CSC Exam 2 Formulas

[Ch13] FORMULA: Dividend Discount Model (constant growth)

Price = D0 × (1 + g) ÷ (r − g) = D1 ÷ (r − g). | IN IT: D0 = dividend just paid, D1 = next year's dividend, r = required return, g = constant growth rate. | WHY/WHEN: values a stable dividend-paying stock (utilities, banks). Requires r > g. | HIGHER g or LOWER r → higher value. Example: D0 $2, g 4%, r 9% → 2.08 ÷ 0.05 = $41.60.

[Ch13] ★ DDM trap: D0 vs D1

If the stem says 'just paid' you have D0 — grow it one year first (× (1+g)). If it says 'expected next year' it's already D1. Using D0 directly understates value.

[Ch14] FORMULA: Working capital (current) ratio

Current assets ÷ Current liabilities. | WHY: liquidity — can the company pay short-term debts? | HIGHER = more liquid (too high may mean idle assets). LOWER = possible cash squeeze. ~2:1 is a common comfort level.

[Ch14] FORMULA: Quick ratio

(Current assets − Inventories) ÷ Current liabilities. | WHY: stricter liquidity test — inventory may be hard to sell fast. | ≥ 1:1 generally acceptable. HIGHER = can meet obligations without selling inventory.

[Ch14] FORMULA: Asset coverage

[Tangible assets − (Current liabilities − Short-term debt)] ÷ Total debt outstanding. | WHY: risk ratio — net tangible assets backing each $1 of debt if liquidated. | HIGHER = safer for lenders. Subtract only the NON-debt current liabilities.

[Ch14] FORMULA: Debt-to-equity

Total debt outstanding ÷ Equity. | WHY: proportion of borrowed vs shareholder funds (financial risk). | HIGHER = more leverage, more risk. Issuing shares → ratio FALLS. Paying down debt → FALLS.

[Ch14] FORMULA: Cash flow / Total debt

Cash flow from operating activities ÷ Total debt outstanding. | WHY: ability to repay debt from operations. | HIGHER = safer; a falling trend warns of trouble.

[Ch14] FORMULA: Interest coverage

Profit before interest and taxes ÷ Interest charges. | WHY: times interest is covered by earnings (bondholder safety). | HIGHER = safer. Use profit BEFORE interest and taxes — never net profit.

[Ch14] FORMULA: Gross profit margin

(Revenue − Cost of sales) ÷ Revenue × 100. | WHY: profitability of the core product after direct costs. | HIGHER = pricing power / cost control.

[Ch14] FORMULA: Net profit margin

(Profit − Share of profit of associates) ÷ Revenue × 100. | WHY: how much of each sales dollar becomes profit from the company's own operations. | HIGHER = more efficient. Remove associates' profit because it isn't from own revenue.

[Ch14] FORMULA: Return on common equity (ROE)

Profit ÷ Total equity × 100 (if preferred shares exist: (Profit − Preferred dividends) ÷ Common equity). | WHY: return management earns on shareholders' money. | HIGHER = better use of equity (check it isn't just from heavy debt).

[Ch14] FORMULA: Inventory turnover

Cost of sales ÷ Inventory. | WHY: how many times inventory is sold and replaced per year. | HIGHER = efficient, fresh stock (too high risks stock-outs). LOWER = slow-moving or obsolete inventory.

[Ch14] FORMULA: Earnings per share (EPS)

(Profit − Preferred dividends) ÷ Weighted average common shares outstanding. | WHY: earnings available to each common share; drives price. | Rising trend = favourable. Fully diluted EPS assumes all convertibles/options are converted (lower, more conservative).

[Ch14] FORMULA: Dividend payout ratio

Common dividends ÷ Profit (available to common) × 100. | WHY: share of earnings paid out vs retained. | HIGHER = mature, income-oriented; LOWER = reinvesting for growth. Very high may be unsustainable.

[Ch14] FORMULA: Dividend yield

Indicated annual dividend per share ÷ Market price × 100. | WHY: income return on the current price. | HIGHER = more income (or price has fallen — check why). Uses MARKET price, not book value.

[Ch14] FORMULA: Price-earnings (P/E) ratio

Market price ÷ EPS. | WHY: how many dollars investors pay per $1 of earnings. | HIGHER = growth expectations/optimism; LOWER = value or pessimism. Compare only within the same industry.

[Ch14] FORMULA: Equity (book) value per common share

Common equity ÷ Number of common shares outstanding. | WHY: accounting net worth per share; compare to market price (P/B). | Price below BVPS may indicate undervaluation.

