Complete Exam Study Guide

LIQUIDITY: Current Ratio = CA/CL | Quick Ratio = (CA−Inventory)/CL PROFITABILITY: ROE = Net Income/Equity | ROA = Net Income/Total Assets | NPM = Net Income/Sales LEVERAGE: D/E = Total Debt/Equity | Interest Coverage = EBIT/Interest ACTIVITY: Asset Turnover = Sales/Total Assets | Inventory Turnover = COGS/Inventory MARKET: P/E = Market Price/EPS | EPS = Net Income/Shares Outstanding

DuPont: ROE = Net Profit Margin × Asset Turnover × Equity Multiplier ROE = (NI/Sales) × (Sales/Assets) × (Assets/Equity) Altman Z-Score (Public firms): Z = 1.2X₁ + 1.4X₂ + 3.3X₃ + 0.6X₄ + 1.0X₅ X₁=Working Capital/Total Assets | X₂=Retained Earnings/Total Assets X₃=EBIT/Total Assets | X₄=Market Cap/Total Liabilities | X₅=Sales/Total Assets Z > 2.99 = Safe | 1.81–2.99 = Grey Zone | Z < 1.81 = Distress

FUTURE VALUE (FV): FV = PV × (1 + r)ⁿ PRESENT VALUE (PV): PV = FV / (1 + r)ⁿ ANNUITY FV: FVA = PMT × [(1+r)ⁿ − 1] / r ANNUITY PV: PVA = PMT × [1 − 1/(1+r)ⁿ] / r ANNUITY DUE: Multiply ordinary annuity × (1 + r) INTEREST RATES: Nominal Rate (kNom) = stated rate Periodic Rate (kPer) = kNom / m EAR = (1 + kNom/m)ᵐ − 1 [m = compounding periods] LOAN AMORTIZATION: Each payment = Interest on balance + Principal repayment Interest portion = Beginning balance × r Principal = Payment − Interest

BOND VALUE: V = [INT × PVIFA(kd,n)] + [M × PVIF(kd,n)] INT = Annual coupon payment | M = Par/Face Value | kd = required return | n = years to maturity CURRENT YIELD = Annual Coupon / Current Market Price YIELD TO MATURITY (YTM) — approximate: YTM ≈ [INT + (M − V)/n] / [(M + V)/2] YIELD TO CALL (YTC): Same formula but use call price & years to call date

COMMON STOCK — DIVIDEND DISCOUNT MODELS: 1. Zero Growth: P₀ = D / ks (constant dividend forever — like a perpetuity) 2. Constant Growth (Gordon Model): P₀ = D₁ / (ks − g) where D₁ = D₀ × (1 + g) ks = Required return | g = constant growth rate 3. Supernormal Growth: Step 1: PV of dividends during supernormal period (year by year) Step 2: Find terminal price at end of supernormal period → P = D(n+1)/(ks−g) Step 3: PV of terminal price Total P₀ = Sum of Step 1 + Step 2 PREFERRED STOCK: Pp = Dp / kp Dp = fixed preferred dividend | kp = required return on preferred

OPERATING LEVERAGE (DOL): DOL = % Change in EBIT / % Change in Sales DOL = Q(P − V) / [Q(P − V) − F] (Contribution / EBIT) FINANCIAL LEVERAGE (DFL): DFL = % Change in EPS / % Change in EBIT DFL = EBIT / (EBIT − Interest) COMBINED (TOTAL) LEVERAGE (DTL): DTL = DOL × DFL = % Change in EPS / % Change in Sales INDIFFERENCE POINT: EPS from Plan A = EPS from Plan B → Find EBIT where EPS is equal (EBIT − I₁)(1 − T)/S₁ = (EBIT − I₂)(1 − T)/S₂

COST OF DEBT: kd = kd(1 − T) [after-tax; interest is tax-deductible] (or use YTM formula if market price given) COST OF PREFERRED: kp = Dp / [Pp(1 − F)] [F = flotation cost %] COST OF EQUITY (ke): CAPM: ke = kRF + β(kM − kRF) Gordon (DCF): ke = D₁/P₀ + g Bond Yield + Risk: ke = kd + Risk Premium WACC = wd·kd(1−T) + wp·kp + we·ke Weights = market value proportions of each capital component MARGINAL COST OF CAPITAL (MCC): MCC rises as firm raises more capital (due to flotation costs & exhausting cheaper sources) Break point = Amount of lower-cost capital / Weight of that component

