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Lesson 3 of 5 11–14% of the exam

You are reading the 2026 curriculum (exams up to November 2026). Sitting in February 2027 or later? Go to the 2027 Equities guide.

Forecasting costs, margins and working capital

Forecast cost of sales as a percentage of sales (a gross margin) and keep it consistent with the revenue mix and competitive story. Passing a cost increase on in money terms keeps gross profit but lowers the margin percentage. Forecast selling, general and administrative expenses (SG&A) by their fixed and variable parts, and working capital balances from days ratios.

6 min cram, 28 min full read. Based on the 2026 CFA® Program Level I curriculum, Equity Investments, Learning Module 7. This is the 2026 version of the lesson. Sitting in February 2027 or later? Read the updated 2027 version.

Tailor this to you: take the self-assessment

Before this: Forecasting revenue: top-down, bottom-up and hybrid

On the exam

  • Explain approaches to forecasting a company’s operating expenses and working capital

Explain approaches to forecasting a company's operating expenses and working capital. Expect: a margin after a cost pass-through; a receivable, inventory or payable balance from a days ratio; the effect of mix and of fixed costs.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

Cram mode: the one-screen version of this lesson. Switch to Full for the explanations, worked examples and interactives.

How do you forecast cost of sales and the gross margin?

Cost of sales is usually the largest cost for a company that makes or sells products, and it is tied directly to sales. So forecast it as a percentage of sales, or equivalently as a gross margin . Disclosure of costs is usually thinner than disclosure of revenue, so analysts often forecast consolidated lines or summary measures such as earnings before interest, taxes, depreciation, and amortization (EBITDA) margins, but the cost forecast must stay coherent with the revenue forecast.

How to forecast operating costs and working capital
Costs and working capitalkeep coherent with the revenue forecast
  • Cost of sales Memorize forecast as a % of sales (a gross margin)
    • Mix Use it faster growth in a low-margin line lowers the total margin
    • Competition Use it share lost to cheaper substitutes presses margin; differentiated launches lift it
    • Input costs Use it volume and price; lag and hedging before they reach customers
  • SG&A Memorize a mix of variable and fixed parts
    • Selling and distribution Use it largely variable: % of sales
    • General corporate costs Use it largely fixed: grow with wage inflation
  • Working capital Memorize days ratio × revenue or cost of sales ÷ 365
    • Receivables Memorize DSO × revenue
    • Inventory Memorize DIO × cost of sales
    • Payables Memorize DPO × cost of sales

Coherence has three parts.

  • Product mix . If a low-margin product, segment or region is forecast to grow faster than the rest, the overall margin should fall, even if you do not know each margin precisely.
  • Competition. A company losing share to cheaper substitutes will usually see margins fall. A company gaining share with differentiated products, especially if it also has a cost advantage, will usually see them rise.
  • Input costs. Where input prices fluctuate and reach customers only after a lag, split sales and costs into volume and price, especially for low-margin businesses, where a sudden cost shock can move operating profit a lot. Check the company’s hedging policy: a company that buys a main input a year ahead feels a price rise a year late.

Small changes matter. Cost of sales is large, so even one percentage point of gross margin on a big revenue base moves operating profit and free cash flow materially.

What happens when a cost rise is passed on?

Memorize

Passing a cost increase on to customers sounds as if it protects the margin. It protects the money, not the percentage. Cost pass-through in money terms adds the same amount to the price and to the cost, so gross profit is unchanged, but the price, which is the base of the margin ratio, is now larger, so the gross margin percentage falls.

Gross margin after a money pass-through Use it
m=P−CP+ΔCm = \frac{P - C}{P + \Delta C}

To keep the percentage, the price has to rise by the same percentage as the cost, which means by more than the money amount.

