/poutine}} = 2.5\text{ poutines}.\n\n* **Worked Constraint Case 2 — Weight Manufacturer (Raw Material Constraint)**:\n * **Operating Parameters**: Import restrictions limit supply of specialized raw material to 5,000\,\text{kg}$at$8\,\$/\text{kg}.\n * Haltères (Dumbbells): Price 180\,\$; Direct material$24\,\$($\frac{24}{8} = 3\,\text{kg}$); Other variable costs$102\,\$; Total$\text{VCu} = 126\,\$;$\text{MCVu} = 54\,\.\n      \text{MCV per kg} = \frac{54}{3} = 18.00\,\$/\text{kg}\n * Plaques (Weight Plates): Price 270\,\$; Direct material$72\,\$($\frac{72}{8} = 9\,\text{kg}$); Other variable costs$90\,\$; Total$\text{VCu} = 162\,\$;$\text{MCVu} = 108\,\.\n      \text{MCV per kg} = \frac{108}{9} = 12.00\,\$/\text{kg}\n * Kettlebells: Price 240\,\$; Direct material$32\,\$($\frac{32}{8} = 4\,\text{kg}$); Other variable costs$148\,\$; Total$\text{VCu} = 180\,\$;$\text{MCVu} = 60\,\.\n      \text{MCV per kg} = \frac{60}{4} = 15.00\,\$/\text{kg}\n * **Priority Ranking**: 1. Haltères (18\,\$/\text{kg}$), 2. Kettlebells ($15\,\$/\text{kg}$), 3. Plaques ($12\,\$/\text{kg}).\n * **Production Decision Under Unlimited Demand**: Fabricate exclusively Haltères (\frac{5,000}{3} = 1,666\text{ units}).\n * **Production Decision Under Finite Demand** (Haltères 800$, Plaques$475$, Kettlebells$400):\n * Constraint verification: (800 \times 3) + (475 \times 9) + (400 \times 4) = 2,400 + 4,275 + 1,600 = 8,275\,\text{kg} > 5,000\,\text{kg}.\n * Step 1: Satisfy full demand of Haltères: 800 \times 3 = 2,400\,\text{kg}$. Remaining:$5,000 - 2,400 = 2,600\,\text{kg}.\n * Step 2: Satisfy full demand of Kettlebells: 400 \times 4 = 1,600\,\text{kg}$. Remaining:$2,600 - 1,600 = 1,000\,\text{kg}.\n * Step 3: Fabricate Plaques with remaining material: \frac{1,000}{9} = 111.11 \rightarrow 111\text{ units}.\n\n* **Worked Constraint Case 3 — Colonial Héritage (Shadow Price / Premium Determination)**:\n * **Data**: Chairs (P = 80\,\$,$\text{VCu} = 30\,\$,$\text{MCVu} = 50\,\$,$2\text{ linear feet}$, monthly demand$600\text{ units}$). Tables ($P = 400\,\$,$\text{VCu} = 200\,\$,$\text{MCVu} = 200\,\$,$10\text{ linear feet}$, monthly demand$100\text{ units}$). Total wood supply available =$2,000\text{ linear feet}$. Fixed costs =$25,000\,\.\n * **Constraint Test**: Total required = (600 \times 2) + (100 \times 10) = 1,200 + 1,000 = 2,200\text{ linear feet} > 2,000\text{ linear feet}. Supply is insufficient.\n * **Ranking by Constraint Unit**:\n * Chairs: \frac{50}{2} = 25\,\$/\text{linear foot}\n * Tables: \frac{200}{10} = 20\,\$/\text{linear foot}\n * Priority: 1. Chairs, 2. Tables.\n * **Optimal Production Plan**:\n * Produce all 600\text{ chairs}$: consumes$600 \times 2 = 1,200\text{ linear feet}.\n * Remaining lumber: 2,000 - 1,200 = 800\text{ linear feet}.\n * Produce Tables: \frac{800}{10} = 80\text{ tables}.\n * **Operating Profit**:\n    \text{Total MCV} = (600 \times 50) + (80 \times 200) = 30,000 + 16,000 = 46,000\,\\n    \text{Profit} = 46,000 - 25,000 = 21,000\,\\n * **Maximum Premium for Additional Constrained Resource**:\n * Any additional linear foot of wood obtained will be allocated to producing additional tables (the unsatisfied product line with unmet demand of 100 - 80 = 20\text{ tables}$, requiring$200\text{ linear feet}).\n * Each linear foot converts into 20\,\ of contribution margin.\n * The firm is willing to pay up to an additional premium of 20\,\ per linear foot above the normal price.\n\n* **Worked Constraint Case 4 — Collins Colored Pencil Boxes (Constraint Combined with Breakeven)**:\n * **Data**: Machine capacity = 600\text{ machine-hours (HM)}$per month across 2 machines ($10\text{ h/day}$,$30\text{ days/month}$, combined capacity$20\text{ HM/day}$). Fixed costs =$9,000\,\.\n * Standard Box: \text{MCVu} = 6\,\$,$0.2\text{ HM/unit}$, demand$500\text{ units}.\n * Deluxe Box: \text{MCVu} = 8\,\$,$0.4\text{ HM/unit}$, demand$1,500\text{ units}.\n * **Capacity Verification and Priority Ranking**:\n * Total hours demanded: (500 \times 0.2) + (1,500 \times 0.4) = 100 + 600 = 700\text{ HM} > 600\text{ HM}.\n * Standard Box: \frac{6}{0.2} = 30\,\$/\text{HM}\n * Deluxe Box: \frac{8}{0.4} = 20\,\$/\text{HM}\n * Priority: Standard first, Deluxe second.\n * **Constrained Production Plan**:\n * Standard: 500\text{ boxes}$(consumes$500 \times 0.2 = 100\text{ HM}$, leaving$500\text{ HM}).\n * Deluxe: \frac{500\text{ HM}}{0.4} = 1,250\text{ boxes}.\n * Total units under constraint: 500 + 1,250 = 1,750\text{ units}.\n * **Breakeven Without Constraint (Demand Mix = 500 Standard, 1,500 Deluxe = 2,000 units)**:\n * Weighted MCVu:\n      \text{MCVu}{\text{pondérée}} = \left(6 \times \frac{500}{2,000}\right) + \left(8 \times \frac{1,500}{2,000}\right) = 1.50 + 6.00 = 7.50\,\\n * Total breakeven: Q^* = \frac{9,000}{7.50} = 1,200\text{ units}.