Why the Business Cycle Can Distort a Multiple
For a cyclical firm, earnings can rise and fall sharply as demand, prices, capacity utilization, and input costs change. Commodity producers, manufacturers, transportation companies, and construction-related businesses are examples of sectors in which earnings may be unusually sensitive to economic conditions. In a strong part of the cycle, reported earnings may be much higher than the firm can sustain over a full cycle. In a weak part, they may be unusually low.
A valuation multiple divides a market value by a financial measure. The price-to-earnings ratio, or P/E, divides the market price per share by earnings per share. If the share price does not move as much or as quickly as earnings, the reported P/E can move in the opposite direction from the firm’s apparent operating performance: it may look low at an earnings peak and high at a trough. That pattern is a warning about the denominator, not a valuation conclusion by itself.
Normalization does not mean choosing whichever earnings figure makes a company look attractive. It requires a reasoned estimate of sustainable activity and profitability, using information such as a full-cycle history, typical margins, capacity utilization, and the firm’s current operating conditions. The method and adjustments should be applied consistently to the company and its comparables.
The Denominator Effect in P/E
Let \(P\) denote share price and \(E\) denote earnings per share for the period used in the calculation. When earnings are positive, the P/E is \(P/E\). If the price is held fixed while earnings increase, the ratio decreases; if earnings decrease, it increases. Thus, a low P/E is not automatically evidence that a share is cheap. The denominator may simply reflect temporarily high cyclical earnings.
A simple model makes the cycle effect explicit. Suppose reported earnings equal normalized earnings multiplied by \(1+c\), where \(c\) is the proportional cyclical deviation from normalized earnings. For example, \(c=0.50\) represents earnings 50% above normalized earnings; \(c=-0.50\) represents earnings 50% below them. If the share price is unchanged, then:
This relationship assumes positive normalized and reported earnings and a fixed share price for the comparison. It does not assert that market prices actually remain fixed through a cycle. Prices may anticipate future earnings, and other information may change investors’ expectations. The equation isolates the mechanical impact of changing the earnings denominator.
The justification follows directly from substitution: replace \(E_{\text{reported}}\) in \(P/E_{\text{reported}}\) with \(E_{\text{normalized}}(1+c)\), then divide the numerator and denominator by \(E_{\text{normalized}}\). When \(c\) is positive, the reported P/E is below the normalized P/E; when \(c\) is negative but greater than \(-1\), it is above the normalized P/E. This is why comparing spot P/Es without considering cycle position can reverse the apparent ranking of firms.
Worked Example: A Firm at the Peak and the Trough
Worked Example: A Firm at the Peak and the Trough
A hypothetical industrial supplier has a share price of $96. Its normalized earnings per share are estimated at $6. At a cycle peak, earnings per share are $10; at a trough, they are $2. Calculate the P/E at each stage and compare them with the normalized P/E.
Method. Divide the same share price by each earnings measure, keeping the period and per-share units consistent.
At the peak: \(\text{P/E}=96/10=9.6\). The firm appears to have a P/E of 9.6 using peak earnings.
At the trough: \(\text{P/E}=96/2=48\). The P/E is 48 using trough earnings.
Using normalized earnings: \(\text{P/E}=96/6=16\). The normalized P/E is 16.
The arithmetic checks: peak earnings are \(10/6=1.6667\) times normalized earnings, so the peak P/E is \(16/1.6667=9.6\). Trough earnings are \(2/6=1/3\) of normalized earnings, so the trough P/E is \(16/(1/3)=48\). The very low peak P/E does not, by itself, show that the shares are inexpensive; the high trough P/E does not, by itself, show that they are expensive.
Common mistake avoided: Treating the 9.6 peak P/E as directly comparable with a peer’s P/E based on ordinary earnings. The comparison is meaningful only after checking whether the peer’s earnings are measured at a similar cycle stage or are normalized on a comparable basis.
Estimating Normalized Earnings
There is no single mechanical normalization formula appropriate to every cyclical company. A practical estimate begins by identifying the source of the cycle and selecting evidence that represents a full cycle rather than one unusually strong or weak year. The analyst may use historical earnings adjusted for unusual items, or build an estimate from sustainable revenue, margins, financing costs, taxes, and share count. The second approach can make assumptions visible; the first can be informative when the history spans a representative cycle.
Determine which operating drivers are unusually strong or weak, such as selling prices, sales volumes, input costs, or capacity utilization.