PAYBACK PERIOD (PBP): Years to recover initial investment. Simple, ignores TVM. Uneven CF: Add up year by year until initial cost recovered. DISCOUNTED PAYBACK: Same but use discounted (PV) cash flows. NPV = -CF₀ + Σ [CFt / (1+k)ᵗ] Accept if NPV > 0. Higher NPV = more value creation. IRR: Discount rate that makes NPV = 0. Trial & error or interpolation: IRR = rL + [NPVL/(NPVL−NPVH)] × (rH−rL) Accept if IRR > WACC. MIRR: Reinvestment at WACC (not IRR) — more realistic. Step 1: FV of positive CFs at WACC → Terminal Value (TV) Step 2: PV of negative CFs at WACC → PV of costs Step 3: MIRR = (TV/PV of costs)^(1/n) − 1 PROFITABILITY INDEX (PI): PI = PV of future CFs / Initial Investment Accept if PI > 1. Useful for capital rationing. CROSSOVER RATE: IRR of difference in cash flows between two projects. Below crossover → prefer higher NPV project; above → other project preferred. CASH FLOW ESTIMATION (Incremental after-tax CFs): Initial Investment = Asset cost + Installation − Tax savings from old asset ± NWC Operating CF = [ΔSales − ΔCosts](1−T) + ΔDepreciation × T Terminal CF = Salvage value ± Tax on gain/loss + Recovery of NWC

CASH CONVERSION CYCLE (CCC): CCC = Inventory Conversion Period + Receivables Collection Period − Payables Deferral Period ICP = Inventory / (COGS/365) RCP = Receivables / (Sales/365) [also called DSO - Days Sales Outstanding] PDP = Payables / (COGS/365) Lower CCC = better liquidity management. Negative CCC (like Amazon) = business is funded by suppliers!

Payout Ratio = Dividends Per Share / EPS Retention Ratio = 1 − Payout Ratio Dividend Yield = DPS / Market Price Total Return = Dividend Yield + Capital Gain Yield STOCK DIVIDEND: Distributes additional shares instead of cash. Does NOT change total wealth — only redistributes into more shares. STOCK SPLIT: e.g. 2-for-1 → doubles shares, halves price. Increases liquidity. SHARE REPURCHASE: Firm buys back own shares → EPS rises → alternative to cash dividend.

CORRELATION (r): r = Σ(X−X̄)(Y−Ȳ) / √[Σ(X−X̄)² · Σ(Y−Ȳ)²] Range: −1 ≤ r ≤ +1 | r² = Coefficient of Determination REGRESSION LINE: Ŷ = a + bX b (slope) = Σ(X−X̄)(Y−Ȳ) / Σ(X−X̄)² a (intercept) = Ȳ − b·X̄ INFERENCE: H₀: β = 0 (no relationship) → t-test or F-test p-value < 0.05 → reject H₀ → X is significant predictor of Y Standard Error of Estimate (SEE): measures scatter around regression line

MODEL: Ŷ = b₀ + b₁X₁ + b₂X₂ + ... + bₖXₖ ADJUSTED R² = 1 − [(1−R²)(n−1)/(n−k−1)] ← use this, not R², for multiple regression ASSUMPTIONS (LINE): L = Linearity | I = Independence of errors N = Normality of residuals | E = Equal variance (Homoscedasticity) MULTICOLLINEARITY: High correlation between predictors → VIF (Variance Inflation Factor) > 10 = serious problem → Fix: remove one variable, use PCA, or ridge regression AUTOCORRELATION: Errors correlated over time → Detected by Durbin-Watson test → DW ≈ 2 → no autocorrelation | DW < 1 or > 3 → problem DUMMY VARIABLES: For categorical predictors → k categories → use k−1 dummies (avoid dummy variable trap)

4 COMPONENTS: Trend (T) · Cyclical (C) · Seasonal (S) · Irregular (I) Multiplicative Model: Y = T × C × S × I SIMPLE MOVING AVERAGE: F(t+1) = (Xₜ + Xₜ₋₁ + ... + Xₜ₋ₙ₊₁) / n WEIGHTED MOVING AVERAGE: F(t+1) = Σ(weight × value) / Σweights EXPONENTIAL SMOOTHING: Fₜ₊₁ = α·Xₜ + (1−α)·Fₜ [0 < α < 1] High α → more weight on recent data (responsive) Low α → more weight on historical data (stable/smooth) TREND ADJUSTED EXPONENTIAL SMOOTHING: Includes trend term: FIT = Ft + Tt ACCURACY MEASURES: MAD = Σ|Actual − Forecast| / n (Mean Absolute Deviation) MSE = Σ(Actual − Forecast)² / n (Mean Squared Error) MAPE = Σ|Actual−Forecast|/Actual / n × 100% (lower = better)