\n * Standard: 1,200 \times \frac{500}{2,000} = 300\text{ units}$; Deluxe:$1,200 \times \frac{1,500}{2,000} = 900\text{ units}.\n * **Breakeven With Constraint (Production Mix = 500 Standard, 1,250 Deluxe = 1,750 units)**:\n * Weighted MCVu:\n      \text{MCVu}{\text{pondérée}} = \left(6 \times \frac{500}{1,750}\right) + \left(8 \times \frac{1,250}{1,750}\right) = \frac{3,000 + 10,000}{1,750} = \frac{13,000}{1,750} = 7.42857\,\\n * Total breakeven: Q^* = \frac{9,000}{7.42857} = 1,211.54 \rightarrow 1,212\text{ units}.\n * Standard: 1,212 \times \frac{500}{1,750} = 346.29 \rightarrow 347\text{ units}$; Deluxe:$1,212 \times \frac{1,250}{1,750} = 865.71 \rightarrow 865\text{ units}.\n * **Timeline to Achieve Breakeven (Best-Case Sequential Execution)**:\n * In sequential scheduling, the highest-ranking product is produced first to maximize the rate of fixed cost recovery.\n * Step 1: Produce all 500\text{ Standard boxes}$. Generates$500 \times 6 = 3,000\,\$contribution margin. Consumes$500 \times 0.2 = 100\text{ HM}.\n * Step 2: Unrecovered fixed costs remaining: 9,000 - 3,000 = 6,000\,\.\n * Step 3: Produce Deluxe boxes needed to clear 6,000\,\$:$\frac{6,000}{8} = 750\text{ Deluxe boxes}$. Consumes$750 \times 0.4 = 300\text{ HM}.\n * Total machine hours to reach breakeven: 100 + 300 = 400\text{ HM}.\n * Combined factory daily capacity: 2\text{ machines} \times 10\text{ h/day} = 20\text{ HM/day}.\n * Operating time required: \frac{400\text{ HM}}{20\text{ HM/day}} = 20\text{ days}.\n\n# Short-Term Differential Decision Making and Pricing\n\n* **Foundations of Differential Analysis**:\n * Focuses strictly on relevant costs and relevant revenues that differ between competing decision alternatives.\n * Sunk costs (depreciation of past acquisitions, historical costs) and future costs that do not vary across choices are irrelevant.\n * **Core Evaluation Rule**:\n    \Delta \text{Profit} = \Delta \text{MCV} - \Delta \text{FC} - \text{Opportunity Cost} > 0\n\n* **Special Order Decision Framework**:\n * Special orders are one-time, non-routine sales contracts that must not disrupt regular market operations.\n * **Condition 1: Sufficient Idle Capacity (No Displacement)**:\n * No regular customers are displaced.\n * Opportunity cost equals zero.\n * Decision rule:\n      P_{\text{special}} > \text{VCu}{\text{special}} + \frac{\Delta \text{FC}{\text{specific}}}{Q_{\text{special}}}\n * **Condition 2: Constrained Capacity (Displacement Exists)**:\n * Regular customer sales must be sacrificed to fulfill the order.\n * Opportunity cost equals the total contribution margin lost on sacrificed regular sales:\n      \text{Opportunity Cost} = \text{MCVu}{\text{regular}} \times Q{\text{sacrificed}}\n * Unit opportunity cost allocated across the special order:\n      \text{Unit Opportunity Cost} = \frac{\text{MCVu}{\text{regular}} \times Q{\text{sacrificed}}}{Q_{\text{special}}}\n * Decision rule:\n      P_{\text{special}} > \text{VCu}{\text{special}} + \frac{\Delta \text{FC}{\text{specific}}}{Q_{\text{special}}} + \frac{\text{MCVu}{\text{regular}} \times Q{\text{sacrificed}}}{Q_{\text{special}}}\n\n* **Comprehensive Special Order Cases**:\n * **Case 1 — Tournesol Inc.**:\n * Plant capacity: 10,000\text{ units}$. Normal operational volume:$8,000\text{ units}$. Idle capacity:$2,000\text{ units}.\n * Normal price: 60\,\$. Regular unit variable cost:$45\,\$. Fixed factory overhead:$40,000\,\.\n * **Order 1 (1,500 units at 45 $)**: Client adds logo (1,500\,\$specific fixed cost); client picks up order, saving$3\,\$in shipping costs (new$\text{VCu} = 45 - 3 = 42\,\).\n * Fits completely within 2,000\text{ units}$idle capacity (Opportunity cost =$0).\n * Incremental contribution margin: 1,500 \times (45 - 42) = 1,500 \times 3 = +4,500\,\\n * Specific fixed costs: -1,500\,\\n * Net change in profit: 4,500 - 1,500 = +3,000\,\\n * Decision: Accept the special order.\n * **Order 2 (3,000 units at 45 $)**:\n * Exceeds idle capacity (2,000\text{ units}$) by$1,000\text{ units}$. Firm must sacrifice$1,000\text{ units} of regular sales.\n * Contribution margin lost on regular sales: 1,000 \times (60 - 45) = 1,000 \times 15 = 15,000\,\\n * Incremental contribution margin: 3,000 \times (45 - 42) = 3,000 \times 3 = +9,000\,\\n * Specific fixed costs: -1,500\,\\n * Net change in profit: 9,000 - 1,500 - 15,000 = -7,500\,\\n * Decision: Reject the special order.\n * **Case 2 — Cross-Capacity Benchmark (Cases I, II, III)**:\n * **Cas I**: Capacity 300,000$, regular sales$250,000$, regular price$40\,\$,$\text{VCu} = 19\,\$,$\text{FCu} = 8\,\$. Special order$50,000\text{ units}$at$26\,\.\n * Idle capacity: 300,000 - 250,000 = 50,000\text{ units}$. Sacrificed units =$0.