FSA M11 - Formulas

Vertical common-size balance sheet

Each balance sheet item ÷ total assets (same period), expressed as a %. Shows the mix of assets used and how the company finances itself; used to compare balance sheet composition across peers.

Vertical common-size income statement

Each income statement item ÷ revenue (or total assets, especially for financial institutions), expressed as a %. Reveals the composition of costs/profit relative to revenue and shifts in revenue mix when multiple revenue sources exist.

Horizontal common-size (fixed base year)

Each item in a given period ÷ the same item's value in a chosen base year. Shows cumulative growth/decline of each item relative to the base year across multiple periods.

Horizontal common-size (prior period basis)

Percent change in each item from the immediately preceding period: (Current period value − Prior period value) ÷ Prior period value. Shows period-over-period growth rates for each line item.

Effective tax rate

Income tax provision ÷ EBT (earnings before tax). Usually a more meaningful comparison than tax as a % of sales, since it reflects the rate applied to pretax profit rather than to top-line revenue.

Four broad ratio categories

Activity ratios measure operating efficiency (e.g., receivables collection, inventory management). Liquidity ratios measure ability to meet short-term obligations. Solvency ratios measure ability to meet long-term obligations (subsets called "leverage" or "long-term debt" ratios). Profitability ratios measure ability to generate profit from assets or sales. Each captures a different aspect of the business but all inform overall cash-flow-generating ability and risk.

Context for interpreting ratios

Ratios can only be interpreted in context — compare to competitors/industry (cross-sectional) and to the company's own prior periods (trend); consistency in a ratio can actually reflect earnings-smoothing accounting choices rather than genuine stability. Evaluate ratios against: prior period trends; pre-set analyst expectations (investigate deviations); industry peers (care needed — multi-line businesses distort aggregates, business models/strategy differ, some ratios are industry-specific, and accounting method differences distort comparisons); the company's own stated goals/strategy; and the current phase of the economic/business cycle (cyclical companies' ratios improve in strong economies, weaken in recessions).

Inventory turnover

Cost of sales (COGS) ÷ Average inventory. Measures how many times inventory is sold and replaced over a period; indicates resources tied up in inventory and inventory management effectiveness (benchmark against industry — high turnover may mean efficient management or inadequate stock; low turnover may mean slow-moving/obsolete inventory).

Days of inventory on hand (DOH)

Number of days in period ÷ Inventory turnover. Shows the average number of days inventory is held before being sold.

Receivables turnover

Revenue ÷ Average receivables. Measures how many times receivables are collected and re-extended over a period; total reported revenue is typically used as a proxy for credit sales, since credit-sales-only data usually isn't available.

Days of sales outstanding (DSO)

Number of days in period ÷ Receivables turnover. Reflects how fast, on average, the company collects cash from customers extended credit.

Payables turnover

Cost of sales (COGS) ÷ Average trade payables. Measures how many times per year the company theoretically pays off all its creditors.

Number of days of payables

Number of days in period ÷ Payables turnover. Reflects the average number of days the company takes to pay its suppliers.

Working capital turnover

Revenue ÷ Average working capital. Measures how efficiently the company generates revenue from its working capital (e.g., a ratio of 4.0 means $4 of revenue per $1 of working capital); not meaningful when working capital is near zero or negative.

Fixed asset turnover

Revenue ÷ Average net fixed assets. Measures efficiency of generating revenue from fixed asset investments; a low ratio can reflect inefficiency, a capital-intensive business, a new business not yet at capacity, or simply newer (less-depreciated, higher carrying value) assets rather than true inefficiency.

Total asset turnover

Revenue ÷ Average total assets. Measures the company's overall ability to generate revenue from its asset base (e.g., a ratio of 1.20 means $1.20 of revenue per $1 of average assets); includes both fixed and current assets, so inefficient working capital management can distort the result — best analyzed alongside working capital and fixed asset turnover separately.

Current ratio

Current assets ÷ Current liabilities. Measures ability to meet short-term obligations using all current assets; higher = greater liquidity, but implicitly assumes inventory and receivables are truly liquid.

