# Level 1 CFA® Exam:

Ratio Analysis

### Common-Size Analysis

We will begin with a common-size analysis. The common-size analysis helps us compare data of different sizes. We distinguish between:

- vertical common-size analysis, and
- horizontal common-size analysis.

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Of course, common-size analysis helps us not only analyze one company but also compare companies with each other. For example, if you know that long-term debt in one company is equal to USD 500,000 and in the other to USD 2 million, you won’t be able to state which of these companies is characterized by bigger leverage. However, if you know that for the first company long-term debt is equal to 40% of total assets and for the second one long-term debt amounts to 20% of total assets, you will be able to better evaluate the situation.

In this example, we’ve analyzed the cross-sectional data, namely the data for more than one entity in the same period. We can also analyze the so-called panel data, that is cross-sectional data for more than one period.

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As we all know a ratio is computed as one value divided by another value. Ratios help us better evaluate what is going on in a given company or companies. Remember that often we are not much interested in ratio values in isolation but rather we as financial analysts prefer to compare ratios with each other.

For example, we compare the same ratio for different companies or compare one ratio with another ratio for one company, or compare the same ratio across different periods. There are a lot of possibilities here.

When you think about ratios, you should think about the comparison and interpretation. It doesn’t mean that absolute values of ratios are not used at all. It very often depends on the goal of the analysis. If for example credit analysis is conducted, then absolute values of ratios are important.

Creditors are very often required to maintain given ratios on a specific level or take care so that ratios do not increase or decrease above or below some specified thresholds.

Financial statement ratios can be divided into specific groups. We distinguish among:

- activity ratios,
- liquidity ratios,
- solvency ratios,
- profitability ratios,
- valuation ratios,
- industry-specific and task-specific ratios,
- ratios used in credit analysis,
- segment ratios.

Remember:

- not all ratios should be used and are relevant for every company,
- when comparing ratios for different companies, remember that average ratios for companies operating in different industries may vary a lot,
- ratios for a given company should be coherent with its strategy,
- ratios for cyclical companies vary over time.

Activity ratios measure:

- how well a company manages various activities,
- how effectively assets are used by the company.

\(DSO = \frac{\text{number of days in period}}{\text{receivables turnover}}\)

- \(DSO\) - days of sales outstanding

Measures: how fast the company collects cash from customers from credit sales (in days)

Interpretation, relations, and usage: compare with norms for the industry; the higher the receivables turnover >> the lower the DSO; may be used for showing receivables aging

\(\text{inventory turnover} = \frac{COGS}{\text{average inventory}}\)

- \(COGS\) - cost of sales or cost of goods sold

**Measures:** how well inventory is managed

**Interpretation, relations, and usage:**

- compare with norms for the industry
- the higher the inventory turnover
**>>**the shorter the time when resources are tied up in inventory

\(DOH = \frac{\text{number of days in period}}{\text{inventory turnover}}\)

- \(DOH\) - days of inventory on hand

**Measures:** how well inventory is managed

**Interpretation, relations, and usage:**

- compare with norms for the industry
- the higher the inventory turnover
**>>**the lower the DOH

\(\text{receivables turnover} = \frac{\text{revenue}}{\text{average receivables}}\)

.

**Measures:** how well receivables are managed

**Interpretation, relations, and usage:**

- compare with norms for the industry
- the higher the receivables turnover
**>>**the faster the company collects cash from credit sales - too high receivables turnover
**>>**the company may lose customers to competitors that offer better credit terms - low receivables turnover
**>>**are the company’s credit and collection procedures effective?

\(PT = \frac{\text{purchases}}{\text{payables}}\)

- \(PT\) - payables turnover
- \(\text{payables}\) -
__average__trade payables

**Measures:** how many times per year the company pays off its all creditors

**Interpretation, relations, and usage:**

- compare with norms for the industry
- if the value of purchases is not available
**>>**instead use:*COGS + ending inventory – beginning inventory*

\(DPO = \frac{\text{number of days in period}}{\text{payables turnover}}\)

- \(DPO\) - number of days of payables (days payable outstanding)

**Measures:** how many days it takes the company to pay off its creditors

**Interpretation, relations, and usage: **

- compare with norms for the industry
- a high number of days of payables relative to the industry
**>>**the company is efficient in using credit facilities available**OR**the company has problems to fulfill its obligations on time