Use a full-cycle history or estimate sustainable revenue and margins. Do not assume that the latest year is representative simply because it is the most recent.
Remove or replace clearly nonrecurring effects where justified, and apply the same treatment to relevant comparison firms.
Divide the market price by normalized earnings per share, then state how the result differs from the multiple based on reported earnings.
A historical average is only as useful as the period and adjustments behind it. A sample containing only boom years is not a full-cycle estimate. A simple average may also be distorted by a major acquisition, a change in business mix, or one-time gains and losses. If the company has changed substantially, older earnings may not describe its current earning capacity. Normalization is therefore an analytical judgment that should be disclosed, not a substitute for judgment.
Worked Example: Building Normalized Earnings From Operations
Worked Example: Building Normalized Earnings From Operations
A hypothetical equipment maker reports amounts in millions of dollars. For a representative year, estimated normalized revenue is $1,000 million and the normalized operating margin is 10%. Annual interest expense is $30 million. Assume a 25% tax rate on positive pretax income and 25 million shares outstanding. The current share price is $42. Calculate normalized earnings per share and the normalized P/E. For context, at the cycle peak, revenue was $1,200 million and operating margin was 15%; at the trough, revenue was $800 million and margin was 5%. Interest expense, tax rate, and shares are the same at each stage.
Method. Estimate normalized net income from sustainable operating profit, then divide by shares to obtain normalized earnings per share. Apply the same sequence to the peak and trough so the comparison is consistent.
Normalized case: Operating income is \(1{,}000\times 0.10=\$100\) million. Pretax income is \(100-30=\$70\) million. Taxes are \(70\times0.25=\$17.5\) million, so net income is \(70-17.5=\$52.5\) million. Earnings per share are \(52.5/25=\$2.10\). The normalized P/E is \(42/2.10=20.0\).
Peak case: Operating income is \(1{,}200\times0.15=\$180\) million. Pretax income is \(180-30=\$150\) million; taxes are \(150\times0.25=\$37.5\) million; net income is \(\$112.5\) million. Earnings per share are \(112.5/25=\$4.50\), giving a peak P/E of \(42/4.50=9.3333\).
Trough case: Operating income is \(800\times0.05=\$40\) million. Pretax income is \(40-30=\$10\) million; taxes are \(10\times0.25=\$2.5\) million; net income is \(\$7.5\) million. Earnings per share are \(7.5/25=\$0.30\), giving a trough P/E of \(42/0.30=140.0\).
The results are internally consistent: the same $42 share price is divided by $4.50, $2.10, and $0.30 per share. The normalized P/E of 20.0 lies between the peak multiple of 9.3333 and the trough multiple of 140.0. These amounts are reported without intermediate rounding; the multiples are rounded to four decimal places.
Common mistake avoided: Comparing revenue or operating income at one cycle stage with net earnings at another. The calculation carries each scenario through interest, taxes, and shares so that every P/E uses earnings per share on the same basis.
Making Cycle-Aware Comparisons
When comparing companies, first establish whether their reported earnings reflect similar conditions. Two firms in the same industry can still occupy different cycle positions because of geography, product mix, contracts, inventory timing, or operating leverage. A firm with fixed costs may experience a larger earnings swing than one with a flexible cost base. Consequently, a sector label alone does not prove that two firms are at equivalent points in the cycle.
If cycle stages differ, comparing normalized multiples may be more informative than comparing current multiples. If reliable normalization is not possible, a cautious comparison can instead describe the stage difference and avoid treating the spot multiple ranking as a definitive valuation ranking. The same discipline applies to other earnings-based ratios: a cyclically elevated or depressed denominator can distort a multiple even if the numerator is defined consistently.
| Observed condition | Potential effect on a reported multiple | Cycle-aware response |
|---|---|---|
| Earnings unusually high | Multiple may look unusually low | Compare with sustainable earnings or firms at a similar peak stage |
| Earnings unusually low but positive | Multiple may look unusually high | Assess trough severity and estimate representative earnings consistently |
| Different cycle stages across peers | Spot multiples may give a misleading ranking | Align the stages or normalize the earnings bases |
| History does not represent the current firm | A historical average may misstate earning capacity | Explain the limitation and use an operating estimate with explicit assumptions |
A P/E based on zero or negative earnings does not have the usual positive-earnings interpretation: division by zero is undefined, and a negative ratio is not a conventional measure of how many dollars investors pay per dollar of positive earnings. In that situation, do not force the standard cyclical P/E interpretation. The discussion here concerns positive earnings and the distortion caused by their cycle position.
