Financial Accounting: Key Ratios, Valuation, and Time Value of Money Formulas

Financial Ratios and Formulas

Liquidity Ratios

Liquidity ratios measure a company's ability to meet its short-term obligations using its most liquid assets.

• Current Ratio: Indicates the ability to pay short-term liabilities with short-term assets. $\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$

• Quick Ratio (Acid-Test Ratio): Measures liquidity excluding inventory. $\text{Quick Ratio} = \frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}}$

Working Capital Ratios

These ratios assess the efficiency of a company's operations and management of current assets and liabilities.

• Accounts Receivable Days: Average number of days to collect receivables. $\text{Acc. Rec. Days} = \frac{\text{Average Accounts Receivable}}{\text{Average Daily Sales}}$

• Accounts Payable Days: Average number of days to pay suppliers. $\text{Acc. Pay. Days} = \frac{\text{Average Accounts Payable}}{\text{Average Daily Purchases}}$

• Inventory Turnover: How many times inventory is sold and replaced. $\text{Inventory Turnover} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}$

Asset Efficiency Ratios

These ratios evaluate how effectively a company uses its assets to generate sales.

• Asset Turnover: Measures sales generated per dollar of assets. $\text{Asset Turnover} = \frac{\text{Sales}}{\text{Total Assets}}$

• Fixed Asset Turnover: Sales generated per dollar of fixed assets. $\text{Fixed Asset Turnover} = \frac{\text{Sales}}{\text{Net Fixed Assets}}$

• Capital Intensity: Inverse of asset turnover; assets needed per dollar of sales. $\text{Capital Intensity} = \frac{\text{Total Assets}}{\text{Sales}}$

Interest Coverage Ratio

This ratio measures a company's ability to meet its interest obligations from operating earnings.

• Interest Coverage: $\text{Interest Coverage} = \frac{\text{EBIT}}{\text{Interest}}$ EBIT = Earnings Before Interest and Taxes

Leverage Ratios

Leverage ratios assess the degree to which a company is using borrowed money.

• Debt-Equity Ratio: Proportion of debt to equity. $\text{Debt-Equity Ratio} = \frac{\text{Total Debt}}{\text{Total Equity}}$

• Debt-Capital Ratio: Proportion of debt in total capital. $\text{Debt-Capital Ratio} = \frac{\text{Total Debt}}{\text{Total Capital}}$

• Debt-Enterprise Ratio: Debt relative to enterprise value. $\text{Debt-Enterprise Ratio} = \frac{\text{Total Debt}}{\text{Enterprise Value}}$

• Net Debt: Debt minus cash and short-term investments. $\text{Net Debt} = \text{Total Debt} - \text{Cash and Short-Term Investments}$

• Equity Multiplier: Measures financial leverage. $\text{Equity Multiplier} = \frac{\text{Total Assets}}{\text{Book Value of Equity}}$

Valuation Ratios

Valuation ratios help investors assess the value of a company relative to key financial metrics.

• P/E Ratio (Price-Earnings Ratio): Price per share relative to earnings per share. $\text{P/E Ratio} = \frac{\text{Share Price}}{\text{Earnings per Share}}$

• PEG Ratio: P/E ratio adjusted for growth. $\text{PEG Ratio} = \frac{\text{P/E Ratio}}{\text{Earnings Growth Rate}}$

• P/B Ratio (Price-Book Ratio): Price per share relative to book value per share. $\text{P/B Ratio} = \frac{\text{Share Price}}{\text{Book Value per Share}}$

• P/S Ratio (Price-Sales Ratio): Price per share relative to sales per share. $\text{P/S Ratio} = \frac{\text{Share Price}}{\text{Sales per Share}}$

Operating Returns

These ratios measure profitability and efficiency in generating returns from assets and equity.

