Connect leverage to return on equity

Harbor and Beacon have equal 12% ROA. Harbor's ROE is 30%; Beacon's is 24%. Before calling Harbor more profitable, locate the six-point difference.

What you will be able to do

You will compute and cross-check the equity multiplier, reconcile average positions and equity, calculate direct ROE, recompose the three-step DuPont identity, and separate leverage amplification from operating return and risk.

Move from assets to equity

The equity multiplier is:

average total assets / average total equity

Beacon's average assets and equity are $200,000 and $100,000, producing 2.00. Harbor's are $200,000 and $80,000, producing 2.50. Harbor's average liabilities are ($115,000 + $125,000) ÷ 2 = $120,000.

Because each endpoint satisfies the accounting equation, the averages do too:

equity multiplier = 1 + average liabilities / average equity

For Harbor, 1 + $120,000/$80,000 = 2.50. Keep the term “liabilities.” The packet does not identify which obligations meet a chosen debt definition.

Reconcile equity before using it

Harbor's rollforward is:

$75,000 opening equity + $24,000 net income − $14,000 distributions
= $85,000 ending equity

Its average is $80,000. The distribution reduces equity outside net income. A smaller average-equity denominator can raise ROE even before comparing capital structures, so this distribution effect is distinct from the asset-to-equity multiplier used in the next section. ROE is not solely an operating score.

Complete the three-step identity

ROE = margin × turnover × equity multiplier

Beacon: 0.10 × 1.20 × 2.00 = 0.24 = 24%
Harbor: 0.08 × 1.50 × 2.50 = 0.30 = 30%

The percentage margin must be converted to decimal form before multiplication.

The same definitions must flow through adjacent terms. If turnover uses ending assets while the multiplier uses average assets, those asset amounts no longer cancel and the stated identity fails.

Amplification carries a second side

With positive ROA, a larger multiplier raises ROE mechanically. With negative ROA, it can deepen the negative equity return. Real financing also brings interest, maturity, liquidity, covenant, collateral, and refinancing effects. The multiplier contains none of that detail.

A debt-to-total-assets ratio asks a related but different date-specific question:

debt-to-total-assets = stated debt measure / total assets at the same date

If this bounded comparison explicitly defines debt as all reported liabilities, Beacon's ending ratio is $110,000 ÷ $220,000 = 50.00%; Harbor's is $125,000 ÷ $210,000 = 59.52%. Those percentages are leverage screens, not current-liquidity measures or repayment conclusions. An analyst using only interest-bearing borrowings, a covenant definition, or another supported debt scope must relabel and recompute the numerator rather than treating “debt” as a universal synonym for liabilities.

The components are not independent business dials. More leverage can change cost, investment capacity, and operating choices. Price changes can affect volume; asset reductions can affect service and capacity. DuPont is an attribution framework, not a strategy to increase every factor.

Work the full identity

Trace an ROE difference to leverage with DuPont analysis calculates both companies, checks the liabilities-to-equity relation, and retains the missing financing evidence.

Practice

Recompose ROE with a three-step DuPont identity uses a new company and amounts. Separate asset return from leverage amplification tests whether your conclusion survives the equal-ROA fact.

Exit check

Two firms have 9% ROA. Firm X has a 1.5 equity multiplier; Firm Y has 3.0. Compute ROE for each. Then explain what the difference establishes, why it is not an operating-efficiency conclusion, and which financing evidence would be required before preferring either structure.

Arithmetic self-check after you work the problem: 0.09 × 1.5 = 13.5% and 0.09 × 3.0 = 27%. The interpretation and evidence request remain yours.