\n * Financial impact: 50,000 \times (26 - 19) = +350,000\,\. Accept.\n * **Cas II**: Capacity 50,000$, regular sales$50,000$, regular price$100\,\$,$\text{VCu} = 63\,\$,$\text{FCu} = 25\,\$. Special order$10,000\text{ units}$at$92\,\.\n * Idle capacity = 0$. Sacrificed regular units =$10,000.\n * Incremental contribution margin: 10,000 \times (92 - 63) = +290,000\,\\n * Opportunity cost: 10,000 \times (100 - 63) = -370,000\,\\n * Net financial impact: 290,000 - 370,000 = -80,000\,\. Reject.\n * **Cas III**: Capacity 50,000$, regular sales$45,000$, regular price$100\,\$,$\text{VCu} = 63\,\$. Special order$10,000\text{ units}$at$92\,\.\n * Idle capacity: 5,000\text{ units}$. Sacrificed regular units:$10,000 - 5,000 = 5,000.\n * Incremental contribution margin: 10,000 \times (92 - 63) = +290,000\,\\n * Opportunity cost: 5,000 \times (100 - 63) = -185,000\,\\n * Net financial impact: 290,000 - 185,000 = +105,000\,\. Accept.\n * **Case 3 — Québecavia (Airline Flight Special Booking)**:\n * Montreal-Quebec flight. Aircraft capacity: 100\text{ seats}$. Fixed operating flight cost:$18,000\,\$. Variable catering/passenger cost:$5.50\,\$. Regular ticket price:$300\,\.\n * School group requests 15\text{ seats}$, offering maximum$150\,\ per ticket.\n * **Evaluation 1: Normal Flight Load Factor at 75 %**:\n * Occupied seats: 75$, empty seats:$25$. The$15\text{ seats} fit without displacement.\n * Incremental profit: 15 \times (150 - 5.50) = 15 \times 144.50 = +2,167.50\,\. Accept.\n * **Evaluation 2: Absolute Minimum Breakeven Price**:\n      P_{\min} > \text{VCu} = 5.50\,\\n * **Evaluation 3: Additional Baggage Handling Costs of 600 $**:\n      P_{\min} > 5.50 + \frac{600}{15} = 5.50 + 40.00 = 45.50\,\\n * **Evaluation 4: Flight Load Factor at 90 % with 600 $ Baggage Fee**:\n * Occupied seats: 90$, empty seats:$10$. Group needs$15\text{ seats}$; airline must turn away$15 - 10 = 5\text{ regular passengers}.\n * Opportunity cost: 5 \times (300 - 5.50) = 5 \times 294.50 = 1,472.50\,\\n * Incremental net profit at 150\,\ offer:\n        \text{Profit} = (15 \times 150) - (15 \times 5.50) - 600 - 1,472.50 = 2,250 - 82.50 - 600 - 1,472.50 = +95.00\,\\n * Minimum acceptable ticket price:\n        P_{\min} > 5.50 + \frac{600}{15} + \frac{1,472.50}{15} = 5.50 + 40.00 + 98.1667 = 143.67\,\\n * **Case 4 — Enterprise MCB**:\n * Plant capacity: 115,000\text{ units}$. Current output:$100,000\text{ units}$. Idle capacity:$15,000\text{ units}.\n * Cost structure: Regular price 21.00\,\$; Direct material$5.00\,\$; Direct labor$4.10\,\$; Variable MOH$2.00\,\$; Fixed MOH$3.50\,\; Variable S&A 0.80\,\; Fixed S&A 1.40\,\.\n * Special order: 25,000\text{ units}$. Displaces$25,000 - 15,000 = 10,000\text{ regular units}.\n * Relevant variable cost per unit: 5.00 + 4.10 + 2.00 + 0.80 = 11.90\,\\n * Contribution margin on regular sales: 21.00 - 11.90 = 9.10\,\\n * Opportunity cost: 10,000 \times 9.10 = 91,000\,\\n * Minimum acceptable price:\n      P_{\min} > 11.90 + \frac{91,000}{25,000} = 11.90 + 3.64 = 15.54\,\\n * **Case 5 — Enterprise "O" (Optical Lenses)**:\n * Normal price: 50\,\$. Variable manufacturing cost:$10\,\$. Fixed manufacturing cost:$18\,\$. Variable selling cost:$1\,\.\n * Special order: 10,000\text{ units}$. Selling costs are entirely bypassed. Special engraving equipment must be purchased for$50,000\,\. Sufficient capacity available.\n * Relevant costs: Variable cost 10\,\$+ Machine purchase$50,000\,\.\n * Minimum price:\n      P_{\min} > 10 + \frac{50,000}{10,000} = 10 + 5 = 15.00\,\\n\n* **Strategic Risks of Marginal Cost Pricing**:\n * Market Cannibalization: Regular clients may discover discount pricing and demand equal concessions.\n * Permanent Customer Alienation: Sacrificing regular clients during temporary constraints risks permanent loss to competitors.\n * Price War Initiation: Competitors may interpret aggressive marginal pricing as price dumping.\n\n* **Long-Term Pricing Architecture**:\n * Over the long horizon, selling prices must recover full absorption costs plus generate a target profit:\n    \text{Price} = \text{VCu} + \frac{\text{FC}}{Q} + \text{Target Margin}\n * **Cost-Plus Approaches (Majoration des coûts)**:\n * **Cost Markup (Majoration des coûts)**:\n      \text{Price} = \text{Cost} \times (1 + \%\text{markup})\n * Example on 15\,\$cost with$20\%$markup:$15 \times (1 + 0.20) = 18.00\,\\n * **Margin on Selling Price (Cible de marge)**:\n      \frac{\text{Price} - \text{Cost}}{\text{Price}} = \%\text{margin} \implies \text{Price} = \frac{\text{Cost}}{1 - \%\text{margin}}\n * Example on 15\,\$cost with$20\%$target margin:$\frac{15}{1 - 0.20} = \frac{15}{0.80} = 18.75\,\\n * **Price Elasticity and Profit Optimization**:\n * Empirical demand schedules demonstrate trade-offs between pricing power