Price that keeps the margin percentage Use it
P∗=P (C+ΔC)CP^* = \frac{P\,(C + \Delta C)}{C}
Rearrange itPassing on a cost increase: margin and the price needed
The question asks for
A product sells for 100.00 with a cost of 40.00. The unit cost rises by 10.00 and the company raises its price by exactly 10.00. Its gross margin becomes closest to:

(100.00 − 40.00) ÷ (100.00 + 10.00) = 54.55%

Gross margin if the same money amount is added to the price54.55%

On your calculator
  1. 100+10=STO1the new price
  2. 100−40÷RCL1=0.545455, so 54.55%

STO store · RCL recall a stored number

  1. 100ENTER40−gross profit, unchanged
  2. 100ENTER10+÷0.545455

ENTER enter (on the HP, puts the number on the stack)

Exam tip ”Same money added to price and cost”: gross profit unchanged, margin percentage down. “Same percentage added to both”: margin percentage unchanged.

Go deeper A mix effect with unchanged segment margins

A company has two lines. Line A has sales of 60 and a 40% margin; line B has sales of 40 and a 10% margin. Total gross profit is 24 + 4 = 28 on 100, a 28.0% margin. Next year A grows 5% to 63 and B grows 20% to 48, and each keeps its own margin. Gross profit is 25.2 + 4.8 = 30.0 on sales of 111: 27.0%. Neither line got less profitable, yet the total margin fell, because the low-margin line grew faster. That is why a revenue forecast by segment should come with a margin view.

Go deeper Why cheaper production does not always lift margins

If a new technology cuts manufacturing costs across a highly competitive industry, every producer gains the cost saving and competition passes most of it to customers in lower prices. The industry’s margins may not change at all. Only a company that gets the technology first, or that is protected from competition, keeps the saving.

How do you forecast SG&A?

SG&A expenses (selling, general and administrative) are the other main operating cost. They have a looser link with sales than cost of sales does, because they mix variable and fixed parts.

  • Selling and distribution costs (commissions, delivery) are often largely variable and can be forecast as a percentage of sales.
  • General corporate costs (head office, systems) are largely fixed and are better grown at a rate based on expected wage inflation.

The approaches from Lesson 1 apply: history, a peer base rate, guidance (management is usually good at forecasting costs it controls) or your own view. Keep one-off costs such as restructuring charges separate from the run rate.

With a large fixed part, SG&A as a percentage of sales falls when sales grow quickly. This is operating leverage.

How do you forecast working capital?

Working capital is forecast through the efficiency ratios you met in the last module, combined with the revenue and cost forecasts. Rearranging each ratio gives a balance.

  • Receivables come from days sales outstanding (DSO), applied to revenue.
  • Inventory comes from days of inventory on hand (DIO, for days inventory outstanding), applied to cost of sales.
  • Payables come from days payables outstanding (DPO), applied to cost of sales.
Receivables from days sales outstanding Memorize
Receivables=DSO×Revenue365\text{Receivables} = \frac{DSO \times \text{Revenue}}{365}
Inventory from days of inventory on hand Memorize
Inventory=DIO×Cost of sales365\text{Inventory} = \frac{DIO \times \text{Cost of sales}}{365}
Payables from days payables outstanding Memorize
Payables=DPO×Cost of sales365\text{Payables} = \frac{DPO \times \text{Cost of sales}}{365}

Holding last year’s days ratios constant is the usual default (a historical-results approach). Change them only for a reason, such as new payment terms or a supply-chain change. A company converging to peers’ ratios could use a base rate instead. Do not simply grow every balance at the sales growth rate: each item has a different base and a different ratio.

Rearrange itWorking capital balance from a days ratio: solve for any one
The question asks for
A company forecasts a days ratio of 30 on a base (revenue or cost of sales, as the ratio requires) of 19.80. Using a 365-day year, the year-end balance is closest to:

30 × 19.80 ÷ 365 = 1.6274

Year-end balance1.63

On your calculator
  1. 30×19.8÷365=
  1. 30ENTER19.8×365÷

ENTER enter (on the HP, puts the number on the stack)

InteractiveForecasting margins and working capital

Try this 0 of 3

  • Margin: switch to keeping the margin % and read the price rise it needs
  • Working capital: set revenue and cost of sales back to last year's 18.0 and 10.0
  • Working capital: keep the 10% growth but make working capital release cash
100Today110Pass on in money

Each bar is the selling price: unit cost (bottom) plus gross profit (top).