\(WCT = \frac{\text{revenue}}{\text{average working capital}}\)

- \(WCT\) - working capital turnover

working capital = current assets – current liabilities

**Measures:** how much revenue is generated from working capital

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the more revenue is generated from working capital - if working capital is close to 0
**>>**the ratio skyrockets**>>**it’s hard to draw useful conclusions**>>**use fixed asset turnover or total asset turnover instead

\(FAT = \frac{\text{revenue}}{\text{fixed assets}}\)

- \(FAT\) - fixed asset turnover
- \(\text{fixed assets}\) -
__average net__fixed assets

**Measures:** how much revenue is generated from the investment in fixed assets

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the more efficient usage of the company’s fixed assets - a low ratio
**>>**inefficiency**OR**capital-intensive business**OR**new business not operating at full capacity - drawbacks: it depends on the age of assets (depreciation impacts the value of assets
**>>**impacts the ratio); it can change a lot from period to period because investments in fixed assets are usually not that smooth as changes in revenue.

\(TAT = \frac{\text{revenue}}{\text{assets}}\)

- \(TAT\) - total asset turnover
- \(\text{assets}\) -
__average total__assets

**Measures:** how much revenue is generated from a given level of total assets

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the more efficient usage of the company’s total assets - if low
**>>**the reason might be e.g. inefficient management of working capital - it’s affected by whether the management opted for a more capital-intensive or labor-intensive strategy

Liquidity ratios measure the company's ability to meet short-term obligations. They also help us assess how quickly the company can convert assets into cash.

\(CR = \frac{\text{current assets}}{\text{current liabilities}}\)

- \(CR\) - current ratio
- \(CA\) - current assets
- \(CL\) - current liabilities

Current ratio is an example of liquidity ratio. Where, liquidity is the company's ability to meet its short-term obligations.

\(QR = \frac{\text{cash }+\text{ marketable securities } + \text{ receivables}}{\text{current liabilities}}\)

- \(QR\) - quick ratio

Quick ratio is an example of liquidity ratio. Where, liquidity is the company's ability to meet its short-term obligations.

\(\text{cash ratio } = \frac{\text{cash }+\text{ marketable securities}}{\text{current liabilities}}\)

Cash ratio is an example of liquidity ratio. Where, liquidity is the company's ability to meet its short-term obligations.

\(DIR = \frac{\text{cash } + MI + \text{ receivables}}{\text{daily cash expenditure}}\)

- \(DIR\) - defensive interval ratio
- \(MI\) -
__short-term__marketable investments

**Measures:** for how many days the company can pay its daily cash expenditures using only its liquid assets

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the liquidity - if very low
**>>**is there enough cash inflow expected in the upcoming future to meet the obligations?

\(CCC = DOH + DSO - DPO\)

- \(CCC\) - cash conversion cycle
- \(DOH\) - days of inventory on hand
- \(DSO\) - days of sales outstanding
- \(DPO\) - number of days of payables (days payable outstanding)

**Also called:** net operating cycle

**Measures: **the time from paying suppliers for materials (or inventory) to collecting the cash from the sale of goods produced from these materials (or inventory).

**Interpretation, relations, and usage:**

- the higher the cash conversion cycle
**>>**the more time it takes to get back the cash used for funding the operations - it’s not a ratio
- it’s presented as number of days

Solvency ratios measure the company's ability to meet long-term debt obligations. In other words, they tell us how much of assets is financed by debt and to what extent earnings and cash flows can cover interest expenses, lease payments, rental payments, etc.

\(DTA = \frac{\text{total debt}}{\text{total assets}}\)

- \(DTA\) - debt-to-assets ratio

**Measures:** what percentage of assets is financed with debt

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the financial risk**>>**the weaker the solvency - ‘total debt’ is defined as interest-bearing short-term debt + interest-bearing long-term debt

\(DTC = \frac{\text{debt}}{\text{debt} + \text{equity}}\)

- \(DTC\) - debt-to-capital ratio
- \(\text{debt}\) -
__total__debt - \(\text{equity}\) -
__total shareholders'__equity

Measures: what percentage of the company's capital is financed with debt.