and total contribution margin:\n * At 8\,\$: Volume =$4,000$,$\text{VCu} = 4\,\$,$\text{MCVu} = 4\,\$, Total$\text{MCV} = 16,000\,\\n * At 9\,\$: Volume =$3,500$,$\text{VCu} = 4\,\$,$\text{MCVu} = 5\,\$, Total$\text{MCV} = 17,500\,\ (Optimal profit point)\n * At 10\,\$: Volume =$2,500$,$\text{VCu} = 4\,\$,$\text{MCVu} = 6\,\$, Total$\text{MCV} = 15,000\,\\n * At 11\,\$: Volume =$2,000$,$\text{VCu} = 4\,\$,$\text{MCVu} = 7\,\$, Total$\text{MCV} = 14,000\,\\n * At 12\,\$: Volume =$1,500$,$\text{VCu} = 4\,\$,$\text{MCVu} = 8\,\$, Total$\text{MCV} = 12,000\,\\n\n# Traditional Cost Accounting Systems and Overhead Allocation\n\n* **System Selection: Job-Order Costing Versus Process Costing**:\n * **Job-Order Costing (Coût de revient par commande)**: Used when an organization produces unique, customized, or diverse goods/services according to customer specifications. Costs are accumulated separately by job or contract.\n * Examples: Commercial aircraft manufacturing (Bombardier), large construction projects, hospitals, architectural and law firms, audit engagements, custom cabinetry, event planning.\n * **Process Costing (Coût de revient en série)**: Used when an organization produces continuous streams of homogeneous units through standard sequential processes. Costs are accumulated by department.\n * Examples: Orange juice concentrate, gold refining, sausage processing, electronic screen assembly, petroleum refining, chemical processing, public utilities.\n\n* **Mechanics of Predetermined Overhead Rates (\text{POHR}, Taux d'imputation prédéterminé)**:\n * Direct costs (\text{DM}$and$\text{DL}) are charged directly to specific jobs as materials are requisitioned and time tickets logged.\n * Indirect factory overhead (\text{MOH}) cannot be traced directly and is allocated using a predetermined rate formulated prior to the fiscal year:\n    \text{POHR} = \frac{\text{Estimated Total Manufacturing Overhead Costs}}{\text{Estimated Total Allocation Base Volume}}\n * Applied overhead assigned to a specific job:\n    \text{Applied MOH} = \text{POHR} \times \text{Actual Units of Allocation Base Used by Job}\n * **Theoretical Rationale for Predetermined Rates (FLUCTUTU Illustration)**:\n * Actual overhead cannot be measured until fiscal year-end.\n * Apportioning actual overhead monthly or quarterly creates distortions caused by seasonal fixed overhead and volume swings.\n * When FLUCTUTU calculates actual quarterly costs, fixed overhead of 100,000\,\$per quarter divided by changing volume ($5,000$;$10,000$;$15,000$;$2,500\text{ units}$) yields fluctuating fixed unit costs of$20.00\,\$,$10.00\,\$,$6.70\,\$, and$40.00\,\$. Total unit cost fluctuates between$46.70\,\$and$80.00\,\ despite identical production methods.\n * A predetermined rate neutralizes volume volatility, stabilizes unit manufacturing costs, and provides prompt cost data for pricing.\n\n* **Accounting for Underapplied and Overapplied Manufacturing Overhead**:\n * At year-end, actual overhead incurred rarely equals overhead applied:\n    \text{Overhead Variance} = \text{Actual MOH Incurred} - \text{Applied MOH}\n * **Underapplied Overhead (Sous-imputation)**:\n * Occurs when \text{Applied MOH} < \text{Actual MOH}.\n * Effect prior to adjustment: \text{COGS} is understated, operating income is overstated, and inventory assets are understated.\n * Adjustment: Close out variance by debiting \text{COGS}$and crediting$\text{MOH}$, increasing$\text{COGS}.\n * **Overapplied Overhead (Surimputation)**:\n * Occurs when \text{Applied MOH} > \text{Actual MOH}.\n * Effect prior to adjustment: \text{COGS} is overstated, operating income is understated, and inventory assets are overstated.\n * Adjustment: Close out variance by crediting \text{COGS}$and debiting$\text{MOH}$, decreasing$\text{COGS}.\n * **Applied Overhead Problem (Tiger Inc.)**:\n * Actual overhead incurred: 1,210,000\,\\n * Predetermined rate: 4.00\,\$per machine-hour ($\text{HM}\n * Actual machine hours worked: 290,000\,\text{HM}\n * Overhead applied: 290,000 \times 4.00 = 1,160,000\,\\n * Variance calculation: 1,160,000 - 1,210,000 = -50,000\,\\n * Conclusion: Overhead is underapplied (sous-imputé) by 50,000\,\.