Key Financial Ratios and Formulas for Business Analysis

Posted on Jan 13, 2025 in Financial and Actuarial Economics

Key Financial Ratios and Formulas

Profitability Ratios

  • Operating Profit Margin (OPM): EBIT / Sales
  • Return on Sales (ROS) or Net Profit Margin (NPM): Net Income (NI) / Sales
  • Return on Assets (ROA): EBIT / Assets = OPM x Asset Turnover (Sales / Assets)
  • Return on Equity (ROE): NI / Equity
  • Return on Investment (ROI): NOPAT / Capital = EBIT(1-T) / (Debt + Equity)
  • Gross Margin: (Sales – COGS) / Sales
  • Gross Margin (excluding depreciation and amortization): EBIT / Sales

Leverage Ratios

  • Degree of Operating Leverage (DOL): Gross Margin / EBIT
  • Degree of Financial Leverage (DFL): EBIT / EBT
  • Degree of Total Leverage (DTL): DOL x DFL

Other Key Formulas

  • Net Income (NI): (EBIT – Interest) x (1 – Tax Rate)
  • Average Daily Purchases (ADP): (Raw Material Purchases + Operating Costs + Taxes) / 365

Activity Ratios (Turnover Ratios)

  • Accounts Payable Turnover: Purchases / Accounts Payable
  • Accounts Payable Days: 365 / Accounts Payable Turnover
  • Accounts Receivable Turnover: Sales / Accounts Receivable
  • Finished Goods Turnover: COGS / Average Finished Goods
  • Raw Materials Turnover: Cost of Raw Materials / Average Raw Materials Stock
  • Inventory Turnover: COGS / Average Inventory
  • Work in Progress Turnover: COGM / Average Work in Progress
  • Fixed Assets Turnover: Sales / Average Fixed Assets

Valuation Metrics

  • Economic Value Added (EVA): EBIT(1-T) – (WACC x Invested Capital)
  • Weighted Average Cost of Capital (WACC): (Cost of Equity x (Equity / (Equity + Debt))) + (Cost of Debt x (1 – Tax Rate) x (Debt / (Equity + Debt)))
  • Invested Capital: Equity + Long-Term Debt
  • Cost of Goods Sold (COGS): Cost of Goods Manufactured (COGM) + Beginning Finished Goods – Ending Finished Goods
  • Earnings Per Share (EPS): NI / Common Shares Outstanding
  • Dividend Payout Ratio: Total Dividends / NI
  • Price-to-Earnings Ratio (P/E): Price per Share / Earnings per Share

Liquidity Ratios

  • Current Ratio: Current Assets / Current Liabilities
  • Cash Ratio: (Cash + Marketable Securities) / Current Liabilities
  • Quick Ratio (Acid Test Ratio): (Current Assets – Inventory) / Current Liabilities
  • Asset to Liability Ratio: Current Assets / Current Liabilities

Solvency Ratios

  • Debt Ratio: Total Debt / Total Assets
  • Debt to Equity Ratio: Total Debt / Total Equity
  • Debt Coverage Ratio: (NI + Depreciation + Amortization (Non-Operating Income)) / Total Debt
  • Interest Coverage Ratio: EBIT / Interest Expense
  • After-Tax Cost of Debt: (Interest Expense / Total Debt) x (1 – Tax Rate)

Operating and Cash Cycle

  • Operating Cycle (OP CY): Inventory Days (Raw Material Days + Work in Progress Days + Finished Goods Days) + Accounts Receivable Days
  • Cash Cycle (Cash CY): Operating Cycle – Accounts Payable Days

Net Operating Funds (NOF)

  • Cost of Goods Sold (COGS): Cost of Goods Manufactured (Purchase) + Beginning Finished Goods – Ending Finished Goods
  • Net Operating Funds (CAN): (ADP x Operating Cycle) – Accounts Payable
  • Days of Sales Outstanding (DOSFT): Raw Materials + Work in Progress + Finished Goods + Accounts Receivable – (Accounts Payable – Operating Costs)
  • Raw Materials: Raw Material Days x (Raw Materials / Sales)
  • Work in Progress: Work in Progress Days x (Work in Progress / Sales)
  • Finished Goods: Finished Goods Days x (Finished Goods / Sales)
  • Accounts Receivable: Accounts Receivable Days x (Accounts Receivable / Sales)
  • Accounts Payable: Accounts Payable Days x (Accounts Payable / Sales)
  • Operating Costs: Operating Cost Days x (Operating Costs / Sales)
  • NOF: (DOSFT x (Sales / 365)) + Minimum Cash Balance (% of Sales)

Invoice Discount and Factoring

  • Effective Annual Rate (EAR): (Nominal / Effective)^(365 / t) – 1
  • Effective Value (E): Nominal x (1 – Discount Rate x (t / 365)) – Commission – Other Costs – Taxes
  • Factoring:
    • Nominal (N) = Accounts Receivable
    • Receivable (X) = N x (1 – % Reserve) = N x (% Advance)
    • Interest (I) = Interest Rate x X x (t / 365)
    • Fee (F) = Fee Rate x N
    • EAR = (X / Cost)^(365 / t) – 1
    • At Start Fee:
      • Cost (Co) = X – I – F
      • Cost Nominal (CN) = N – X
    • End Fee:
      • Cost (Co) = X – I
      • Cost Nominal (CN) = N – X – F
  • Reverse Factoring Total Cost: (Receivable x Factoring Rate + Fee Rate) + Fee – (Accounts Payable x Advance Rate – Advance Time)

