What is the Degree of Financial Leverage (DFL)?
– Definition: The degree of financial leverage (DFL) quantifies how a percentage change in a company’s operating income (EBIT: earnings before interest and taxes) translates into a percentage change in earnings per share (EPS). It isolates the effect of fixed financing costs (interest) on EPS volatility assuming shares outstanding and interest expense are unchanged.
Why DFL matters
– DFL shows how sensitive shareholders’ earnings are to swings in business performance. A larger DFL means EPS will move proportionally more than operating income when EBIT changes. Management uses DFL when deciding how much debt to carry; investors use it to gauge earnings risk tied to capital structure. Different industries typically tolerate different DFL levels: capital-intensive or highly leveraged sectors (airlines, utilities, banks, some retailers) often run higher DFLs than low-capital businesses.
Key formulas (with assumptions)
– Percentage-change definition:
DFL = (% change in EPS) / (% change in EBIT)
Assumptions: number of shares constant; interest expense fixed; taxes ignored or treated separately.
– Algebraic shortcut (when taxes and share count are constant):
DFL = EBIT / (EBIT − Interest)
This comes from EPS = (EBIT − Interest) / Shares; rearrange to express EPS sensitivity to EBIT.
What to watch out for (important caveats)
– If EBIT − Interest is very small or zero, DFL → very large or undefined. That indicates EPS is extremely sensitive (or that EPS would be zero/negative).
– The simple formula ignores taxes, preferred dividends, convertible securities, and changes in share count (e.g., buybacks or issuance). Adjustments are needed when those items matter.
– A high DFL raises potential reward and risk: it amplifies gains when operating income rises and magnifies losses when operating income falls.
– Acceptable DFL varies by industry and business cycle; there is no universal “safe” number.
Worked numeric example (step-by-step)
Assumptions:
– Company: BigBox Inc.
– Year 1: EBIT = $100 million, Interest expense = $10 million, Shares outstanding = 100 million.
– Ignore taxes for simplicity and assume interest and shares remain constant.
Step 1 — Compute EPS in Year 1
– EPS1 = (EBIT − Interest) / Shares = ($100m − $10m) / 100m = $90m / 100m = $0.90 per share.
Step 2 — Compute DFL using shortcut formula
– DFL = EBIT / (EBIT − Interest) = $100m / ($100m − $10m) = 100 / 90 ≈ 1.111… ≈ 1.11.
– Interpretation: A 1% change in EBIT will produce about a 1.11% change in EPS.
Step 3 — Apply a 20% increase in EBIT to Year 2
– New EBIT = $100m × 1.20 = $120m.
– EPS2 = ($120m − $10m) / 100m = $110m / 100m = $1.10.
– EPS change = ($1.10 − $0.90) / $0.90 = $0.20 / $0.90 ≈ 22.22%.
– Check with DFL: 1.11 × 20% ≈ 22.2% → matches the direct EPS calculation.
Step 4 — Apply a 30% decrease in EBIT
– New EBIT = $100m × 0.70 = $70m.
– EPS = ($70m − $10m) / 100m = $60m / 100m = $0.60.
– EPS change = ($0.60 − $0.90) / $0.90 = −0.33… = −33.33%.
– Check with DFL: 1.11 × (−30%) = −33.33% → matches.
Practical checklist — How to compute and use DFL
1. Gather inputs:
– Current EBIT (operating income).
– Current interest expense (fixed financing cost).
– Shares outstanding (if you want EPS levels).
2. Verify assumptions:
– Are shares fixed? Is interest fixed? Are taxes negligible or to be modelled separately?
3. Calculate DFL:
– Use DFL = EBIT / (EBIT − Interest) for a quick sensitivity factor.
– Or compute % changes in
% changes in EPS and EBIT and take the ratio:
– DFL = (%ΔEPS) / (%ΔEBIT).
4. Run a sanity check with a numeric example
– Example inputs (simple): EBIT = $50m, Interest = $10m, Shares = 20m.
– Compute DFL by formula: DFL = 50 / (50 − 10) = 50 / 40 = 1.25.
– Simulate a 20% fall in EBIT: New EBIT = 50 × 0.80 = 40.
– EPS before = (EBIT − Interest) / Shares = (50 − 10) / 20 = 40 / 20 = $2.00.
– EPS after = (40 − 10) / 20 = 30 / 20 = $1.50.
– %ΔEBIT = −20%; %ΔEPS = (1.50 − 2.00) / 2.00 = −25%.
– Check: DFL × %ΔEBIT = 1.25 × (−20%) = −25% → matches.
Why the simple formula works (brief derivation)
– EPS = (EBIT − Interest) × (1 − t) / Shares, where t is the tax rate.
– %ΔEPS = ΔEBIT / (EBIT − Interest) because Interest and Shares are fixed and (1 − t)
…cancels out. Rearranging the approximate percentage-change relationship gives the familiar simple DFL formula at a particular EBIT level:
DFL = EBIT / (EBIT − Interest)
This is the “degree of financial leverage” at that EBIT point. It tells you how many percent EPS (earnings per share) will change for a 1% change in EBIT, holding interest, shares, and (for small changes) tax rate constant.
Worked recap (using the numbers from the prior example)
– EBIT = 50; Interest = 10 → DFL = 50 / (50 − 10) = 50 / 40 = 1.25.
– Interpretation: a 1% change in EBIT produces a 1.25% change in EPS (for small changes).