Interpretation, relations, and usage:

the higher the ratio >> the higher the financial risk >> the weaker the solvency

'total debt' is defined as interest-bearing short-term debt + interest-bearing long-term debt

\(D/E = \frac{\text{total debt}}{\text{total equity}}\)

- \(D/E\) - debt-to-equity ratio

Debt-to-equity ratio is an example of solvency ratio. Where, solvency is the company's ability to fulfill long-term obligations.

\(\text{financial leverage} = \frac{\text{total assets}}{\text{total equity}}\)

Financial leverage is an example of solvency ratio. Where, solvency is the company's ability to fulfill long-term obligations.

\(D_{EBITDA} = \frac{\text{total debt}}{EBITDA}\)

- \(D_{EBITDA}\) - debt to EBITDA ratio
- \(EBITDA\) - earnings before interest, taxes, depreciation, and amortization

\(\text{interest coverage} = \frac{EBIT}{\text{interest payments}}\)

- \(EBIT\) - earnings before deducting interest and taxes

Measures: how many times EBIT is higher than interest payments

Interpretation, relations, and usage:

the higher the ratio >> the higher the solvency

the higher the ratio >> the easier for the company to service its debt from its operating earnings

\(FCC = \frac{\text{EBIT } + \text{ lease payments}}{\text{interest payments } + \text{ lease payments}}\)

- \(FCC\) - fixed charge coverage
- \(\text{EBIT}\) - earnings before interest and taxes

**Measures:** how many times earnings before interest, taxes, and lease payments are higher than interest payments and lease payments

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the solvency - the higher the ratio
**>>**the easier for the company to service its debt from its normal earnings

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\(GPM=\frac{GP}{R}\)

- \(GPM\) - gross profit margin
- \(GP\) - gross profit (= revenue - COGS)
- \(R\) - revenue

\(OPM = \frac{\text{operating profit}}{\text{revenue}}\)

- \(OPM\) - operating profit margin

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the profitability - operating income = gross profit – operating costs
- instead of operating income, EBIT can be used (remember: be consistent)

\(PM = \frac{\text{pretax profit}}{\text{revenue}}\)

- \(PM\) - pretax margin
- \(\text{pretax profit}\) - earnings before taxes (EBT)

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the profitability - pretax income = operating income – interest – non-operating expenses + non-operating income

\(NPM=\frac{NP}{R}\)

- \(NPM\) - net profit margin
- \(NP\) - net profit
- \(R\) - revenue

Net profit margin is also named return on sales.

\(ROA = \frac{\text{net income}}{\text{assets}}\)

- \(ROA\) - return on the assets
- \(\text{assets}\) -
__average total__assets

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the more net income is generated by a given level of assets - some analysts use net income + interest x (1 – tax rate) in the numerator
**>>**the reason for the adjustment is because the total assets are financed by equity and debt and net income relates to equity holders only

\(ROA = \frac{\text{operating income}}{\text{assets}}\)

- \(ROA\) - operating return on assets
- \(\text{assets}\) -
__average total__assets

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the profitability - operating income = gross profit – operating costs
- instead of operating income, EBIT can be used (remember: be consistent)

\(RTC = \frac{EBIT}{DE}\)

- \(RTC\) - return on total capital
- \(EBIT\) - earnings before interest and taxes
- \(DE\) - average short-term & long-term debt and equity

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the higher the profitability - instead of EBIT, operating income can be used (remember: be consistent)

\(ROE = \frac{NI}{E}=\frac{NI}{A}\times \frac{A}{E}=ROA\times{\text{leverage}}\)

- \(ROE\) - return on equity
- \(NI\) - net income
- \(E\) - average shareholders' equity
- \(A\) - average total assets

**Interpretation, relations, and usage:**

1. the higher the ratio >> the more net income is generated by a given level of equity

2. total equity = common equity + preferred equity + minority equity

\(ROE = \frac{NI}{R} \times \frac{R}{A} \times \frac{A}{E}=\\ROS\times{\text{asset turnover}}\times{\text{leverage}}\)

- \(ROE\) - return on equity
- \(NI\) - net income
- \(R\) - revenue
- \(A\) - average total assets
- \(E\) - average shareholders' equity

\(ROE = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{R} \times \frac{R}{A} \times\frac{A}{E}=\\=\text{tax burden}\times{\text{interest burden}}\times\\\times{\text{EBIT margin}}\times{\text{asset turnover}}\times{\text{leverage}}\)

- \(ROE\) - return on equity
- \(NI\) - net income
- \(EBT\) - earnings before taxes
- \(EBIT\) - earnings before deducting interest and taxes
- \(R\) - revenue
- \(A\) - average total assets
- \(E\) - average shareholders' equity

DuPont analysis is about the decomposition of ROE into its components.

