Financial Management Formulas
Financial management questions on the BAR section of the CPA exam test your ability to evaluate investment decisions, calculate cost of capital, and manage working capital. This cheat sheet covers the critical formulas and decision rules.
Time Value of Money (TVM)
| Concept | Formula | Use |
|---|
| Future Value (single sum) | FV = PV × (1 + r)n | What a lump sum today will be worth in the future |
| Present Value (single sum) | PV = FV / (1 + r)n | What a future lump sum is worth today |
| Future Value of Annuity | FVA = PMT × [((1 + r)n − 1) / r] | What a series of equal payments will accumulate to |
| Present Value of Annuity | PVA = PMT × [(1 − (1 + r)−n) / r] | What a series of equal future payments is worth today |
| Annuity Due Adjustment | Multiply ordinary annuity factor by (1 + r) | Payments at beginning of period instead of end |
Capital Budgeting Methods
| Method | Formula / Approach | Decision Rule | Considers TVM? |
|---|
| Net Present Value (NPV) | PV of future cash inflows − Initial investment | Accept if NPV > 0 | Yes |
| Internal Rate of Return (IRR) | Discount rate that makes NPV = 0 | Accept if IRR > Required rate of return (WACC) | Yes |
| Profitability Index (PI) | PV of cash inflows / Initial investment | Accept if PI > 1.0 | Yes |
| Payback Period | Initial investment / Annual cash inflow (if equal); cumulative method if unequal | Accept if payback < Maximum acceptable period | No |
| Discounted Payback | Same as payback but using discounted cash flows | Accept if discounted payback < Maximum period | Yes |
| Accounting Rate of Return (ARR) | Average annual accounting profit / Average investment | Accept if ARR > Target rate | No |
Key rule: NPV is the preferred method. When NPV and IRR conflict (mutually exclusive projects), always follow NPV.
Weighted Average Cost of Capital (WACC)
WACC = (E/V) × re + (D/V) × rd × (1 − T)
| Variable | Definition |
|---|
| E | Market value of equity |
| D | Market value of debt |
| V | E + D (total firm value) |
| re | Cost of equity |
| rd | Cost of debt (before tax) |
| T | Corporate tax rate |
Cost of Equity Methods
| Method | Formula |
|---|
| CAPM | re = Rf + β × (Rm − Rf) |
| Dividend Discount Model (Gordon Growth) | re = (D1 / P0) + g |
| Bond Yield Plus Risk Premium | re = Company's bond yield + Equity risk premium |
Working Capital Management
| Metric | Formula | Interpretation |
|---|
| Operating Cycle | Days in Inventory + Days Sales Outstanding | Time from purchasing inventory to collecting cash from sales |
| Cash Conversion Cycle | Operating Cycle − Days Payable Outstanding | Net days the firm must finance operations |
| Economic Order Quantity (EOQ) | √(2 × D × S / H) | Optimal order quantity to minimize total inventory costs (D = annual demand, S = order cost, H = holding cost per unit) |
| Reorder Point | Lead time demand + Safety stock | Inventory level that triggers a new order |
Capital Structure Concepts
- Modigliani-Miller (no taxes): Capital structure is irrelevant; firm value is independent of how it is financed
- Modigliani-Miller (with taxes): Firm value increases with debt due to the interest tax shield; VL = VU + T × D
- Trade-off Theory: Optimal capital structure balances the tax shield benefit of debt against the costs of financial distress
- Pecking Order Theory: Firms prefer internal financing first, then debt, then equity (least information asymmetry first)
- Financial Leverage: Using debt to amplify returns; increases both potential return AND risk
Degree of Leverage Formulas
| Measure | Formula |
|---|
| Degree of Operating Leverage (DOL) | % Change in EBIT / % Change in Sales = CM / EBIT |
| Degree of Financial Leverage (DFL) | % Change in EPS / % Change in EBIT = EBIT / (EBIT − Interest) |
| Degree of Total Leverage (DTL) | DOL × DFL = CM / (EBIT − Interest) |
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