Essential Financial Formulas and Valuation Concepts

Posted on Jul 24, 2025 in Finance

Cost of Capital & Equity Valuation

Weighted Average Cost of Capital (WACC)

  • WACC = Wd(YTM(1-Tax)) + (We * re) + (Wpfd * rpfd)

Cost of Equity

  • Cost of Equity (Dividend Growth Model) = Div1 / P0 + g
  • CAPM Expected Return (re) = Risk-Free Rate + [Beta * (Market Return – Risk-Free Rate)]
  • Stock Excess Return = Market Excess Return x Beta
  • Investment Expected Return = Risk-Free Rate + [Beta * (Market Return – Risk-Free Rate)]
  • Market Value of Equity = Number of Shares x Share Price (also known as Market Capitalization)

Dividend Discount Models (DDM)

  • P0 = (D1 + P1) / (1 + rE)
  • rE = Dividend Yield + Capital Gains Yield
  • Dividend Yield = D1 / P0 (or D2 / P1)
  • Capital Gains Yield = (P1 – P0) / P0 (or (P2 – P1) / P1)
  • P1 = D2 / (rE – g)
  • D2 = D0 * (1 + g)^2
  • No-Growth Dividend Model: P0 = D1 / rE
  • Constant Growth Model: P0 = D1 / (rE – g)
  • Constant Growth Model (Solving for rE): rE = D1 / P0 + g
  • Constant Growth Model (Solving for g): g = rE – (D1 / P0)
  • One-Year Holding Period Model:
    • P0 = (D1 + P1) / (1 + rE)
    • rE = (D1 / P0) + [(P1 – P0) / P0]
    • P1 = P0 * (1 + rE) – D1

Preferred Stock Valuation

  • rE (Preferred Stock) = D1 / P0

Dividend Policy & Growth

  • Dividend Payout Ratio + Retention Rate = 1
  • Net Income – Dividends = Change in Retained Earnings
  • g (Growth Rate) = Retention Rate x Return on New Investment (RONI)
  • Dividends = Earnings x Dividend Payout Ratio
  • P0 (with new payout/growth) = (EPS1 x Dividend Payout Ratio) / (rE_new – g_new)
  • rE (with new payout/growth) = (EPS1 / P0) – g (Note: g is often 0 in some models)

Interest Rates & Return Measures

Nominal vs. Real Rates

  • Nominal Rate = (1 + Real Rate) * (1 + Inflation Rate) – 1
  • Sample Calculation: If Nominal Rate (NR) = 4.3% and Inflation Rate (INFR) = 2%, then Real Rate = (1.043 / 1.02) – 1
  • Negative Real Interest Rates diminish incentives to save.

Effective Annual Rate (EAR) & Annual Percentage Rate (APR)

  • Effective Annual Rate (EAR) = (1 + APR/m)^m – 1
  • Annual Percentage Rate (APR) = [(1 + EAR)^(1/m) – 1] * m
  • Interest Rate per Period (I/Y) = APR / m
  • r (monthly rate) = APR / 12 (if breaking down monthly)
  • EAR: The interest rate that would earn the same interest with annual compounding.
  • APR: A simple, stated interest rate.
  • APR vs. EAR: APR will always be less than EAR, except when compounding annually (m=1), in which case EAR = APR.
  • Equivalent Quarterly Discount Rate = (1 + EAR)^(1/4) – 1

Average Returns

  • Realized Return = [Dividend + (P2 – P1)] / P1
  • Arithmetic Average Return = (1/n) * (R1 + R2 + … + Rn)
  • Geometric Average Return = [(1 + R1) * (1 + R2) * … * (1 + Rn)]^(1/n) – 1
  • Multi-Period Total Return = [(1 + R1) * (1 + R2) * … * (1 + Rn)] – 1
  • Portfolio Expected Return = w1E(R1) + w2E(R2) + …

Bond Valuation & Characteristics

Bond Terminology & Formulas

  • Coupon Payment = (Coupon Rate x Face Value) / Number of Payments per Year
  • Coupon Rate = (Coupon Payment x Number of Payments per Year) / Face Value
  • Bond Pricing Relationship:
    • Coupon Rate = YTM (at Par)
    • Coupon Rate > YTM (at Premium)
    • Coupon Rate < YTM (at Discount)
  • Bond Calculations (Financial Calculator Inputs):
    • Par/Face Value = FV
    • Term to Maturity = N
    • Coupon Payment = PMT
    • Yield to Maturity (YTM) = I/Y
    • Current Price = PV
  • Issued at Par: Coupon Rate = YTM.