New price110.00
Gross profit per unit60.00 (was 60)
Gross margin54.5% (was 60.0%)
Price rise to keep the margin25.0%

Price rises 10.0% but cost rises 25.0%: gross profit holds at 60.00, yet the margin falls from 60.0% to 54.5%.

Show working

Today: gross margin = (100 − 40) ÷ 100 = 60.00%.

Pass on in money: price 100 + 10 = 110; gross profit 110 − 50 = 60; margin 60 ÷ 110 = 54.55% (cost share 45.45%).

Keep the margin: price = new cost ÷ cost share = 50 ÷ 0.4 = 125.00, a price rise of 25.00%.

Margin after a pass-through on your calculator
  1. 100+10=STO1price 110
  2. −50=÷RCL1=margin 0.545455
  3. 50÷0.4=price to keep the margin 125

STO store · RCL recall a stored number

  1. 100ENTER10+STO1price 110
  2. 50−RCL1÷margin 0.545455
  3. 50ENTER0.4÷price to keep the margin 125

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Keeping gross profit isn't keeping margin; and growth needs more working capital even if nothing else changes.

Exam tip Receivables are about sales, so use revenue. Inventory and payables are about purchases, so use cost of sales.

Go deeper Hedging and the lag before a cost reaches the price

A company that hedges its main input a year ahead sees today’s market price only next year. A company that does not hedge sees it at once, and its margin moves with the commodity unless it can raise prices quickly. Hedging policy is usually described in the notes to the accounts, though positions are not. A short-term forecast for such a company needs volume and price split out. A long-term forecast can use the overall relationship between sales and input costs.

Memorize this

MemorizeWorking capital balances

BalanceFormulaBase
ReceivablesDSO × revenue ÷ 365revenue
InventoryDIO × cost of sales ÷ 365cost of sales
PayablesDPO × cost of sales ÷ 365cost of sales

Memory hook Receivables are owed from sales, so they use revenue. Stock and suppliers are about purchases, so they use cost of sales.

Know it cold Hold last year's days unless there is a reason to change them. Growth in revenue raises receivables and inventory, absorbing cash.

MemorizeCost pass-through

Memory hook Same money added to price and cost: profit unchanged, price (the base) bigger, so the percentage falls.

Know it cold Money pass-through: margin = (P − C) ÷ (P + ΔC). To keep the margin percentage, the price must rise by the same percentage as the cost.

MemorizeOperating cost rules

Memory hook Fixed costs give leverage: sales up, fixed cost share down.

Know it cold Cost of sales: % of sales, coherent with mix. SG&A: fixed part grows with inflation or wages; variable part with sales. Mix shifting toward a low-margin line lowers the total margin.

How to forecast operating costs and working capital
Costs and working capitalkeep coherent with the revenue forecast
  • Cost of sales Memorize forecast as a % of sales (a gross margin)
    • Mix Use it faster growth in a low-margin line lowers the total margin
    • Competition Use it share lost to cheaper substitutes presses margin; differentiated launches lift it
    • Input costs Use it volume and price; lag and hedging before they reach customers
  • SG&A Memorize a mix of variable and fixed parts
    • Selling and distribution Use it largely variable: % of sales
    • General corporate costs Use it largely fixed: grow with wage inflation
  • Working capital Memorize days ratio × revenue or cost of sales ÷ 365
    • Receivables Memorize DSO × revenue
    • Inventory Memorize DIO × cost of sales
    • Payables Memorize DPO × cost of sales
Gross margin after a money pass-through Use it
m=P−CP+ΔCm = \frac{P - C}{P + \Delta C}
Quick example

Price 80, cost 48; cost rises 8 and the price rises 8. (88 − 56) ÷ 88 = 32 ÷ 88 = 36.4%, down from 40.0%. Gross profit stays 32.