LP STRUCTURE: Maximize/Minimize Z = c₁X₁ + c₂X₂ Subject to: a₁₁X₁ + a₁₂X₂ ≤ b₁ (constraint 1) a₂₁X₁ + a₂₂X₂ ≤ b₂ (constraint 2) X₁, X₂ ≥ 0 (non-negativity) GRAPHICAL METHOD: 1. Plot each constraint as equality line 2. Identify feasible region (satisfies ALL constraints) 3. Evaluate objective function at each corner point 4. Optimal solution is at one of the corner points SENSITIVITY ANALYSIS: Shadow Price = increase in Z per 1-unit increase in RHS of binding constraint Binding constraint: uses all resource (slack = 0, shadow price > 0) Non-binding: has leftover resource (slack > 0, shadow price = 0) Allowable range = range over which current basis stays optimal PRIMAL-DUAL: Every max LP (primal) has a corresponding min LP (dual) Dual variables = shadow prices of primal constraints

TRANSPORTATION MODEL: Minimize Σ Σ cij·xij (total shipping cost) Subject to: supply constraints at each source demand constraints at each destination Balanced: Σ supply = Σ demand (add dummy if unbalanced) INITIAL SOLUTIONS: 1. North-West Corner: Start top-left, allocate max possible, move right/down 2. Least Cost Method: Always allocate to cheapest available cell 3. VAM (Vogel's): Compute penalty (2nd − 1st min) per row/col, allocate to min-cost cell in max-penalty row/col → BEST initial solution OPTIMALITY TEST (MODI/UV Method): Assign ui + vj = cij for basic cells → find Δij = cij − ui − vj for non-basic If all Δij ≥ 0 → optimal. If any Δij < 0 → improve along loop. ASSIGNMENT MODEL (Hungarian Method): Step 1: Row reduction (subtract row minimum from each row) Step 2: Column reduction (subtract col minimum from each column) Step 3: Cover all zeros with minimum lines Step 4: If lines = n → optimal assignment. Else: find min uncovered value, subtract from uncovered, add to doubly-covered cells, repeat Basic variables in transport solution = m + n − 1

CPM: Deterministic times → find critical path (longest path = min project duration) FORWARD PASS: ES(j) = max[EF of all immediate predecessors] EF = ES + Duration BACKWARD PASS: LF(i) = min[LS of all immediate successors] LS = LF − Duration FLOAT: Total Float = LS − ES = LF − EF Free Float = ES(successor) − EF(current) Critical activities: Total Float = 0 PERT: Probabilistic times — 3 estimates te = (a + 4m + b) / 6 (Expected time) σ² = [(b − a) / 6]² (Variance of one activity) Project σ² = Σ variances of critical path activities Project σ = √(project variance) PROBABILITY CALCULATIONS: Z = (Ts − Te) / σ where Ts = scheduled time, Te = expected project time Use normal distribution table to find P(finish by Ts)

GDP CONCEPTS: GDP → GNP: Add Net Factor Income from Abroad (NFIA) GNP − Depreciation = NNP (Net National Product) NNP at FC = NNP at MP − Indirect Taxes + Subsidies = National Income PI (Personal Income) = NI − Retained Earnings − Corp Tax + Transfer Payments DI (Disposable Income) = PI − Personal Tax THREE MEASUREMENT METHODS (give same GDP theoretically): 1. Expenditure: GDP = C + I + G + (X − M) 2. Income: GDP = W + R + I + P (wages + rent + interest + profit) 3. Product (GVA): Sum of value added at each production stage; avoids double-counting NOMINAL vs REAL GDP: Real GDP = Nominal GDP / GDP Deflator × 100 GDP Deflator = (Nominal GDP / Real GDP) × 100 Growth Rate = (Real GDP_t − Real GDP_{t-1}) / Real GDP_{t-1} × 100 PPP vs MARKET RATE: Market rate: converts using official exchange rates → undervalues developing countries PPP: adjusts for price level differences → better for comparing living standards