Worked Example: Ranking Two Firms on a Consistent Basis
Worked Example: Ranking Two Firms on a Consistent Basis
Two hypothetical, similar materials firms have positive earnings throughout the observed cycle. Firm A’s earnings per share over four years of a representative cycle were $2, $4, $6, and $8; its current share price is $120, and the current year is its peak. Firm B’s earnings per share over a representative cycle were $1, $2, $3, and $4; its current share price is $50, and the current year is its trough. Use the arithmetic average of the four annual earnings figures as normalized earnings per share. Compare the current and normalized P/Es.
Method. Calculate each firm’s current P/E, then calculate the four-year average earnings per share and use that common normalization rule to obtain its normalized P/E.
Firm A: Current P/E is \(120/8=15.0\). Normalized earnings per share are \((2+4+6+8)/4=20/4=\$5\). Its normalized P/E is \(120/5=24.0\).
Firm B: Current P/E is \(50/1=50.0\). Normalized earnings per share are \((1+2+3+4)/4=10/4=\$2.50\). Its normalized P/E is \(50/2.50=20.0\).
On current P/E, Firm A appears to have the lower multiple: 15.0 versus 50.0. On the stated normalized basis, Firm B has the lower multiple: 20.0 versus 24.0. The ranking reverses because Firm A is currently at a peak and Firm B at a trough. This conclusion is conditional on the problem’s equal four-year averaging method and the assumed comparability of the firms; it is not a claim that a lower normalized multiple alone establishes greater value.
Common mistake avoided: Concluding that Firm A is necessarily cheaper because its current P/E is lower. The calculation checks the cycle position and applies the same averaging method to both firms before interpreting the ranking.
Common Traps and Interpretation Limits
The most common trap is to read the multiple without asking whether the earnings are representative. Consider a firm priced at $60 with peak earnings per share of $6 and normalized earnings per share of $3. The reported peak P/E is \(60/6=10\). A mistaken conclusion is, “The shares are inexpensive because the P/E is only 10.” The correction is to calculate \(60/3=20\) on normalized earnings and recognize that peak earnings have halved the reported multiple relative to that basis.
A second trap is to treat normalization as certainty. A through-cycle estimate is an estimate, not a guarantee of future earnings. It can be wrong if the business’s economics have changed, the observed history is incomplete, or an apparently temporary condition persists. State the cycle period, the earnings measure, and material adjustments. When reasonable alternative assumptions produce different results, report that sensitivity rather than presenting one normalized P/E as exact.
Check Your Understanding
For each problem, calculate the requested multiple or comparison using the stated assumptions.
- A hypothetical firm has a share price of $45, current earnings per share of $2.25, and normalized earnings per share of $3. Calculate its current and normalized P/E. (Answer: current P/E 20.0; normalized P/E 15.0)
- A cyclical producer’s share price is $72. Its earnings per share are $6 at the peak, $3.60 on a normalized basis, and $1.80 at the trough. Calculate all three P/Es and identify which reported stage produces the lowest multiple. (Answer: peak 12.0; normalized 20.0; trough 40.0; peak produces the lowest multiple)
- A hypothetical firm has normalized revenue of $500 million and a normalized operating margin of 8%. Interest expense is $8 million, the tax rate on positive pretax income is 25%, shares outstanding are 12 million, and the share price is $30. Calculate normalized earnings per share and normalized P/E. (Answer: normalized earnings per share $2.00; normalized P/E 15.0)
- Firm A has a price of $84, current earnings per share of $7, and normalized earnings per share of $4. Firm B has a price of $30, current earnings per share of $0.75, and normalized earnings per share of $2.50. Calculate current and normalized P/Es and state which firm has the lower multiple on each basis. (Answer: A current 12.0 and normalized 21.0; B current 40.0 and normalized 12.0; A is lower on current P/E, B on normalized P/E)
- A firm’s four annual earnings-per-share figures are $2, $4, $8, and $6. The $8 figure includes a one-time gain of $2 per share; assume the gain is removed before calculating a four-year arithmetic average. The share price is $81, and current reported earnings per share are $8. Calculate the current P/E and normalized P/E. (Answer: current P/E 10.125; adjusted normalized earnings per share $4.50; normalized P/E 18.0)