\n\n* **Financial Statement Schedules and Cost Flows**:\n * **Schedule of Cost of Goods Manufactured (État du coût de fabrication)**:\n * Direct Materials Section:\n      \text{Beginning Raw Materials Inventory} + \text{Raw Material Purchases} = \text{Raw Materials Available for Use}\n      \text{Raw Materials Available} - \text{Ending Raw Materials Inventory} = \text{Direct Materials Used} \n * Total Manufacturing Additions:\n      \text{Total Manufacturing Costs Incurred} = \text{Direct Materials Used} + \text{Direct Labor} + \text{Applied MOH}\n * Work in Process Adjustments:\n      \text{Cost of Goods Manufactured (COGM)} = \text{Total Manufacturing Costs} + \text{Beginning WIP} - \text{Ending WIP}\n * **Cost of Goods Sold and Income Statement Flow**:\n    \text{Beginning Finished Goods Inventory} + \text{COGM} = \text{Goods Available for Sale}\n    \text{Goods Available for Sale} - \text{Ending Finished Goods Inventory} = \text{Unadjusted Cost of Goods Sold}\n    \text{Gross Margin} = \text{Sales Revenue} - \text{Cost of Goods Sold}\n    \text{Net Operating Income} = \text{Gross Margin} - \text{Selling Expenses} - \text{Administrative Expenses}\n\n* **Comprehensive Job-Order Accounting Applications**:\n * **Application 1 — Aux Plaisirs Gastronomiques (E5.10)**:\n * Given financial balances:\n * Sales: 643,000\,\\n * Direct labor: 90,000\,\\n * Purchases of raw materials: 132,000\,\\n * Selling expenses: 100,000\,\\n * Administrative expenses: 43,000\,\\n * Applied manufacturing overhead: 210,000\,\\n * Beginning inventories: \text{RM} = 8,000\,\$;$\text{WIP} = 5,000\,\$;$\text{FG} = 70,000\,\\n * Ending inventories: \text{RM} = 10,000\,\$;$\text{WIP} = 20,000\,\$;$\text{FG} = 25,000\,\\n * Schedule of Cost of Goods Manufactured:\n * Raw materials used: 8,000 + 132,000 - 10,000 = 130,000\,\\n * Direct labor: 90,000\,\\n * Applied manufacturing overhead: 210,000\,\\n * Total manufacturing costs: 130,000 + 90,000 + 210,000 = 430,000\,\\n * Plus beginning \text{WIP}$:$5,000\,\\n * Less ending \text{WIP}$:$-20,000\,\\n * Cost of Goods Manufactured: 430,000 + 5,000 - 20,000 = 415,000\,\\n * Income Statement Preparation:\n * Beginning \text{FG}$inventory:$70,000\,\\n * Plus \text{COGM}$:$415,000\,\\n * Goods available for sale: 485,000\,\\n * Less ending \text{FG}$inventory:$-25,000\,\\n * Cost of Goods Sold (\text{COGS}$):$460,000\,\\n * Sales revenue: 643,000\,\\n * Gross margin: 643,000 - 460,000 = 183,000\,\\n * Less selling expenses: -100,000\,\\n * Less administrative expenses: -43,000\,\\n * Net operating income: 183,000 - 100,000 - 43,000 = 40,000\,\\n * **Application 2 — Single Job Cost Card (Order WR53)**:\n * Direct materials: 200\,\\n * Direct labor: 10\text{ hours}$at$25\,\$/\text{hour} = 250\,\\n * Annual budgeted overhead: 760,000\,\$; Annual budgeted labor:$20,000\text{ DLH}\n * Predetermined overhead rate: \frac{760,000}{20,000} = 38.00\,\$/\text{DLH}\n * Overhead applied to WR53: 10 \times 38 = 380\,\\n * Total cost accumulated for Order WR53: 200 + 250 + 380 = 830.00\,\\n * **Application 3 — Enterprise Commandito (Inventory Tracking Across Jobs)**:\n * Predetermined overhead rate: 1.50\,\$per direct labor hour ($\text{DLH}\n * Direct labor hourly wage: 20.00\,\ per hour\n * Beginning \text{WIP}$inventory:$4,500\,\ (represented entirely by incomplete Job #A2)\n * Current period additions:\n * Job #B1: Direct materials 2,000\,\$; Direct labor$20\text{ DLH}$($20 \times 20 = 400\,\$); Applied overhead$20 \times 1.50 = 30\,\$. Total cost =$2,000 + 400 + 30 = 2,430\,\.\n * Job #A2: Direct materials 1,500\,\$; Direct labor$40\text{ DLH}$($40 \times 20 = 800\,\$); Applied overhead$40 \times 1.50 = 60\,\$. Current period additions =$1,500 + 800 + 60 = 2,360\,\. Cumulative cost of Job #A2 = 4,500 + 2,360 = 6,860\,\.\n * Job #D3: Direct materials 15,000\,\$; Direct labor$120\text{ DLH}$($120 \times 20 = 2,400\,\$); Applied overhead$120 \times 1.50 = 180\,\$. Total cost =$15,000 + 2,400 + 180 = 17,580\,\.\n * Status at year-end: Jobs #A2 and #D3 are completed; Job #B1 remains in progress.\n * Ending \text{WIP} inventory balance (Job #B1): 2,430.00\,\\n * Cost of Goods Manufactured (Completed Jobs #A2 + #D3):\n      \text{COGM} = 6,860 + 17,580 = 24,440.00\,\\n * Reconciliation via \text{COGM} formula:\n * Total raw materials used: 2,000 + 1,500 + 15,000 = 18,500\,\\n * Total direct labor: 400 + 800 + 2,400 = 3,600\,\\n * Total applied overhead: 30 + 60 + 180 = 270\,\\n * Total manufacturing additions: 18,500 + 3,600 + 270 = 22,370\,\\n * Plus beginning \text{WIP}$:$+4,500\,\\n * Less ending \text{WIP}$:$-2,430\,\\n * \text{COGM} = 22,370 + 4,500 - 2,430 = 24,440.00\,\\n\n# Activity-Based Costing (ABC / CPA)\n\n* **Limitations of Traditional Volume-Based Costing**:\n * Traditional systems allocate overhead through one plantwide rate or departmental rates based strictly on volume drivers (\text{DLH}, machine-hours, material dollars).\n * Modern manufacturing cost structures have shifted: direct labor has plummeted as a percentage of total cost, while indirect factory overhead has surged due to automated technology, computerization, and production support activities.\n * Traditional assumptions treat all overhead costs as variable with respect to output volume, causing severe product cross-subsidization:\n * High-volume, simple products consume minimal setup and support per unit but are assigned excessive overhead because of high aggregate volume.