Quick ratio

(Cash + Short-term marketable investments + Receivables) ÷ Current liabilities. A more conservative liquidity measure than the current ratio, excluding inventory and other less-liquid current assets (e.g., prepaid expenses); better than the current ratio when inventory is illiquid (low inventory turnover).

Cash ratio

(Cash + Short-term marketable investments) ÷ Current liabilities. The most conservative liquidity measure, including only cash and highly marketable short-term investments; normally reliable even in a crisis, though a severe market crisis could still reduce the fair value of marketable securities.

Defensive interval ratio

(Cash + Short-term marketable investments + Receivables) ÷ Daily cash expenditures. Measures how many days the company could pay its operating expenses using only existing liquid assets, with no additional cash inflow; daily cash expenditures ≈ (total income statement expenses − non-cash expenses like D&A) ÷ days in period, excluding taxes.

Cash conversion cycle (net operating cycle)

Days of inventory on hand (DOH) + Days of sales outstanding (DSO) − Number of days of payables. Measures the time from investing in working capital to collecting cash; a shorter cycle means greater liquidity (less time financing inventory/receivables), a longer cycle means lower liquidity.

Debt-to-assets ratio

Total debt ÷ Total assets. Measures the percentage of total assets financed with debt; higher = higher financial risk, weaker solvency. Also called the "total debt ratio."

Debt-to-capital ratio

Total debt ÷ (Total debt + Total shareholders' equity). Measures the percentage of a company's capital (debt plus equity) represented by debt; higher = weaker solvency.

Debt-to-equity ratio

Total debt ÷ Total shareholders' equity. Measures debt capital relative to equity capital; higher = weaker solvency. A ratio of 1.0 (equal debt and equity) equals a 50% debt-to-capital ratio.

Financial leverage ratio

Average total assets ÷ Average total equity. Measures the amount of total assets supported by each unit of equity (e.g., a value of 3 means €1 of equity supports €3 of assets); higher = more leveraged, i.e., greater use of debt/liabilities to finance assets.

Debt-to-EBITDA ratio

Total or net debt ÷ EBITDA. Estimates how many years it would take to repay total debt using EBITDA as a proxy for operating cash flow; commonly used in debt covenants.

Interest coverage ratio

EBIT ÷ Interest payments. Measures how many times EBIT could cover interest payments (a.k.a. "times interest earned"); higher = stronger solvency, greater assurance debt can be serviced from operating earnings; common in lender/bond covenants.

Fixed charge coverage ratio

(EBIT + Lease payments) ÷ (Interest payments + Lease payments). Measures how many times earnings (before interest, taxes, and lease payments) cover combined interest and lease obligations; higher = stronger solvency and, in some contexts, a more secure preferred dividend.

Net debt (or net cash)

(Interest-bearing short-term debt + Interest-bearing long-term debt) − (Cash + Cash equivalents + Marketable securities). Reflects the idea that only debt exceeding readily available liquid assets needs to be covered by future operating cash flows; result is "net cash" if liquid assets exceed debt.

Gross profit margin

Gross profit ÷ Revenue. Shows the % of revenue left to cover operating/other expenses and generate profit; higher margin reflects some combination of higher pricing power (competitive advantage) and/or lower product costs.

Operating profit margin

Operating income ÷ Revenue. Operating income = gross profit − operating costs; a margin rising faster than gross margin signals improving control of operating costs, while a declining margin signals deteriorating cost control.

Pretax margin

EBT (earnings before tax, after interest) ÷ Revenue. Reflects the effect of leverage and non-operating items on profitability; if driven mainly by rising non-operating income, check whether that reflects a genuine, lasting shift in business focus.

Net profit margin

Net income ÷ Revenue. Net income includes both recurring and non-recurring items; the net income used should generally be adjusted for non-recurring items to better reflect potential future profitability.

Operating ROA

Operating income (or EBIT) ÷ Average total assets. Measures return on all assets before deducting interest on debt capital, reflecting the return on all financing sources (debt, liabilities, and equity) invested in the company.

ROA (standard form)

Net income ÷ Average total assets. Measures overall return earned on assets; issue: net income is the return to equity holders only (interest to creditors is already subtracted), even though assets are financed by both.