It gives us the answer to the following question: **What factors drive the changes in the ROE?**

As we can see ROE is a function of: tax rate, interest burden, operating profitability, efficiency, and leverage.

\(RCE = \frac{\text{net income } - \text{ preferred dividends}}{\text{average common equity}}\)

- \(RCE\) - return on common equity

**Interpretation, relations, and usage:**

- the higher the ratio
**>>**the more net income is generated by a given level of equity - it’s the return made only by common equity

Valuation ratios are used in the valuation process to value the equity of the company.

Examples of valuation ratios:

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In different industries, we may use different ratios to compare companies from the same industry. The role of industry-specific ratios & task-specific ratios is to cover issues and characteristics typical of a given industry.

\(NIM = \frac{\text{net interest income}}{\text{total interest-earning assets}}\)

- \(NIM\) - net interest margin

\(SPM = \frac{\text{revenue}}{TS}\)

- \(SPM\) - sales per square meter
- \(TS\) - total retail space per square meters

\(RPE = \frac{\text{revenue}}{\text{total number of employees}}\)

- \(RPE\) - revenue per employee

\(CA = \frac{CC}{RM}\)

- \(CA\) - capital adequacy
- \(CC\) - various components of capital
- \(RM\) - various measures connected with risk, e.g. market risk exposure

\(V_{OI} = \frac{\sigma_{OI}}{AOI}\)

- \(V_{OI}\) - coefficient of variation of operating income
- \(\sigma_{OI}\) - standard deviation of operating income
- \(AOI\) - average operating income

\(NIE = \frac{\text{net income}}{\text{total number of employees}}\)

- \(NIE\) - net income per employee

\(MRR = \frac{\text{reserves}}{SDL}\)

- \(MRR\) - monetary reserve requirement
- \(\text{reserves}\) - reserves
__held at central bank__ - \(SDL\) - specified deposit liabilities

**Also called:** cash reserve ratio.

\(V_{NI} = \frac{\sigma_{NI}}{ANI}\)

- \(V_{NI}\) - coefficient of variation of net income
- \(\sigma_{NI}\) - standard deviation of net income
- \(ANI\) - average net income

\(ADR = \frac{\text{room revenue}}{\text{number of rooms sold}}\)

- \(ADR\) - average daily rate

\(LAR = \frac{\text{approved "readily marketable" securities}}{\text{specified deposit liabilities}}\)

- \(LAR\) - liquid asset requirement

\(V_{R} = \frac{\sigma_{R}}{AR}\)

- \(V_{R}\) - coefficient of variation of revenues
- \(\sigma_{R}\) - standard deviation of revenue
- \(AR\) - average revenue

\(OR = \frac{\text{number of rooms sold}}{\text{number of rooms available}}\)

- \(OR\) - occupancy rate

Credit risk is the risk of incurring a loss as a result of the counterparty not being able to make full and timely payments.

Credit analysis is used for the evaluation of credit risk.

\(Z=1.2\times\frac{\text{current assets }-\text{ current liabilities}}{\text{total assets}}+\\+1.4\times\frac{\text{retained earnings}}{\text{total assets}}+\\+3.3\times\frac{\text{EBIT}}{\text{total assets}}+\\+0.6\times\frac{\text{market value of stock}}{\text{book value of liabilities}}+\\+1.0\times\frac{\text{sales}}{\text{total assets}}\)

- \(Z\) - Z-score by Altman

Z-score by Altman is used for predicting bankruptcy. The score lower than 1.81 indicates possible failure.

