Expense models: margins, itemization and operating leverage

What are the three ways to forecast expenses?

A constant growth model assumes expenses grow with revenue. A disaggregated model lets the gross and operating margins change from the base year, according to the company’s cost structure. There are three approaches: a historical expense model (past growth, or a regression on revenue), itemization of the economically significant expenses, and a direct profit margin assumption.

Expense or profit modelkeep costs coherent with revenue

• Historical Memorize past growth, or regress expense changes on revenue changes
  • Intercept a Memorize fixed cost component
  • Slope b Memorize variable with revenue
• Itemization Memorize model big costs the vendor data hide, from as-reported statements
• Direct margin assumption Memorize assume the gross or operating margin; check the implied cost growth

Whichever you pick, keep the cost forecast coherent with the revenue forecast.

• 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.

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

How do you forecast an expense from revenue with a regression?

Use it

Growing an expense at its own past rate ignores its link to revenue. A regression of expense changes on revenue changes uses that link.

$$\Delta \text{Expense}_t = a + b \times \Delta \text{Revenue}_t$$

The intercept as the fixed cost component , a, estimates growth that has nothing to do with revenue. The slope as the variable component , b, estimates how much the expense moves per unit of revenue change. Use changes (absolute or percentage), never levels, because regressing levels on levels can suggest a relationship that is not there. The method suits mature companies with a stable cost structure and is weak for early-stage or highly cyclical ones. The regression itself is covered in Quantitative Methods.

Exam tip A positive intercept with a slope below 1 means costs outgrow revenue in slow years and lag it in fast years. A negative intercept with a slope above 1 means the reverse.

Why itemize the costs that matter?

Standardized statements from data vendors can hide a company’s most important costs, which is the gap between standardized versus as-reported statements . An airline’s fuel and staff costs, or a trucking company’s diesel and driver wages, may sit inside one “cost of services” line. When a cost follows its own driver (fuel prices are not set by the company’s revenue), find it in the as-reported statements or the annual report and give it its own line. That is the itemization of economically significant expenses .

What does a margin assumption imply about costs?

Use it

Instead of forecasting each expense, an analyst can make a direct profit margin assumption : the margin on earnings before interest and taxes (EBIT), a driver of both free cash flow to the firm and free cash flow to equity, or, where direct costs dominate, the gross margin. Every margin assumption implies an expense growth rate, so check the implied expense growth .

$$\text{COGS}_{t+1} = (1 - m_{t+1}) \times \text{Revenue}_{t+1}$$

Rising margins mean revenue must outgrow expenses on average, which needs company and industry analysis to back it.

A net margin also carries items unrelated to revenue, such as write-downs, one-off restructuring or legal costs, interest expense and income, and taxes. Forecast gross or operating margins from the business and treat those items separately.

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.

How do you forecast selling, general and administrative expenses (SG&A)?

SG&A expenses are the other main operating cost. They have a looser link with sales than COGS does, because they mix fixed and variable costs .

• 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.

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. In regression terms, the fixed part shows up in the intercept and the variable part in the slope.

Go deeper SG&A with a fixed and a variable part

A company has SG&A of 25 on sales of 100: a fixed 15 and a variable 10 (10% of sales). Sales are forecast to grow 20% to 120, and the fixed part rises 3% with wages.

1. Fixed part: 15 × 1.03 = 15.45. Variable part: 10% × 120 = 12.00.
2. SG&A: 15.45 + 12.00 = 27.45.
3. As a percentage of sales: 27.45 ÷ 120 = 22.9%, down from 25.0%. Forecasting SG&A at a flat 25% would give 30.0 and overstate costs by 2.55.

On your calculator

TI BA II Plus HP 12C

1. 15×1.03=STO1 15.45
2. 0.1×120+RCL1= 27.45
3. ÷120= 0.22875

STO store · RCL recall a stored number

1. 15ENTER1.03× 15.45
2. 0.1ENTER120×+ 27.45
3. 120÷ 0.22875

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

How do fixed costs swing margins across scenarios?

When part of the cost base is fixed, margins rise sharply in strong years and fall in weak ones, because the fixed part is spread over more or less revenue. That is operating leverage .

$$\text{COGS} = F + v \times \text{Revenue} \qquad \text{Gross margin} = 1 - \text{COGS} \div \text{Revenue}$$

Working capital belongs to the asset model in the next lesson, where it grows with assumed rates. Forecasting it from days ratios is taught in Financial Statement Analysis, financial statement modeling.