\n * Low-volume, complex products require disproportionate setups, specialized tooling, and quality inspections but are assigned minimal overhead due to low aggregate volume.\n\n* **Activity-Based Costing Architecture**:\n\n\n\n * **Core Logic of ABC**: Activities consume resources; cost objects consume activities.\n * **Resources**: Total organizational expenses (salaries, supplies, rent, depreciation).\n * **Resource Drivers (Inducteurs de ressources)**: Factors that measure the consumption of resources by activities (e.g., floor space, square footage, percentage of staff time, headcount).\n * **Activities**: Aggregations of tasks performed by personnel and equipment to produce output.\n * **Activity Drivers / Allocation Bases (Inducteurs d'activités / Unités d'œuvre)**: Factors that measure the demand placed on activities by cost objects (e.g., number of setups, machine-hours, number of orders, parts count).\n * **Cost Objects**: Products, services, customer accounts, programs, or organizational units whose cost is being measured.\n\n* **ABC Five-Step Implementation Process**:\n 1. Identify, define, and classify operational activities.\n 2. Assign resource costs to activity cost pools using resource drivers.\n 3. Calculate activity rates (\text{Activity Rate} = \frac{\text{Budgeted Activity Overhead}}{\text{Total Activity Driver Volume}}).\n 4. Assign overhead costs to cost objects by multiplying activity rates by actual activity driver units consumed.\n 5. Compile managerial reports to support operational analysis and strategic decision-making.\n\n* **Activity-Based Management (ABM) Presentation — HR Department Illustration**:\n * **Traditional Accounting Presentation (By Expense Category)**:\n * Salaries: 50,000\,\\n * Supplies: 5,000\,\\n * Insurance: 12,500\,\\n * Employee Benefits: 2,500\,\\n * Miscellaneous: 25,000\,\\n * Total HR Budget: 95,000\,\\n * **Activity-Based Presentation (By Operational Function)**:\n * Employee Recruiting & Hiring: 45,000\,\\n * Administering Benefits: 10,000\,\\n * Management Report Production: 5,000\,\\n * Handling CNESST Workplace Injury Files: 20,000\,\\n * Managing Law 90 (Loi 90) Regulatory Compliance: 15,000\,\\n * Total HR Budget: 95,000\,\\n * **Managerial Value**: While total spending is identical (95,000\,\), the ABC perspective reveals which operational tasks generate expenses, providing actionable targets for process re-engineering and waste elimination.\n\n* **Benchmark Case Study — Resolving Cross-Subsidization (Problem P7.17)**:\n * **Operational Data**:\n * Model X200: Low-volume, complex model requiring specialized equipment. Annual volume = 5,000\text{ units}$. Direct labor =$1.8\text{ DLH/unit}$($9,000\text{ DLH}$total). Direct materials =$72.00\,\ per unit.\n * Model X99: High-volume, standard model. Annual volume = 30,000\text{ units}$. Direct labor =$0.9\text{ DLH/unit}$($27,000\text{ DLH}$total). Direct materials =$50.00\,\ per unit.\n * Total factory volume = 35,000\text{ units}$; Total direct labor =$36,000\text{ DLH}.\n * Direct labor hourly wage rate: 20.00\,\ per hour.\n * Total manufacturing overhead budget (\text{MOH}$):$1,800,000\,\.\n * **Part 1: Traditional Cost Accounting (Plantwide DLH Allocation)**:\n * Predetermined overhead rate:\n      \text{POHR} = \frac{1,800,000\,\}{36,000\text{ DLH}} = 50.00\,\/\text{DLH}\n * **Model X200 Unit Manufacturing Cost**:\n * Direct materials: 72.00\,\\n * Direct labor (1.8 \times 20.00$):$36.00\,\\n * Applied overhead (1.8 \times 50.00$):$90.00\,\\n * Unit manufacturing cost: 72.00 + 36.00 + 90.00 = 198.00\,\\n * **Model X99 Unit Manufacturing Cost**:\n * Direct materials: 50.00\,\\n * Direct labor (0.9 \times 20.00$):$18.00\,\\n * Applied overhead (0.9 \times 50.00$):$45.00\,\\n * Unit manufacturing cost: 50.00 + 18.00 + 45.00 = 113.00\,\\n * **Aggregate Factory Cost Breakdown**:\n * Total direct materials: (5,000 \times 72) + (30,000 \times 50) = 360,000 + 1,500,000 = 1,860,000\,\$($42.47\% of total)\n * Total direct labor: (5,000 \times 36) + (30,000 \times 18) = 180,000 + 540,000 = 720,000\,\$($16.44\% of total)\n * Total overhead: 1,800,000\,\$($41.10\% of total)\n * Total factory production cost: 4,380,000\,\\n * **Part 2: Activity-Based Costing Implementation**:\n * **Activity Pools, Budgeted Costs, and Drivers**:\n * Machine Setups: Budget = 360,000\,\$; Driver = Number of setups ($150\text{ setups}$: X200 =$50$, X99 =$100).\n        \text{Setup Activity Rate} = \frac{360,000}{150} = 2,400.00\,\$/\text{setup}\n * Special Processing: Budget = 180,000\,\$; Driver = Machine-hours ($12,000\text{ HM}$: X200 =$12,000$, X99 =$0).