Introduction to Financial Principles — Formula Cheat Sheet
Modules 6–10 · every formula with variables defined
Module 6 — Investment Decision Rules
| Measure | Formula | Decision rule |
|---|
| Net Present Value | NPV = Σ CFₜ / (1+r)ᵗ | Accept if NPV > 0; pick highest NPV |
| Internal Rate of Return | 0 = Σ CFₜ / (1+IRR)ᵗ | Accept if IRR > r (normal project) |
| Payback period | Years until ΣCF = 0 | Accept if < cut-off |
| Profitability Index | PI = PV(inflows) / Investment | Accept if PI > 1 (capital rationing) |
CFₜ = cash flow in period t (CF₀ is the initial outlay, usually negative) · r = cost of capital · When rules conflict on a choice, NPV wins. IRR ignores scale & timing.
Module 7 — Capital Budgeting
| Item | Formula |
|---|
| Unlevered net income | EBIT × (1 − τℂ) |
| Free Cash Flow | (Rev − Costs − Dep)(1 − τℂ) + Dep − CapEx − ΔNWC |
| FCF (shortcut form) | (Rev − Costs)(1 − τℂ) + τℂ·Dep − CapEx − ΔNWC |
| Depreciation tax shield | τℂ × Depreciation |
| After-tax salvage value | Sale − τℂ(Sale − Book) |
τℂ = corporate tax rate · ΔNWC = change in net working capital (recovered at project end). Include: opportunity costs, side effects/cannibalization. Exclude: sunk costs, interest/financing (it's in WACC).
Module 8 — Risk & Return
| Measure | Formula |
|---|
| Expected return | E[R] = Σ pᵢ Rᵢ |
| Variance | Var(R) = Σ pᵢ (Rᵢ − E[R])² |
| Standard deviation (volatility) | SD = √Var(R) |
| Portfolio return | E[Rₚ] = w₁E[R₁] + w₂E[R₂] + ... |
| Portfolio variance (2 assets) | w₁²σ₁² + w₂²σ₂² + 2 w₁ w₂ ρ₁₂ σ₁ σ₂ |
| Covariance | Cov(R₁,R₂) = ρ₁₂ σ₁ σ₂ |
| Correlation | ρ₁₂ = Cov(R₁,R₂) / (σ₁ σ₂), −1 ≤ ρ ≤ +1 |
| Beta | βᵢ = Cov(Rᵢ, Rₘₖₜ) / Var(Rₘₖₜ) |
| CAPM (Security Market Line) | E[Rᵢ] = R + βᵢ(E[Rₘₖₜ] − R) |
pᵢ = probability of state i · w = portfolio weights (sum to 1) · ρ = correlation · R = risk-free rate · (E[Rₘₖₜ] − R) = market risk premium. Diversification removes firm-specific risk; market (systematic) risk remains and is measured by β.
Module 9 — Cost of Capital
| Component | Formula |
|---|
| Cost of equity (CAPM) | rₐ = R + βₐ(E[Rₘₖₜ] − R) |
| Cost of equity (dividend model) | rₐ = Div₁ / P₀ + g |
| After-tax cost of debt | rₜ (1 − τℂ) |
| WACC | (E/V) rₐ + (D/V) rₜ(1 − τℂ) |
Div₁ = next year's dividend · P₀ = current share price · g = dividend growth rate · rₜ = yield to maturity on debt (not the coupon) · E, D = market values of equity & debt, V = E + D. WACC is the right discount rate only for projects of average firm risk.
Module 10 — Financial Options
| Item | Formula |
|---|
| Long call payoff | max(S − K, 0) |
| Long put payoff | max(K − S, 0) |
| Short call / put payoff | −max(S − K, 0) / −max(K − S, 0) |
| Profit (long / short) | Payoff − Premium / Premium − Payoff |
| Call break-even | S = K + premium |
| Put-call parity | C + PV(K) = P + S₀ |
| Option value | Intrinsic value + Time value |
S = stock price at expiry · K = strike/exercise price · C, P = call & put prices · PV(K) = K / (1 + r)ᵗ · Higher volatility raises both call and put value. Call value ↑ with S, σ, T, r; ↓ with K.