• Return on Equity (ROE): Net income generated per dollar of equity. $\text{ROE} = \frac{\text{Net Income}}{\text{Book Value of Equity}}$

• Return on Assets (ROA): Net income generated per dollar of assets. $\text{ROA} = \frac{\text{Net Income}}{\text{Total Assets}}$

Growth Rates

Growth rates estimate how quickly a company can expand its assets or equity based on retained earnings and profitability.

• Sustainable Growth Rate: Maximum growth rate without changing leverage. $\text{Sustainable Growth Rate} = \text{ROE} \times (1 - \text{Payout Ratio})$

• Internal Growth Rate: Maximum growth rate without external financing. $\text{Internal Growth Rate} = \text{ROA} \times (1 - \text{Payout Ratio})$

DuPont Model

The DuPont Model breaks down ROE into component ratios to analyze profitability, efficiency, and leverage.

• DuPont Equation: $\text{ROE} = \frac{\text{Net Income}}{\text{Equity}} = \frac{\text{Net Income}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Total Assets}} \times \frac{\text{Total Assets}}{\text{Equity}}$

Time Value of Money and Other Financial Formulas

Present and Future Value Formulas

These formulas are used to calculate the value of cash flows at different points in time, considering interest rates.

• Present Value (PV) of a Cash Flow Stream: $PV = C_1 \cdot \frac{1}{1+r} + C_2 \cdot \frac{1}{(1+r)^2} + \ldots + C_n \cdot \frac{1}{(1+r)^n}$

• Present Value of a Perpetuity: $PV = \frac{C}{r}$

• Present Value of a Growing Perpetuity: $PV = \frac{C}{r-g}$

• Present Value of an Annuity: $PV = C \times \frac{1 - (1 + r)^{-n}}{r}$

• Future Value of an Annuity: $FV = C \times \frac{(1 + r)^n - 1}{r}$

Compound Interest

Compound interest calculations determine the future value of investments with interest earned on both principal and accumulated interest.

• Future Value (FV) of a Lump Sum: $FV = C_0 (1 + r)^n$

Interest Rate Conversions

These formulas convert between different types of interest rates.

• Effective Annual Rate (EAR): The actual annual rate earned or paid after compounding. $EAR = (1 + \frac{APR}{k})^k - 1$ where APR is the annual percentage rate and k is the number of compounding periods per year.

• APR (Annual Percentage Rate): The nominal annual rate not accounting for compounding. $APR = \text{Periodic Rate} \times k$

Summary Table: Key Ratios and Formulas

Category	Ratio / Formula	Equation
Liquidity	Current Ratio	$\frac{\text{Current Assets}}{\text{Current Liabilities}}$
Liquidity	Quick Ratio	$\frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}}$
Efficiency	Asset Turnover	$\frac{\text{Sales}}{\text{Total Assets}}$
Leverage	Debt-Equity Ratio	$\frac{\text{Total Debt}}{\text{Total Equity}}$
Valuation	P/E Ratio	$\frac{\text{Share Price}}{\text{Earnings per Share}}$
Profitability	ROE	$\frac{\text{Net Income}}{\text{Book Value of Equity}}$
Time Value	PV of Perpetuity	$\frac{C}{r}$

Example: Calculating ROE Using the DuPont Model

Suppose a company has the following data: Net Income = $100, Sales = $1,000, Total Assets = $500, Equity = $250.

• Net Profit Margin = $\frac{100}{1000} = 0.10$

• Asset Turnover = $\frac{1000}{500} = 2.0$

• Equity Multiplier = $\frac{500}{250} = 2.0$

• ROE = $0.10 \times 2.0 \times 2.0 = 0.40$ or 40%

Additional info:

• Some formulas and ratios are used in both financial accounting and corporate finance. Their application may vary depending on the context (e.g., valuation vs. performance analysis).

• Enterprise Value (EV) is often calculated as Market Value of Equity + Debt - Cash.

• EBIT stands for Earnings Before Interest and Taxes, a key measure of operating performance.