ROA (interest add-back form)

[Net income + Interest expense × (1 − Tax rate)] ÷ Average total assets. Adjusts ROA by adding back after-tax interest expense to account for the fact that assets are financed by both creditors and equity holders.

Return on invested capital (ROIC)

EBIT × (1 − Effective tax rate) ÷ Average total short- and long-term debt and equity. Measures after-tax profitability earned on all capital employed (debt and equity combined), before deducting interest on debt capital.

ROE

Net income ÷ Average total equity. Measures return earned on all equity capital (minority, preferred, and common); interest on debt capital is excluded from the numerator since it's a return to creditors, not equity.

Return on common equity

(Net income − Preferred dividends) ÷ Average common equity. Measures the return earned specifically on common equity, excluding the portion of net income paid out as preferred dividends (a return to preferred equity).

DuPont two-way decomposition: ROE = ROA × Leverage

ROE = (Net income / Average total assets) × (Average total assets / Average shareholders' equity) = ROA × Leverage. With no leverage (leverage = 1.0), ROE equals ROA exactly. If the company borrows at a rate below its marginal return on invested funds, increasing leverage raises ROE; if borrowing costs exceed that marginal return, increasing leverage lowers ROE (by depressing ROA).

DuPont three-way decomposition: ROE = Net profit margin × Total asset turnover × Leverage

ROE = (Net income / Revenue) × (Revenue / Average total assets) × (Average total assets / Average shareholders' equity). Net profit margin indicates profitability, total asset turnover indicates efficiency, and leverage indicates solvency/financing choices — together these three factors decompose ROE (note ROA = Net profit margin × Total asset turnover).

DuPont five-way decomposition: ROE = Tax burden × Interest burden × EBIT margin × Total asset turnover × Leverage

ROE = (Net income/EBT) × (EBT/EBIT) × (EBIT/Revenue) × (Revenue/Average total assets) × (Average total assets/Average shareholders' equity). Tax burden = Net income/EBT (≈ 1 − average tax rate; higher value = lower tax rate). Interest burden = EBT/EBIT (higher borrowing costs lower this term, reducing ROE; using operating income instead of EBIT also captures non-operating income effects). EBIT margin = EBIT/Revenue (operating profitability). The last two terms are total asset turnover (efficiency) and leverage (financing), as in the three-way decomposition.

Coefficients of variation (business risk)

Coefficient of variation of operating income = Std. dev. of operating income ÷ Average operating income; of net income = Std. dev. of net income ÷ Average net income; of revenues = Std. dev. of revenue ÷ Average revenue. All measure relative volatility (business risk) of the respective income statement metric.

Bank capital adequacy ratio

Various components of capital ÷ Various risk measures (risk-weighted assets, market risk exposure, or operational risk assumed). Attempts to relate a bank's solvency requirement directly to its specific level of risk exposure.

Monetary reserve requirement (cash reserve ratio)

Reserves held at central bank ÷ Specified deposit liabilities. Reflects a bank's regulatory liquidity requirement tied to monetary policy.

Liquid asset requirement (banks)

Approved "readily marketable" securities ÷ Specified deposit liabilities. A regulatory liquidity requirement measuring highly liquid securities held against deposit liabilities.

Net interest margin

Net interest income ÷ Total interest-earning assets. Measures a bank's profitability on its interest-earning asset base.

Same (comparable) store sales

Average revenue growth year over year, for stores open in both periods (no denominator; expressed as a growth rate). Isolates organic sales growth at existing stores from growth due to new store openings — key in retail.

Sales per square meter/foot

Revenue ÷ Total retail space (square meters or feet). Measures retail space productivity.

Revenue and net income per employee

Revenue ÷ Total number of employees (revenue per employee); Net income ÷ Total number of employees (net income per employee). Measure of service-company workforce productivity/profitability.

Hotel average daily rate and occupancy rate

Average daily rate = Room revenue ÷ Number of rooms sold. Occupancy rate = Number of rooms sold ÷ Number of rooms available. Together measure hotel pricing power and capacity utilization.

Average revenue per user (ARPU)

Revenue ÷ Average number of subscribers or users. Key metric for subscription or relationship-based businesses, measuring revenue generated per customer.