AD = C + I + G + (X − M) Consumption Function: C = a + bY (a = autonomous, b = MPC, 0 < b < 1) Savings: S = Y − C = −a + (1−b)Y (MPS = 1 − MPC) EQUILIBRIUM (2-sector): Y = C + I → Y = a + bY + I₀ → Y* = (a + I₀) / (1 − b) MULTIPLIER: k = 1/(1−MPC) = 1/MPS ΔY = k × ΔI (any autonomous spending change multiplied) PARADOX OF THRIFT: If all households save more → AD falls → income falls → savings may not increase 3-SECTOR (with Govt): Y = C + I + G Govt Expenditure Multiplier = 1/(1−b) Tax Multiplier = −b/(1−b) [negative because tax reduces disposable income] Balanced Budget Multiplier = 1 (always, regardless of MPC) 4-SECTOR (Open): Y = C + I + G + X − M Open economy multiplier = 1/(1−b+m) where m = marginal propensity to import ACCELERATOR: I = v × ΔY (investment responds to CHANGE in income, not level)

IS CURVE: Goods market equilibrium Y = C + I + G Slopes DOWNWARD (↑r → ↓I → ↓Y) Shifts RIGHT if: ↑G, ↓T, ↑investment confidence, ↑exports LM CURVE: Money market equilibrium Ms = Md Slopes UPWARD (↑Y → ↑Md → ↑r to restore equilibrium) Shifts RIGHT if: ↑Money supply (NRB expansionary policy) IS-LM EQUILIBRIUM: Point where both curves intersect → simultaneous equilibrium in goods & money markets Fiscal policy shifts IS curve Monetary policy shifts LM curve Crowding out: ↑G → ↑r → ↓I (fiscal expansion crowds out private investment)

HARROD-DOMAR: g = s / v (g = growth rate, s = savings rate, v = capital-output ratio) SOLOW: Δk = sf(k) − (n + δ)k At steady state: sf(k*) = (n + δ)k* [investment = depreciation + dilution] Golden Rule: Maximize consumption in steady state → MPK = n + δ

PRODUCTIVITY: Productivity = Output / Input Partial productivity = Output / Single Input (labor, capital, etc.) Multifactor productivity = Output / (Labor + Capital + Materials + Energy) Total factor productivity = Output / All inputs Productivity improvement: technology, training, process improvement, better management Reasons for org failure: poor operations, poor financial management, poor strategy

FORECASTING METHODS (same as STT 502 Unit 3): Naïve: F(t+1) = Xₜ (just use last period) Simple MA, Weighted MA, Exponential Smoothing Trend Equation: Ŷ = a + bt (fit trend line using regression) Trend Adjusted ES: tracks both level and trend ACCURACY: MAD, MSE, MAPE (see STT U3 for formulas) SCHEDULING: Sequence jobs to optimize performance measures FCFS (First come first served) | SPT (Shortest Processing Time) EDD (Earliest Due Date) | LPT (Longest Processing Time) SPT minimizes average flow time and WIP

EOQ (Economic Order Quantity): EOQ = √(2DS / H) D = annual demand | S = ordering cost per order | H = holding cost per unit per year Cycle time = EOQ / D Reorder Point = d × L (d = daily demand, L = lead time in days) Total Cost = (D/Q)×S + (Q/2)×H + purchase cost

EMV (Expected Monetary Value) = Σ Pᵢ × Payoffᵢ EVPI (Expected Value of Perfect Information): EVPI = EV with perfect info − Best EMV without info EVPI = Expected opportunity loss (EOL) of best strategy Minimax Regret: Regret = Best payoff in that state − Actual payoff → minimize max regret

STATISTICAL PROCESS CONTROL (SPC) — Control Charts: X̄ CHART (Mean Chart): UCL = X̄̄ + A₂·R̄ | CL = X̄̄ | LCL = X̄̄ − A₂·R̄ R CHART (Range Chart): UCL = D₄·R̄ | CL = R̄ | LCL = D₃·R̄ p-CHART (Proportion defective): p̄ = total defectives / total inspected UCL = p̄ + 3√(p̄(1−p̄)/n) | LCL = p̄ − 3√(p̄(1−p̄)/n) c-CHART (Defects per unit — Poisson): UCL = c̄ + 3√c̄ | LCL = c̄ − 3√c̄ Points outside control limits = process out of control

ROI = (Revenue Generated − Marketing Cost) / Marketing Cost × 100% ROAS = Revenue from Ads / Ad Spend CAC = Total Marketing & Sales Spend / Number of New Customers Acquired CLV = Average Order Value × Purchase Frequency × Customer Lifespan LTV:CAC Ratio > 3 = healthy business model