On your calculator
  1. 80+8=STO1 88
  2. 80−48÷RCL1= 0.3636

STO store · RCL recall a stored number

  1. 80ENTER48− 32
  2. 80ENTER8+÷ 0.3636

ENTER enter (on the HP, puts the number on the stack)

Price that keeps the margin percentage Use it
P∗=P (C+ΔC)CP^* = \frac{P\,(C + \Delta C)}{C}
Quick example

Price 80, cost 48, cost +8. P = 80 × 56 ÷ 48 = 93.33, a 16.7% price rise, the same percentage as the cost rise (8 ÷ 48)

On your calculator
  1. 48+8×80÷48= 93.33
  1. 48ENTER8+80×48÷ 93.33

ENTER enter (on the HP, puts the number on the stack)

Receivables from days sales outstanding Memorize
Receivables=DSO×Revenue365\text{Receivables} = \frac{DSO \times \text{Revenue}}{365}
Quick example

Revenue 730, DSO 40. 40 × 730 ÷ 365 = 80. Revenue, not cost of sales.

On your calculator
  1. 40×730÷365= 80
  1. 40ENTER730×365÷ 80

ENTER enter (on the HP, puts the number on the stack)

Inventory from days of inventory on hand Memorize
Inventory=DIO×Cost of sales365\text{Inventory} = \frac{DIO \times \text{Cost of sales}}{365}
Quick example

Cost of sales 292, DIO 45. 45 × 292 ÷ 365 = 36.0. Cost of sales, not revenue.

On your calculator
  1. 45×292÷365= 36
  1. 45ENTER292×365÷ 36

ENTER enter (on the HP, puts the number on the stack)

Payables from days payables outstanding Memorize
Payables=DPO×Cost of sales365\text{Payables} = \frac{DPO \times \text{Cost of sales}}{365}
Quick example

Cost of sales 292, DPO 60. 60 × 292 ÷ 365 = 48.0. A longer DPO means a larger payable and less cash tied up.

On your calculator
  1. 60×292÷365= 48
  1. 60ENTER292×365÷ 48

ENTER enter (on the HP, puts the number on the stack)

How it is asked

  1. Balance from a days ratio

    Revenue 730, DSO stays at 40 days. Year-end receivables?

    40 × 730 ÷ 365 = 80.0. Dividing revenue by DSO (18.25) is the trap.

  2. Margin after a money pass-through

    Price 100, cost 60; cost +10 and price +10. New gross margin?

    (110 − 70) ÷ 110 = 36.4%. Assuming the margin is unchanged (40%) is the trap.

  3. Fixed SG&A and growth

    SG&A is largely fixed; revenue grows 20%. SG&A as a % of revenue?

    Falls (operating leverage).

  4. Basis for inventory

    Cost of sales 292, revenue 400, DIO 45. Inventory?

    45 × 292 ÷ 365 = 36.0. Using revenue (49.3) is the trap.

Exam traps

  • Assuming the margin percentage is unchanged when a cost increase is passed on in money terms: gross profit is kept, the margin falls.
  • Using revenue instead of cost of sales for inventory and payables, or cost of sales for receivables.
  • Forecasting SG&A as a fixed percentage of sales when much of it is fixed.
  • Growing every working-capital item at the sales growth rate: each item has its own base and days ratio.
  • Forecasting margins line by line without checking mix: a faster-growing low-margin line lowers the total margin.

Checkpoint

4 exam-style questions. About 90 seconds each.

