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Worked-example setupScope and assumptions
- Beacon's Year 5 income and cash flows cover the full year ended December 31.
- Opening and ending positions use the same entity, currency, units, aggregate reporting basis, and statement version.
- No material midyear event makes the beginning-ending average unrepresentative in this bounded exercise.
- Total equity is positive and no preferred equity or noncontrolling interest is present.
- Period
- Year 5 ended December 31
- Units
- Whole USD for source amounts; ratios in decimal form and percentages as stated
- Rounding
- Full precision internally; percentages displayed to two decimal places when needed
Start from the labels, not the calculator
Beacon's Year 5 net sales and net income are period flows. The opening asset and equity balances are measured at the start of Year 5; the ending balances are measured at December 31. All amounts belong to Beacon, use whole USD, and share the stipulated reporting basis.
That labeling is part of the calculation. Without it, $24,000 ÷ $110,000
looks just as executable as the intended ROE.
Build the two average denominators
average total assets = ($180,000 + $220,000) ÷ 2 = $200,000
average total equity = ($90,000 + $110,000) ÷ 2 = $100,000
The opening and ending equations also tie:
$180,000 = $90,000 liabilities + $90,000 equity
$220,000 = $110,000 liabilities + $110,000 equity
The averages preserve that relation: $200,000 = $100,000 + $100,000.
Compute the declared returns
ROA = $24,000 ÷ $200,000 = 12%
ROE = $24,000 ÷ $100,000 = 24%
If an analyst silently used ending balances, ROA would be about 10.91% and ROE about 21.82%. Those quotients are not arithmetic errors. They answer a different, unstated measurement question by pairing a full-year flow with a closing-date stock.
Reconciliation and reasonableness
Beacon's equity rollforward provides another control:
$90,000 opening equity + $24,000 net income − $4,000 distributions
= $110,000 ending equity
The ratio workpaper should retain that tie rather than treating average equity as a detached field.
Interpretation
Beacon reports twelve cents of net income per average asset dollar and twenty-four cents per average equity dollar under this module's convention. The calculation does not prove that the two-point average represents a year with a large acquisition or seasonal swing. A real analyst would inspect the balance path and change the convention openly if the endpoints were not representative.
Common wrong paths
- Use ending balances because they are newest: recency does not repair the stock-versus-flow mismatch.
- Average unmatched observations: the prior and current balances must share entity, scope, units, basis, and version.
- Call the average exact: it is a declared approximation whose adequacy depends on the year's balance path.
Verified calculation · performance return analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- entities
- 1 field
Inspect data
{
"beacon": {
"defined_debt_at_end": null,
"ending": {
"total_assets": 220000,
"total_equity": 110000,
"total_liabilities": 110000
},
"net_income": 24000,
"net_sales": 240000,
"opening": {
"total_assets": 180000,
"total_equity": 90000,
"total_liabilities": 90000
},
"reported_operating_cash_flow": 30000
}
}Recomputed result
| Measure | Value |
|---|---|
| average total assets | 200,000 |
| average total equity | 100,000 |
| average total liabilities | 100,000 |
| leverage identity difference | 0 |
| return on assets | 0.12 |
| return on equity | 0.24 |
| roa identity difference | 0 |
| roe identity difference | 0 |