[Ch14] ★ Ratio calculation case data trap

Read which profit the formula wants: interest coverage = PBIT; net margin = profit less associates; ROE/EPS/payout = net profit. Picking the wrong profit line is the usual wrong distractor.

[Ch15] FORMULA: Return / Expected return on a security

(Cash flow received + Capital gain) ÷ Beginning value × 100. | Denominator = what the investor PAID. | Example: buy $50, $2 dividend, sell $56 → (2 + 6) ÷ 50 = 16%.

[Ch15] ★ Ex-post vs ex-ante return

Ex-post = ACTUAL historical return (used to compare results vs expectations and benchmarks). Ex-ante = EXPECTED (future) return.

[Ch15] FORMULA: Expected return using probabilities

E(R) = Σ (Probability of scenario × Return in scenario). | WHY: forecast return across possible outcomes. Probabilities must total 100%.

[Ch15] FORMULA: Real return

Real ≈ Nominal return − Inflation rate. | WHY: purchasing-power gain. | Example: 7% nominal, 2.5% inflation → 4.5% real.

[Ch15] FORMULA: Portfolio expected return

Σ (Weight of each holding × its return). | Weights = each holding's MARKET VALUE ÷ total portfolio value. | Example: $5,000@20%, $1,500@−10%, $4,000@12% (total $10,500) → 47.6%×20 + 14.3%×(−10) + 38.1%×12 = 12.66%.

[Ch16] ★ How to diversify a fixed-income portfolio

Mix domestic and foreign bonds, DIFFERENT maturities, a RANGE of credit ratings, and different coupon rates. ('Same maturity' or 'similar coupon' = no diversification.)

[Ch16] FORMULA: Total return (portfolio)

(Ending value − Beginning value + Income) ÷ Beginning value × 100. Formula Finder: Increase in market value ÷ Beginning value × 100. | Example: $200,000 → $218,000 = 9%.

[Ch16] FORMULA: Sharpe ratio

(Portfolio return − Risk-free rate) ÷ Portfolio standard deviation. | WHY: excess return per unit of total risk (risk-adjusted performance). | HIGHER = better. Example: Rf 3%; A 12%/σ18 = 0.50; B 9%/σ10 = 0.60 → B wins.

[Ch17] FORMULA: NAVPS

(Total assets − Total liabilities) ÷ Units outstanding. | WHY: the per-unit price for buying (before load) and redeeming. Calculated at end of each valuation day. | Example: ($52M − $2M) ÷ 4M = $12.50.

[Ch17] FORMULA: Offering price (front-end load)

NAVPS ÷ (100% − Sales charge %). | WHY: the price paid including the load (load is a % of the offering price). | Example: $12.50 ÷ 0.95 = $13.16. Multiplying 12.50 × 1.05 = $13.13 is the wrong distractor.

[Ch17] ★ Working BACKWARD: NAVPS from offering price

NAVPS = Offering price × (1 − Load). | Example: offering $78.50, 4% load → 78.50 × 0.96 = $75.36. (78.50 × 1.04 = $81.64 is the direction-inversion trap.)

[Ch17] ★ Fee paid to the distributor on a front-end load purchase

Amount invested × Front-end load %. Example: $4,000 × 3% = $120. MER and TER are fund expenses, not paid to the distributor at purchase.

[Ch17] FORMULA: Redemption price (deferred sales charge)

NAVPS − Sales commission (DSC). | Example: NAVPS $20, 3% DSC → 20 − 0.60 = $19.40. DSC typically declines each year held.

[Ch17] FORMULA: Management expense ratio (MER)

Aggregate fees and expenses ÷ Average NAV × 100. | WHY: annual cost of owning the fund; reduces returns. | HIGHER = more drag. Excludes trading commissions. Use AVERAGE NAV — not year-end NAV or total assets. Example: $1.8M ÷ $75M = 2.40%.

[Ch18] ★ ACB with reinvested distributions

ACB = all purchases + all REINVESTED distributions. Example: $25,000 + $580 reinvested + $5,000 = $30,580; sold for $31,000 → capital gain $420 (taxable gain $210).

[Ch18] ★ What happens to NAVPS when a fund pays a distribution?

NAVPS falls by the distribution amount (like a stock going ex-dividend). Reinvested units = distribution total ÷ POST-distribution NAVPS.

[Ch18] ★ Reinvested distribution example

1,000 units, NAVPS $6, distribution $1/unit → $1,000 reinvested at $5 = 200 new units → 1,200 units total.