Present Value Calculations

  • Present Value (no growth): -Cost x Quantity + Price x Quantity
  • Present Value (with growth): -Cost x Quantity x (1 + Growth Rate) + ((Price x Quantity) x (1 + Growth Rate x (1 – Discount Rate) x Probability)) / (1 + Interest Rate x (t / 365))
  • EAR with Discount: (Nominal / (Nominal x (1 – Discount Rate)))^(365 / (t2 – t1)) – 1
  • Perpetuity Present Value (no growth): ((-Cost x Quantity) x (1 + Interest Rate)) / Interest Rate + (Price x Quantity) / Interest Rate
  • Perpetuity Present Value (with growth): Same as above, but (Price x Quantity x Probability) / Interest Rate

Treasury Management

Baumol Model

  • Optimal Cash Balance (C*): Square Root((2 x Total Cash Needed x Fixed Cost per Transaction) / Interest Rate)
  • Total Cash Needed (T): Annual Cash Needs
  • Interest Rate (K): Interest Rate
  • Opportunity Cost: Interest Rate x (C / 2)
  • Transaction Cost: Fixed Cost per Transaction x (T / C)
  • Number of Transactions: T / C*

Miller-Orr Model

  • Spread (Z): Cube Root((3 x Variance x Fixed Cost per Transaction) / (4 x Daily Interest Rate)) + Lower Limit
  • Upper Limit (U): 3Z – 2 x Lower Limit
  • Daily Variance: Annual Variance / 365 or Monthly Variance / 30
  • Daily Interest Rate: (1 + Annual Interest Rate)^(1 / 365) – 1

Debt Service Coverage Ratios

  • Debt Service Coverage Ratio (DSCR): Cash Flow / (Amortization + Interest)
  • Amortization: Debt (t-1) – Debt (t)
  • Interest: Cost of Debt x Debt (t-1)
  • Loan Life Coverage Ratio (LLCR): (Sum of (Cash Flow / (1 + Cost of Debt)^t) for t = 1 to Loan Duration) / Debt Outstanding
  • Project Life Coverage Ratio (PLCR): (Sum of (Cash Flow / (1 + Cost of Debt)^t) for t = 1 to Project Duration) / Debt Outstanding
  • Tail: PLCR – LLCR

Additional Problems and Solutions

  1. a) Present Value Calculations

    • Present Value (no growth): -Cost x Quantity + Price x Quantity
    • Present Value (with growth): -Cost x Quantity x (1 + Growth Rate) + ((Price x Quantity) x (1 + Growth Rate x (1 – Discount Rate) x Probability)) / (1 + Interest Rate x (t / 365))
    • Cost (C): Cost per Unit
    • Price (P): Price per Unit
    • Growth Rate (g): Growth Rate
    • Probability (h): Probability

    b) Equating Present Values

    • Set Present Value (no growth) = Present Value (with growth) and solve for the unknown variable (e.g., Price).

    c) Adjusted Quantity for Probability

    • Probability x Quantity = Adjusted Quantity (Q*)
    • Present Value (with adjusted quantity): -Cost x Q* + (Price x Q*) / (1 + Interest Rate x (t / 365)) – X
    • X: Total contract price. Divide X by the initial quantity to get the price per unit.

  2. Loan Life Coverage Ratio (LLCR)

    • LLCR: 1.5 = (Sum of (Cash Flow / (1 + Cost of Debt)^t) for t = 1 to Loan Duration) / Debt Outstanding
    • PLCR: (Sum of (Cash Flow / (1 + Cost of Debt)^t) for t = 1 to Project Duration) / Debt Outstanding
    • If LLCR is less than 1.7 (for example) and debt is 150, do not grant credit.
    • Net Income (NI): Earnings Before Taxes (EBT) x (1 – Tax Rate)
    • EBIT: EBT + Interest
    • EBITDA: EBIT + Depreciation + Amortization
    • Gross Margin (GM): EBITDA + Operating Expenses or Sales – Costs

  3. Coverage Ratio

    • Coverage Ratio = EBIT / Interest Expense
    • EBIT = Coverage Ratio x Interest Expense
    • NI (e.g., 150) = (Coverage Ratio x Interest – Interest) x (1 – Tax Rate)
    • Interest (e.g., 160) = Cost of Debt x Debt

  4. Factoring

    • End:
      • 3500 = 80% x Accounts Receivable x (1 – Interest Rate x (t / 365)). Solve for Accounts Receivable.
      • 80% x Accounts Receivable + Interest x Accounts Receivable = X
      • EAR = (X / 3500)^(365 / t) – 1
  5. Start:
  • 3500 = 80% x Accounts Receivable – Fee x Accounts Receivable – Interest Rate x (t / 365) x 80% x Accounts Receivable
  • EAR = (80% x Accounts Receivable / 3500)^(365 / 90) – 1

Baumol Model

  • Number of Days: T / C
  • T: Annual Cash Needs = Number of Units x Cost per Unit
  • C*: Square Root((2 x Fixed Cost per Transaction x (Number of Units x Cost per Unit)) / Interest Rate). Solve for T.
  • If C* is greater than the current cash level, sell C* minus the cash level.