When the simple formula needs adjustment
– Preferred dividends: If the firm pays preferred dividends, they reduce earnings available to common shareholders. The DFL becomes:
DFL = EBIT / [EBIT − Interest − PrefDiv/(1 − t)]
where PrefDiv is preferred dividends and t is the tax rate. This follows from linearizing EPS = [(EBIT − Interest)(1 − t) − PrefDiv] / Shares.
– Very large changes: The percent-change linear approximation breaks down for large ΔEBIT. Use actual recalculation of EPS before and after a scenario rather than relying on DFL for big shocks.
– Variable interest or changing shares: If interest expense or share count will change with the scenario (floating-rate debt, planned buybacks/issuance), the simple
simple formula is misleading. If interest expense or the share count will change under the scenario (floating-rate debt, planned buybacks or issuance), recalculate EPS with the new interest and/or shares rather than plugging changed EBIT into the static DFL formula.
Other practical considerations
– Taxes and preferred dividends: If taxes or preferred dividends are material, use the adjusted denominator that converts preferred dividends to a pre‑tax-equivalent amount: Denominator = EBIT − Interest − PrefDiv/(1 − t). This comes from linearizing EPS = [(EBIT − Interest)(1 − t) − PrefDiv] / Shares. State assumptions about t (marginal tax rate) and whether pref dividends are fixed.
– Small vs large changes: DFL is a linear (first‑order) approximation. For large changes in EBIT, compute EPS before and after the scenario and measure the exact percentage change in EPS rather than relying on the approximate DFL multiplier.
– Changing capital structure items: If debt interest, shares outstanding, or preferred dividends will change as EBIT changes, incorporate those new values in the “after” EPS calculation. That yields an accurate percentage change.
– Negative or zero denominators: If EBIT is close to the break‑even point (EBIT ≈ Interest + PrefDiv/(1 − t)), the denominator approaches zero and DFL → ∞ (very high sensitivity). Interpret such results with caution; they indicate a small adverse move could wipe out EPS or make it negative.
Step‑by‑step: how to calculate DFL (practical checklist)
1. Choose the baseline EBIT (E0) and the alternative EBIT (E1) for the scenario you want to test. For small changes you may use a small ΔEBIT (e.g., ±1%).
2. Gather financing items at baseline: interest expense (I), preferred dividends (PrefDiv), tax rate (t), and shares outstanding (S). Decide whether any of these will change under the scenario; if so, prepare post‑scenario values.
3. Compute baseline EPS: EPS0 = [(E0 − I) (1 − t) − PrefDiv] / S.
4. Compute scenario EPS: EPS1 = [(E1 − I′) (1 − t) − PrefDiv′] / S′ (use primes for changed values).
5. Percent changes:
– %ΔEBIT = (E1 − E0) / E0.
– %ΔEPS = (EPS1 − EPS0) / EPS0.
6. Exact scenario DFL = %ΔEPS / %ΔEBIT.
7. For a quick approximation (small change, no preferred dividends or tax adjustments), use DFL ≈
≈ EBIT / (EBIT − Interest)
Explanation and quick check
– This approximation assumes: small percentage changes in EBIT, no preferred dividends, constant tax rate, and no change in shares outstanding. Under those conditions the (1 − t) and shares cancel and DFL reduces to EBIT divided by (EBIT − interest expense).
– Numerical quick check: if EBIT = $200 and interest = $50, DFL ≈ 200 / (200 − 50) = 200 / 150 = 1.333. A 5% rise in EBIT would then imply roughly a 6.67% rise in EPS (5% × 1.333).
Worked exact-example (step-by-step)
1. Inputs
– Baseline EBIT (E0) = $200
– Interest expense (I) = $50
– Tax rate (t) = 30% (0.30)
– Shares outstanding (S) = 1,000
– No preferred dividends
2. Baseline EPS
– EPS0 = [(E0 − I) × (1 − t)] / S
– EPS0 = [(200 − 50) × 0.70] / 1000 = (150 × 0.70) / 1000 = 105 / 1000 = $0.105
3. Scenario: EBIT increases by 5% → E1 = 200 × 1.05 = $210
– EPS1 = [(210 − 50) × 0.70] / 1000 = (160 × 0.70) / 1000 = 112 / 1000 = $0.112
4. Percent changes
– %ΔEBIT = (210 − 200) / 200 = 0.05 = 5%
– %ΔEPS = (0
.0666667) / 0.105 = 0.007 / 0.105 = 0.0666667 = 6.6667%
– DFL = %ΔEPS / %ΔEBIT = 6.6667% / 5% = 1.3333 (or 4/3)
5. Alternate (direct) formula and interpretation
– For small changes, DFL at a given EBIT is: DFL = EBIT / (EBIT − Interest)
– Plugging in baseline values: DFL = 200 / (200 − 50) = 200 / 150 = 1.3333
– Interpretation: A DFL of 1.3333 means EPS changes about 33.33% more (in percentage terms) than EBIT. Higher interest (more financial leverage) raises DFL; higher EBIT (relative to interest) lowers DFL.
Assumptions and caveats
– This uses a small-change (linear) approximation; for very large percentage moves the approximation becomes less precise.
– Taxes and number of shares cancel in the DFL ratio here because EPS is proportional to (EBIT − Interest) when no preferred dividends exist.
– DFL measures sensitivity of EPS to changes in operating income (EBIT). It is not a full measure of default or bankruptcy risk.
Educational disclaimer
This is educational information, not individualized investment advice. Do your own research or consult a licensed financial professional before making investment or financing decisions.
References
– Investopedia — Degree of Financial Leverage (DFL): https://www.investopedia.com/terms/d/dfl