\n        \text{Special Processing Rate} = \frac{180,000}{12,000} = 15.00\,\$/\text{HM}\n * General Production: Budget = 1,260,000\,\$; Driver = Direct labor hours ($36,000\text{ DLH}$: X200 =$9,000$, X99 =$27,000).\n        \text{Production Activity Rate} = \frac{1,260,000}{36,000} = 35.00\,\$/\text{DLH}\n * **Overhead Allocation Under ABC**:\n * **Model X200 Total Overhead**:\n * Setups: 50 \times 2,400 = 120,000\,\\n * Special processing: 12,000 \times 15 = 180,000\,\\n * General production: 9,000 \times 35 = 315,000\,\\n * Total overhead: 120,000 + 180,000 + 315,000 = 615,000\,\\n * Overhead per unit: \frac{615,000}{5,000} = 123.00\,\\n * **Model X99 Total Overhead**:\n * Setups: 100 \times 2,400 = 240,000\,\\n * Special processing: 0 \times 15 = 0\,\\n * General production: 27,000 \times 35 = 945,000\,\\n * Total overhead: 240,000 + 0 + 945,000 = 1,185,000\,\\n * Overhead per unit: \frac{1,185,000}{30,000} = 39.50\,\\n * **ABC Unit Manufacturing Cost Comparison**:\n * **Model X200**:\n        \text{Unit Cost} = 72.00 (\text{DM}) + 36.00 (\text{DL}) + 123.00 (\text{Overhead}) = 231.00\,\\n * Traditional unit cost: 198.00\,\$. ABC reveals X200 was undercosted by$33.00\,\$($+16.67\%).\n * **Model X99**:\n        \text{Unit Cost} = 50.00 (\text{DM}) + 18.00 (\text{DL}) + 39.50 (\text{Overhead}) = 107.50\,\\n * Traditional unit cost: 113.00\,\$. ABC reveals X99 was overcosted by$5.50\,\$($-4.87\%).\n * **Strategic Explanation of Cost Distortion**: Traditional costing allocated overhead using direct labor hours (25\%$to X200 and$75\%$to X99). However, non-unit-level costs do not track labor hours: X200 consumes$33.33\%$of machine setups ($50 / 150$) and$100\%$of special machine processing, despite generating only$14.29\% of total production volume. By using activity-specific drivers, ABC eliminates cross-subsidization and charges complex products for the specialized activities they consume.\n\n* **Comprehensive Batch-Level Case — Société Chemise**:\n * **Operational Data**: Standard shirt sold at 30.00\,\$; Deluxe shirt sold at$40.00\,\$. Normal production: Standard =$1,000\text{ units}$, Deluxe =$200\text{ units}.\n * Direct materials: Standard = 10,000\,\$($10.00\,\$/\text{unit}$); Deluxe = 2,500\,\ ($12.50\,\$/\text{unit}$).

  • Direct labor: Standard = 5,000\,\ (5.00\,\/\text{unit}$); Deluxe =$1,000\,\$($5.00\,\$/\text{unit}).\n * Total direct prime costs: Standard = 15.00\,\$/\text{unit}$; Deluxe =$17.50\,\$/\text{unit}.\n * Traditional system: Overhead applied at 1.25\,\ per dollar of direct materials.\n * Traditional overhead: Standard = 10,000 \times 1.25 = 12,500\,\$($12.50\,\$/\text{unit}$); Deluxe =$2,500 \times 1.25 = 3,125\,\$($15.625\,\$/\text{unit}).\n * Traditional unit manufacturing cost: Standard = 27.50\,\$; Deluxe =$33.125\,\.\n * Traditional gross margin: Standard = 30.00 - 27.50 = +2.50\,\$; Deluxe =$40.00 - 33.125 = +6.88\,\ (Deluxe appears substantially more profitable).\n * **Activity-Based Overhead Analysis**:\n * Actual overhead total = 15,625\,\$($12,500 + 3,125), split into two pools:\n 1. Production Engineering: 5,725\,\$paid to an external consultant who configures machines by shirt model. Driver = Number of models ($2\text{ models}).\n         \text{Engineering Rate} = \frac{5,725}{2} = 2,862.50\,\$/\text{model}\n 2. Machine Setups: 9,900\,\ in wages paid to three technicians who calibrate machines before every batch. Driver = Number of production batches.\n * Standard shirts produced in batches of 200\text{ units}$:$\frac{1,000}{200} = 5\text{ batches}.\n * Deluxe shirts produced in batches of 20\text{ units}$:$\frac{200}{20} = 10\text{ batches}.\n * Total batches = 5 + 10 = 15\text{ batches}.\n         \text{Setup Rate} = \frac{9,900}{15} = 660.00\,\$/\text{batch}\n * **ABC Overhead Assignment and Profitability Analysis**:\n * **Standard Shirt**:\n * Engineering: 1 \times 2,862.50 = 2,862.50\,\\n * Setups: 5 \times 660.00 = 3,300.00\,\\n * Total overhead: 2,862.50 + 3,300.00 = 6,162.50\,\\n * Total manufacturing cost: 10,000 (\text{DM}) + 5,000 (\text{DL}) + 6,162.50 (\text{Overhead}) = 21,162.50\,\\n * Unit manufacturing cost: \frac{21,162.50}{1,000} = 21.1625 \approx 21.16\,\\n * True gross margin per unit: 30.00 - 21.16 = +8.84\,\$(Up from$2.50\,\ under traditional costing)\n * **Deluxe Shirt**:\n * Engineering: 1 \times 2,862.50 = 2,862.50\,\\n * Setups: 10 \times 660.00 = 6,600.00\,\\n * Total overhead: 2,862.50 + 6,600.00 = 9,462.50\,\\n * Total manufacturing cost: 2,500 (\text{DM}) + 1,000 (\text{DL}) + 9,462.50 (\text{Overhead}) = 12,962.50\,\\n * Unit manufacturing cost: \frac{12,962.50}{200} = 64.8125 \approx 64.81\,\\n * True gross margin per unit: 40.00 - 64.81 = -24.81\,\ (Substantial operating loss per unit)\n * **Strategic Decision Takeaway**: Traditional costing created the false impression that Deluxe shirts were a high-margin premium product (+6.88\,\$), whereas short batch runs ($20\text{ units/batch}$) consume$66.67\%$of setup activity ($10 / 15$). Under ABC, Deluxe shirts lose$24.81\,\ per unit, prompting management to either raise the selling price, increase batch run sizes, or terminate the model.