Yield to Maturity (YTM)

  • YTM = Annualized return realized if bond is held to maturity.
  • When calculating YTM for semi-annual bonds, I/Y is divided by 2 for the period rate, and then multiplied by 2 to annualize the result.
  • If interest rates fall, I/Y (Yield to Maturity) goes down as well.
  • When comparing bonds, use YTM for calculations.
  • For semi-annual bonds, I/Y (per period) = Annual Yield / 2.

Bond Price Sensitivity

  • Bond Sensitivity: Longer maturity bonds are more sensitive to interest rate changes.
  • Example: A 30-year, $1000 par, 5% semi-annual coupon bond is preferred over a 10-year bond if coupon rates drop by 1%.
  • Zero-Coupon Bonds: Always trade at a discount to par value (unless at maturity).
  • Interest Rate Impact on Bond Prices: As Bond Prices go Up, Yields (Rates) go down (and vice versa).
  • Bond Strategy for Rate Changes:
    • For falling interest rates: Long maturity bonds (especially zero-coupon) are preferred due to higher price sensitivity.
    • For rising interest rates: Short maturity bonds (especially high-coupon) are preferred due to lower price sensitivity.

Key Financial Concepts & Principles

Risk Measures

  • Volatility (Standard Deviation) = Total Risk
  • Beta = Measure of Systematic Risk
  • Standard Deviation (SD) for a 95% Confidence Interval: Average Annual Return +/- (1.96 x Standard Deviation)

Corporate Structure & Taxation

  • C-Corporation: Subject to double taxation (Corporate Tax + Personal Tax on dividends).
  • Effective Tax Rate = Total Tax Paid / Earnings Before Tax (EBT) (Example: 1.5 / 5)
  • Tax on Sale of Asset = (Sales Price – Book Value) x Tax Rate
  • When corporate tax rates decline, the net cost of debt financing increases.

Annuities & Perpetuities

  • Annuity: Payments end after a fixed period.
  • Perpetuity: Payments continue indefinitely.

Financial Calculator Notes

  • In financial calculator inputs, Present Value (PV), Payment (PMT), and Future Value (FV) must reflect cash flow direction (e.g., inflows positive, outflows negative).
  • When calculating loan payments with a financial calculator, the Future Value (FV) is typically set to 0.
  • If the same Interest Rate per Period (I/Y) is used for different cash flows, examine the payments.

Market-to-Book Ratio

  • Market-to-Book Ratio of 1.29 means investors are willing to pay 1.29 times the book value for the company’s equity.

Loan Amortization

  • Loan Payment (P) = PV / [(1/r) * (1 – 1/(1+r)^n)]
  • Interest Payment = Present Value (PV) x r
  • Principal Repayment = Payment – Interest
  • Loan Amortization: Early payments consist of more interest and less principal; later payments consist of less interest and more principal.

Capital Budgeting & Project Analysis

Cash Flow Calculation

  • Depreciation Expense (Straight-Line): Initial Investment / Project Life
  • Incremental Earnings = EBIT * (1 – Tax Rate)
  • Incremental Free Cash Flow (FCF) = EBIT * (1 – Tax Rate) + Depreciation – Capital Expenditures – Change in Net Working Capital
  • Terminal Cash Flow = Recovery of Net Working Capital + After-Tax Sale Proceeds of Equipment
  • Depreciation Tax Shield = Depreciation Expense x Corporate Tax Rate
  • MACRS Depreciation Tax Shield = MACRS Depreciation x Corporate Tax Rate

Project Evaluation Metrics

  • Internal Rate of Return (IRR) = The annual rate of return a project is expected to generate.
  • Net Present Value (NPV) = The monetary value a project will add to the firm in today’s dollars.
  • Payback Rule:
    • Column 1: Year
    • Column 2: Cash Flows
    • Column 3: Cumulative Cash Flows
    • Calculation: N + |Unrecovered Amount| / Cash Flow in Next Period
  • Profitability Index (PI) = NPV / Initial Investment
  • Equivalent Annual Annuity (EAA): Converts NPV into an equivalent annual cash flow.
  • EAA Interpretation: Lower EAA is better for costs; Higher EAA is better for benefits.
  • IRR vs. NPV: If IRR > Cost of Capital (rE), then NPV is positive.

Other Capital Budgeting Notes

  • WACC replaces I/Y and rE when calculating cash flows for project valuation.
  • Higher Discount Rate leads to Lower Present Value.
  • When comparing investments, ignore T-bill rate if the investment is not riskless.

Additional Financial Notes

Share Voting

  • Share Votes (for Cumulative Voting): Number of Shares * (Number of Directors to be Elected + 1) / Total Shares Voted. (Round down when receiving results)

Price Change Calculation

  • Percentage Change in Price = (New Price / Old Price) – 1.