\(\text{FOCF-to-Debt} = \frac{CFO - \text{ capital expenditures}}{\text{total debt}}\)

- \(\text{FOCF-to-Debt}\) - free operating cash flow to debt
- \(CFO\) - cash flow from operations

\(\text{interest coverage} = \frac{EBIT}{\text{interest payments}}\)

- \(EBIT\) - earnings before deducting interest and taxes

Measures: how many times EBIT is higher than interest payments

Interpretation, relations, and usage:

the higher the ratio >> the higher the solvency

the higher the ratio >> the easier for the company to service its debt from its operating earnings

\(IC_{EBITDA} = \frac{EBITDA}{\text{interest expense}}\)

- \(IC_{EBITDA}\) - EBITDA interest coverage
- \(EBITDA\) - earnings before interest, taxes, depreciation, and amortization
- \(\text{interest expense}\) - interest expense (
__including non˗cash interest on conventional debt instruments__)

\(\text{FFO-to-Debt} = \frac{FFO}{\text{total debt}}\)

- \(\text{FFO-to-Debt}\) - funds from operations to debt ratio
- \(FFO\) - funds from operations

FFO = funds from operations = EBITDA – net interest expense – current tax expense

\(D_{EBITDA} = \frac{\text{total debt}}{EBITDA}\)

- \(D_{EBITDA}\) - debt to EBITDA ratio
- \(EBITDA\) - earnings before interest, taxes, depreciation, and amortization

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### Segment Ratios

The same as for the company, we can compute ratios for segments. They will help analyze performance, efficiency, etc. for segments.

Note: The construction of segment ratios is the same as in the case of ratios for the whole company with the exception that we choose data for a segment, e.g. in the case of segment margin, we use segment profit in the numerator and segment revenue in the denominator.

\(SM = \frac{\text{segment profit}}{\text{segment revenue}}\)

- \(SM\) - segment margin ratio

According to IFRS 8, an operating segment is a component of the company:

- that engages in activities that may generate revenue and create expenses, and
- whose results are regularly supervised by the company senior management, and
- for which discrete financial information is available.

**Examples of the segment:** subsidiaries, operating units, operations in different countries, etc.

\(ST = \frac{\text{segment revenue}}{\text{segment assets}}\)

- \(ST\) - segment turnover ratio

According to IFRS 8, an operating segment is a component of the company:

- that engages in activities that may generate revenue and create expenses, and
- whose results are regularly supervised by the company senior management, and
- for which discrete financial information is available.

**Examples of the segment:** subsidiaries, operating units, operations in different countries, etc.

\(S_{ROA} = \frac{\text{segment profit}}{\text{segment assets}}\)

- \(S_{ROA}\) - segment return on assets

According to IFRS 8, an operating segment is a component of the company:

- that engages in activities that may generate revenue and create expenses, and
- whose results are regularly supervised by the company senior management, and
- for which discrete financial information is available.

**Examples of the segment:** subsidiaries, operating units, operations in different countries, etc.

\(SD = \frac{\text{segment liabilities}}{\text{segment assets}}\)

- \(SD\) - segment debt ratio

According to IFRS 8, an operating segment is a component of the company:

- that engages in activities that may generate revenue and create expenses, and
- whose results are regularly supervised by the company senior management, and
- for which discrete financial information is available.

**Examples of the segment:** subsidiaries, operating units, operations in different countries, etc.

- According to the vertical common-size analysis, we analyze the data from one financial statement, for example, a balance sheet, an income statement, or a cash flow statement, for a given period and divide all relevant items from this financial statement by one common item.
- Horizontal common-size analysis assumes that we compare a given item to the same item but from a different year.
- To check the sensitivity of the earnings forecasting on the inputs, we can use 3 techniques: sensitivity analysis (aka. ‘what if’ analysis), scenario analysis, and simulation.
- Financial statement ratios can be divided into specific groups. We distinguish among: activity ratios, liquidity ratios, solvency ratios, profitability ratios, valuation ratios, industry-specific and task-specific ratios, ratios used in credit analysis, and segment ratios.
- Activity ratios measure: how well a company manages various activities and how effectively assets are used by the company.
- Liquidity ratios measure the company's ability to meet short-term obligations. They also help us assess how quickly the company can convert assets into cash.
- Solvency ratios measure the company's ability to meet long-term debt obligations.
- Profitability ratios tell us what is the profitability of the company measured by different categories of profit and in relation to different measures like revenue, total assets, equity, etc.
- Valuation ratios are used in the valuation process to value the equity of the company.
- The role of industry-specific ratios & task-specific ratios is to cover issues and characteristics typical of a given industry.
- A company discloses separate information about the segment if it constitutes at least 10% of total revenue, assets, or profit.