\n\n* **Comprehensive Full-Cost ABC Case — Urban Nord**:\n * **Operational Data**: Quebec apparel firm producing two sweater models sold at 79.00\,\$. Monthly volume: Pierrot =$1,000\text{ units}$, Leslie =$3,000\text{ units}.\n * Direct costs:\n * Pierrot: Variable 42,000\,\$($42.00\,\$/\text{unit}$), Fixed$21,000\,\$($21.00\,\$/\text{unit}$). Total direct =$63,000\,\$($63.00\,\$/\text{unit}).\n * Leslie: Variable 126,000\,\$($42.00\,\$/\text{unit}$), Fixed$63,000\,\$($21.00\,\$/\text{unit}$). Total direct =$189,000\,\$($63.00\,\$/\text{unit}).\n * Indirect activities across full value chain (Manufacturing & Commercial):\n * Finishing Activity: Inspection, quality verification, manual alteration. Cost = 15,000\,\$. Driver = Number of sweaters ($4,000\text{ sweaters}$: Pierrot =$1,000$, Leslie =$3,000).\n        \text{Finishing Rate} = \frac{15,000}{4,000} = 3.75\,\$/\text{sweater}\n * Promotional Activity: Sending targeted digital promotional messages. Cost = 12,600\,\$. Driver = Promotional messages ($21,000\text{ messages}$: Pierrot =$10,000$, Leslie =$11,000).\n        \text{Promotion Rate} = \frac{12,600}{21,000} = 0.60\,\$/\text{message}\n * Order Processing Activity: Order entry, picking, packaging, shipping. Cost = 16,632\,\$. Driver = Number of customer orders ($1,512\text{ orders}$: Pierrot =$600$, Leslie =$912).\n        \text{Order Processing Rate} = \frac{16,632}{1,512} = 11.00\,\$/\text{order}\n * Total indirect costs = 15,000 + 12,600 + 16,632 = 44,232\,\\n * **Assignment of Indirect Costs and Unit Full Cost Calculation**:\n * **Pierrot Model (1,000 units)**:\n * Direct costs: 63,000.00\,\\n * Finishing (1,000 \times 3.75$):$3,750.00\,\\n * Promotion (10,000 \times 0.60$):$6,000.00\,\\n * Order processing (600 \times 11.00$):$6,600.00\,\\n * Total indirect costs: 3,750 + 6,000 + 6,600 = 16,350.00\,\\n * Full cost: 63,000 + 16,350 = 79,350.00\,\\n * Unit full cost: \frac{79,350}{1,000} = 79.35\,\\n * Net margin at 79.00\,\$selling price:$79.00 - 79.35 = -0.35\,\ (Operating loss)\n * **Leslie Model (3,000 units)**:\n * Direct costs: 189,000.00\,\\n * Finishing (3,000 \times 3.75$):$11,250.00\,\\n * Promotion (11,000 \times 0.60$):$6,600.00\,\\n * Order processing (912 \times 11.00$):$10,032.00\,\\n * Total indirect costs: 11,250 + 6,600 + 10,032 = 27,882.00\,\\n * Full cost: 189,000 + 27,882 = 216,882.00\,\\n * Unit full cost: \frac{216,882}{3,000} = 72.294 \approx 72.29\,\\n * Net margin at 79.00\,\$selling price:$79.00 - 72.29 = +6.71\,\ (Profitable product)\n\n* **Strategic Evaluation of ABC**:\n * **Operational Advantages**:\n * Aligns cost accounting with advanced manufacturing setups involving robotics, just-in-time logistics, and flexible cells.\n * Accurately reflects true product consumption of organizational overhead.\n * Facilitates Value-Added Analysis: separates value-added activities from non-value-added activities, establishing the quantitative baseline for process re-engineering.\n * Enhances pricing strategy and profitability reporting.\n * **Implementation Obstacles and Limitations**:\n * High administrative cost of defining, measuring, and maintaining extensive activity databases.\n * Complexity in capturing employee time allocations and activity cost driver volumes.\n * Subjective allocation required for company-sustaining common costs.\n * **Diagnostic Symptoms Requiring ABC Implementation**:\n * Management seeks to discontinue product lines that conventional reports indicate are highly profitable.\n * Complex, difficult-to-manufacture products show high gross margins that production managers find unbelievable.\n * Competitors sell high-volume commodity items at prices lower than the firm's reported manufacturing cost.\n * Operating departments bypass central cost accounting and create shadow spreadsheets to calculate accurate costs.\n * Customers do not protest price increases on complex, low-volume product lines.\n * Competitive bidding outcomes produce inexplicable wins on complex contracts and unexpected losses on simple jobs.\n * **Criteria for Identifying High-Potential ABC Candidates**:\n * High product diversity and complex manufacturing processes.\n * Indirect overhead costs exceed 20\%$$ of total operating expenses.

  • Fast-growing period and support costs relative to direct manufacturing expenses.

  • Competitive pressure limiting pricing freedom, requiring accurate cost information.