  1. 1A company forecasts revenue of EUR 730 million and expects its days sales outstanding to stay at 40 days. Its forecast year-end receivables are closest to:

  2. 2A product's cost of sales is 60 per unit and its price 100. Input costs rise by 10 per unit and the company raises its price by exactly 10. Its gross margin becomes closest to:

  3. 3A company's SG&A is largely fixed. If its revenue is forecast to grow 20%, SG&A as a percentage of revenue will most likely:

  4. 4A company forecasts revenue of USD 400 million, cost of sales of USD 292 million and a days of inventory on hand of 45. Using a 365-day year, forecast inventory is closest to:

Key takeaways

  • Cost of sales is forecast as a percentage of sales, coherent with mix, competition and input costs.
  • Passing on a cost rise in money terms keeps gross profit but lowers the margin percentage.
  • A large fixed share in SG&A gives operating leverage: its share of sales falls as sales grow.
  • Working capital balance = days ratio × (revenue or cost of sales) ÷ 365. Growth absorbs cash.
Gross margin after a money pass-through Use it
m=P−CP+ΔCm = \frac{P - C}{P + \Delta C}
Quick example

Price 80, cost 48; cost rises 8 and the price rises 8. (88 − 56) ÷ 88 = 32 ÷ 88 = 36.4%, down from 40.0%. Gross profit stays 32.

On your calculator
  1. 80+8=STO1 88
  2. 80−48÷RCL1= 0.3636

STO store · RCL recall a stored number

  1. 80ENTER48− 32
  2. 80ENTER8+÷ 0.3636

ENTER enter (on the HP, puts the number on the stack)

Price that keeps the margin percentage Use it
P∗=P (C+ΔC)CP^* = \frac{P\,(C + \Delta C)}{C}
Quick example

Price 80, cost 48, cost +8. P = 80 × 56 ÷ 48 = 93.33, a 16.7% price rise, the same percentage as the cost rise (8 ÷ 48)

On your calculator
  1. 48+8×80÷48= 93.33
  1. 48ENTER8+80×48÷ 93.33

ENTER enter (on the HP, puts the number on the stack)

Receivables from days sales outstanding Memorize
Receivables=DSO×Revenue365\text{Receivables} = \frac{DSO \times \text{Revenue}}{365}
Quick example

Revenue 730, DSO 40. 40 × 730 ÷ 365 = 80. Revenue, not cost of sales.

On your calculator
  1. 40×730÷365= 80
  1. 40ENTER730×365÷ 80

ENTER enter (on the HP, puts the number on the stack)

Inventory from days of inventory on hand Memorize
Inventory=DIO×Cost of sales365\text{Inventory} = \frac{DIO \times \text{Cost of sales}}{365}
Quick example

Cost of sales 292, DIO 45. 45 × 292 ÷ 365 = 36.0. Cost of sales, not revenue.

On your calculator
  1. 45×292÷365= 36
  1. 45ENTER292×365÷ 36

ENTER enter (on the HP, puts the number on the stack)

Payables from days payables outstanding Memorize
Payables=DPO×Cost of sales365\text{Payables} = \frac{DPO \times \text{Cost of sales}}{365}
Quick example

Cost of sales 292, DPO 60. 60 × 292 ÷ 365 = 48.0. A longer DPO means a larger payable and less cash tied up.

On your calculator
  1. 60×292÷365= 48
  1. 60ENTER292×365÷ 48

ENTER enter (on the HP, puts the number on the stack)

Questions about this lesson?

Where this comes back

Questions candidates ask

How do analysts forecast cost of sales?

Usually as a percentage of sales (a gross margin), adjusted for product mix, competition and input cost trends. Companies with low margins and volatile inputs need price and volume split out.

How do you forecast accounts receivable?

Multiply the forecast days sales outstanding by forecast revenue and divide by 365. Inventory and payables work the same way with cost of sales.

Does passing on a cost increase protect margins?

Only if the price rises by the same percentage as the cost. Passing on the same money amount keeps gross profit but lowers the margin percentage.

Spotted an error? Tell us and we will fix it.

  1. What to forecast, how, and over what horizon
  2. Forecasting revenue: top-down, bottom-up and hybrid
  3. Forecasting costs, margins and working capital
  4. Forecasting capital expenditure and capital structure
  5. Scenario analysis in forecasting

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