01 / Learn the method
What you will learn
Build a profit bridge that reconciles budget to actuals; distinguish the effects of volume, price, unit variable cost and fixed cost; explain findings without presenting untested causes as facts.
A bridge explains the movement
For each product, contribution = units sold × (selling price per unit - variable cost per unit). Operating profit is total contribution less period fixed costs. Revenue growth can coexist with lower profit when the contribution per unit falls or fixed costs rise.
Choose an explicit attribution sequence. In this exercise change volume first, price second, and unit variable cost third. Then add the fixed-cost change. Using a different order moves interaction effects between drivers; do not combine formulas from different conventions.
| Driver | Formula; positive = favorable to profit |
|---|---|
| Volume | (Actual units - Budget units) × (Budget price - Budget unit cost) |
| Price | Actual units × (Actual price - Budget price) |
| Unit variable cost | -Actual units × (Actual unit cost - Budget unit cost) |
| Fixed cost | Budget fixed costs - Actual fixed costs |
Calculate the first three effects separately for each product, then sum them. The volume effect includes the effect of the product quantities changing in different proportions. It is not a separate pure-volume / mix decomposition. The bridge is an arithmetic attribution, not proof of causality.
Smaller worked example
A separate one-product business budgets 100 units at a $20 price and $12 unit cost, with $300 fixed costs. Actuals are 110 units at $19 and $13, with $320 fixed costs. Budget profit is $500; actual profit is $340. The bridge is +$80 volume, -$110 price, -$110 unit cost and -$20 fixed cost = -$160. Check: $500 - $160 = $340.
“Price reduced profit by $110” is supported by the numbers. “Discounting caused the price reduction” requires invoice or commercial evidence. A good question names the owner and the evidence that could confirm or reject a hypothesis.
02 / Put it to work
Your assignment
You are the analyst at fictional Cedar Office Products. The CFO asks why September 2026 revenue exceeded budget while operating profit missed it. Use USD whole dollars. All units were sold in the period; ignore inventory timing, returns, tax, financing and foreign exchange. Fixed costs are period totals. The case operating-profit measure is simplified, not a full statutory income statement.
| Product / measure | Budget | Actual |
|---|---|---|
| A - units | 1,000 | 1,200 |
| A - price per unit | $100 | $95 |
| A - variable cost per unit | $60 | $65 |
| B - units | 500 | 450 |
| B - price per unit | $200 | $210 |
| B - variable cost per unit | $120 | $130 |
| Total fixed costs | $30,000 | $38,000 |
Comments from the business
Sales: “We ran a campaign for Product A.” Operations: “We used some expedited freight.” Finance: “Several overhead lines moved.” No customer-level pricing, usage, freight detail or recurring / one-off overhead split has been supplied. Treat these comments as leads to investigate.
Submit three things
-
A formula-based budget / actual P&L and reconciled profit bridge in the student workbook. Show product-level workings, totals and a residual check. Retain the source inputs.
-
Three questions: name an owner, specify evidence needed and explain the decision the evidence would inform.
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A CFO email of no more than 200 words, including the numeric result, material drivers, evidence gaps and recommended next actions. The supplied workbook has space for all three deliverables.
Use the defined volume → price → cost convention. Round only displayed results, not intermediate calculations. Check amounts within $0.01; percentage displays within 0.1 percentage point. Do not type balancing plugs.
Optional extension
Recompute the bridge with price changed before volume, keeping unit cost last. Explain which driver allocations change and why the total must stay the same. This extension is outside the 100-point rubric.
03 / Review your work
Try the assignment before opening the answer.