[Ch18] ★ Mutual fund tax: 45% bracket, buys 100 @ $20, $1.50/unit cap gains distribution, sells @ $30

Distribution $150 + sale gain $1,000 = $1,150 → × 50% inclusion = $575 → × 45% = $258.75. Skipping the 50% step gives $517.50 (trap).

[Ch18] FORMULA: Life expectancy-adjusted withdrawal

Portfolio value ÷ (Life expectancy − Current age). | WHY: spreads capital over expected remaining life; recalculated yearly. | Example: $240,000 ÷ (88 − 72) = $15,000.

[Ch19] ★ Exchange-traded notes (ETNs) vs ETFs

ETN = unsecured debt note of the issuer promising an index return → credit risk, no tracking error, not an investment fund. Similarity: BOTH TRADE ON AN EXCHANGE.

[Ch20] ★ High-water mark

Incentive fee is paid only on gains ABOVE the fund's previous peak value. Example: −$10M year 1, +$15M year 2 → fee on net $5M × 10% = $500,000.

[Ch21] ★ Convertible arbitrage — mechanics

Buy the convertible bond and SHORT the underlying common shares (relative value). Profit/loss = gain/loss on the bond leg + gain/loss on the short leg.

[Ch21] FORMULA: Net exposure (long/short fund)

(Long positions − Short positions) ÷ Capital × 100. | WHY: the fund's net market exposure (directional bet). | HIGHER = more market-sensitive; ~0% = market neutral. Example: ($18M − $8M) ÷ $20M = 50%. Gross exposure = (Long + Short) ÷ Capital = 130% (measures leverage).

[Ch22] ★ Seg fund payout rule

Always the GREATER of market value or the guaranteed amount. Example: $145,000 invested, 75% guarantee = $108,750; market value $114,000 → receives $114,000.

[Ch22] ★ Split share capital share leverage

Capital share price movement is magnified because preferred holders funded part of the underlying shares. % change = change in underlying value ÷ capital share price (the investor's own money).

[Ch23] ★ Stock basket-linked PPN

Return = effective AVERAGE of the basket's share returns, usually with a maximum (cap) per share. Example: 25, 20, −20, 30, 50% with 30% cap → (25+20−20+30+30) ÷ 5 = 17%. Ignoring the cap gives 21% (trap).

[Ch23] FORMULA: Index-linked GIC return

Index growth = (Ending index − Initial index) ÷ Initial index × 100; Overall return = Index growth × Participation rate. | WHY: bank deposit with market upside and CDIC protection. | Example: 15,000 → 18,600 = 24% × 75% = 18%.

[Ch24] FORMULA: Tax on a capital gain (tax ladder)

Gain = Proceeds − ACB (both net of commissions) → × 50% inclusion = taxable capital gain → × marginal rate = tax. | Count the steps — stopping after the gain or skipping 50% is the trap.

[Ch24] FORMULA: Federal tax on eligible Canadian dividends

1) Gross-up: Dividend × 1.38. 2) Tax = Grossed-up × federal rate. 3) Dividend tax credit = Grossed-up × 15.02%. 4) Tax payable = step 2 − step 3. | Example: $5,000 → $6,900 × 29% = $2,001 − $1,036 = $965.

[Ch24] ★ Dividend tax trap — stopping early

$2,001 is the tax BEFORE the dividend tax credit. Always finish with the subtraction: $2,001 − $1,036 = $965.

[Ch24] ★ Dividend tax credit calculation

DTC = Dividend × 1.38 × 15.02%. Example: $1,320 × 1.38 = $1,821.60 × 15.02% ≈ $274. (The federal rate in the stem doesn't change the credit.)

[Ch24] ★ Foreign (e.g., U.S.) dividends

No gross-up and no dividend tax credit — taxed like INTEREST at the full marginal rate. Example: $1,000 × 29% = $290. Foreign tax withheld can be claimed as a foreign tax credit.

[Ch24] ★ Bond capital gain with accrued interest

Capital gain = Sale price − Purchase price, EXCLUDING all accrued interest. Example: bought $10,650 + $175 accrued, sold $10,980 + $210 accrued → gain $330.

[Ch24] ★ Earned income for RRSP purposes

Includes employment income and NET RENTAL income (also self-employment). Does NOT subtract deductions such as student-loan interest. Example: $55,000 + $4,500 rental = $59,500.

[Ch27] ★ Who manages the relationship when a company wants to acquire a private competitor?

INVESTMENT BANKER (M&A advisory). Investment banking = corporate finance, public finance, mergers & acquisitions.