Open the worked answer and teaching notes
Worked answer
| USD | Budget | Actual | Change |
|---|---|---|---|
| Revenue | 200,000 | 208,500 | 8,500 |
| Variable cost | 120,000 | 136,500 | 16,500 |
| Contribution | 80,000 | 72,000 | -8,000 |
| Fixed cost | 30,000 | 38,000 | 8,000 |
| Operating profit | 50,000 | 34,000 | -16,000 |
| Profit effect / USD | Product A | Product B | Total |
|---|---|---|---|
| Volume | 8,000 | -4,000 | 4,000 |
| Price | -6,000 | 4,500 | -1,500 |
| Unit variable cost | -6,000 | -4,500 | -10,500 |
| Fixed cost | Not allocated | Not allocated | -8,000 |
| Total change | -16,000 |
Revenue rose 4.25% (displayed 4.3%); operating profit fell 32.0%. The $4,000 favorable volume effect could not offset $20,000 of adverse price, unit-cost and fixed-cost effects. Actual profit is $50,000 + $4,000 - $1,500 - $10,500 - $8,000 = $34,000. Bridge residual is $0.00.
Questions worth asking
Sales: which customers or approved discounts explain Product A’s lower realized price? Request invoice-level pricing before changing discount rules. Operations: which supplier rates, usage or freight items explain each unit-cost increase? Finance: which fixed-cost accounts moved and will they recur? Request account detail before updating the forecast run rate.
Example CFO email
Subject: September profit shortfall - pricing and cost review
September revenue was $208,500, $8,500 above budget (+4.3%), while operating profit was $34,000, $16,000 below budget (-32.0%). Product-level volume changes at budget margins added $4,000. Price changes reduced profit by $1,500; unit variable cost increases reduced it by $10,500; and higher fixed costs reduced it by $8,000. These effects reconcile to the shortfall.
The commercial team mentions a campaign and operations mentions expedited freight, but neither comment quantifies the cause. I recommend Sales review Product A pricing and Operations review supplier, usage and freight costs. Finance should separate recurring from one-off fixed costs. We should update the forecast after those owners provide supporting detail; the bridge alone does not establish causation.
Scoring rubric - 100 points
| Dimension | Points | Awarding guidance |
|---|---|---|
| Calculation | 40 | P&L 10; volume 8; price 6; unit cost 6; fixed cost 4; bridge total and actual profit 6. Credit correct method after an isolated input error. |
| Interpretation | 25 | Revenue versus profit 8; recognize mix within volume 5; separate causes from evidence 6; three relevant questions 6 (2 each). |
| Controls / audit trail | 20 | Traceable source formulas 8; residual check calculated independently against actual profit 8; explicit units and sign convention 4. A typed zero earns no check points. |
| Communication | 15 | Clear headline 5; owner / evidence / next action 6; <=200-word coherent email 4. |
Numerical tolerance: $0.01, with percentages within 0.1 percentage point when rounded. Award method credit without double-penalizing one arithmetic error. Reasoned alternative questions are valid. A different fully reconciled convention can earn arithmetic credit, but it must be labeled and does not satisfy the requested convention in full. No universal passing score is prescribed.
Common mistakes and staged hints
Mistakes: confusing revenue variance with profit variance; using budget volumes in the price effect after already changing volume; reversing the cost sign; allocating fixed costs per unit; calling the campaign a proven cause; typing a balancing amount.
Hint 1: calculate contribution separately for each product. Hint 2: freeze budget unit margin for volume, then use actual volumes for the remaining unit changes. Hint 3: compare the summed bridge with actual profit less budget profit, using separately calculated P&Ls.
Instructor use
Suggested 60-minute session: 10 minutes on the smaller example, 25 minutes individual workbook work, 15 minutes peer review of the bridge and evidence claims, 10 minutes CFO-email discussion. For a 45-minute session assign the lesson beforehand. The timing is an untested planning estimate.
Before class, open both files in the intended spreadsheet application and confirm formulas calculate. Keep the worked solution out of the initial handout. These solutions are intentionally available for learning; the exercise is not a secure hiring test. For beginners provide the formulas; for advanced students use the optional sequence extension. The extension changes volume to $2,500 and price to $0, with unit cost -$10,500 and fixed cost -$8,000; the total remains -$16,000.
Continue this learning path
FPA-02 · Build a Driver-Based Quarterly Forecast
FPA-03 · Hire Now or Wait? A Headcount Investment Decision
AI-assisted synthetic teaching case. Expert review and native Excel / Sheets testing pending.