CA Final · Advanced Financial Management

Security Analysis: formula sheet

Full chapter guide

Key formulas

Intrinsic value decision rule: Intrinsic value > Market price → undervalued (buy); Intrinsic value < Market price → overvalued (sell); State the conclusion in every answer, with the reason.
Earnings per share (EPS): EPS = (Net profit after tax − Preference dividend) ÷ Number of equity shares; Use weighted average shares if shares changed during the year.
Price-earnings ratio: P/E = Market price per share ÷ EPS; Value by multiple: Estimated price = EPS × appropriate P/E.
Dividend yield: Dividend yield = Dividend per share ÷ Market price per share × 100; Shows cash return only, not capital gain.
Dividend payout ratio: Payout ratio = DPS ÷ EPS; Retention ratio = 1 − payout ratio.
Return on equity: ROE = Net profit after tax ÷ Shareholders' equity; Sustainable growth g = ROE × retention ratio, when ROE and retention stay constant.
Constant growth value: P₀ = D₁ ÷ (Ke − g); Valid only when Ke > g and growth is constant.
Book value per share: Book value per share = Equity shareholders' funds ÷ Number of equity shares; Price-to-book = Market price ÷ Book value per share.
Simple moving average (n periods): SMA = (P1 + P2 + ... + Pn) ÷ n; Each price has equal weight. Drop the oldest price and add the newest as you move forward.
Exponential moving average: EMA today = (Price today × k) + (EMA yesterday × (1 − k)), where k = 2 ÷ (n + 1); Gives more weight to recent prices, so it reacts faster than SMA. Use the given first EMA, or SMA, as the starting value.
Relative Strength (RS): RS = Average gain ÷ Average loss; Averages are over the chosen period (commonly 14). Losses are taken as positive numbers.
Relative Strength Index: RSI = 100 − [100 ÷ (1 + RS)]; Ranges from 0 to 100. Commonly above 70 is read as overbought and below 30 as oversold.
Rate of change / momentum: ROC = [(Price today − Price n periods ago) ÷ Price n periods ago] × 100; Positive means upward momentum. A fall in ROC while price rises warns of weakness.
Moving average crossover rule: Short MA crosses above long MA = buy; short MA crosses below long MA = sell; Also: price crossing above its moving average is a buy signal and below is a sell signal.
Dow Theory trend rule: Higher highs and higher lows = uptrend; lower highs and lower lows = downtrend; A trend is assumed to continue until a clear reversal is confirmed.
Weak form: Price already reflects: past prices and volumes; Technical analysis and chart patterns are useless. Fundamental analysis and insider information may still work.
Semi-strong form: Price already reflects: all public information (includes weak form); Both technical and fundamental analysis are useless. Only insider information can give abnormal returns.
Strong form: Price already reflects: all public and private information (includes semi-strong); No one earns consistent abnormal returns, not even insiders.
Random walk: Pₜ = Pₜ₋₁ + expected return + random error (unpredictable news); Successive price changes are independent. Past changes give no help in predicting the next change.
Abnormal return: Abnormal return = Actual return − Expected (required) return; Used in event studies. In a semi-strong efficient market, abnormal return appears only on the announcement day and is not repeated afterwards.
Dividend discount model (finite holding): P0 = Σ Dt ÷ (1 + ke)^t + Pn ÷ (1 + ke)^n; Pn is the expected price at the end of year n. Discount every cash flow at ke.
Gordon growth model: P0 = D1 ÷ (ke − g) = D0 × (1 + g) ÷ (ke − g); Valid for constant growth forever and ke > g. Check whether the given dividend is D0 or D1.
Cost of equity by CAPM: ke = Rf + β × (Rm − Rf); Rm − Rf is the market risk premium. If Rm is given, subtract Rf first.
Growth from retention: g = b × r, where b = 1 − payout ratio; r is return on equity (or on retained earnings). Use it when the question gives payout and ROE.
Multi-stage terminal value: Pn = Dn+1 ÷ (ke − gn); Gives the value at the end of the high-growth phase. Discount it by (1 + ke)^n.
P/E valuation: Value per share = EPS × P/E ratio; Use the same EPS basis (current or forward) as the P/E ratio.
Justified P/E under Gordon: P/E = Payout ratio × (1 + g) ÷ (ke − g); This is based on trailing EPS (E0); with forward EPS (E1) it is Payout ÷ (ke − g).
EV/EBITDA valuation: Equity value = EBITDA × multiple − Net debt; Net debt = debt − cash. Divide equity value by number of shares for value per share.
Bond price: P = Σ [C ÷ (1 + y)^t] + M ÷ (1 + y)^n; C = coupon per period, M = redemption value, y = required yield per period, n = number of periods. For semi-annual bonds use half the coupon, double the periods and half the annual yield.
Perpetual bond price: P = C ÷ y; Use for irredeemable bonds with fixed coupon.
Current yield: Current yield = Annual coupon ÷ Market price × 100; Ignores capital gain or loss and time value.
Approximate YTM: YTM ≈ [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2]; Quick estimate. Use it as the first trial rate for interpolation.
YTM by interpolation: YTM = Lower rate + [(PV at lower − Price) ÷ (PV at lower − PV at higher)] × (Higher rate − Lower rate); Choose two rates so that the price lies between the two present values.
Macaulay duration: D = Σ [t × PV of cash flow at t] ÷ Σ PV of cash flows; Σ PV of cash flows equals the bond price when discounted at the YTM. Measured in years.
Modified duration: MD = D ÷ (1 + y); y is the yield per period matching the compounding of D. Annual compounding: use the annual YTM.
Price change using duration: ΔP ÷ P ≈ − MD × Δy; Linear estimate. Put Δy in decimals: a 1% rise is Δy = 0.01. The minus sign shows price falls when yield rises.
Convexity: Convexity = [1 ÷ (P × (1 + y)^2)] × Σ [t × (t + 1) × CF_t ÷ (1 + y)^t]; y is in decimals (10% = 0.10). Use consistently with the adjustment formula below.
Price change with convexity: ΔP ÷ P ≈ − MD × Δy + ½ × Convexity × (Δy)^2; Valid with the convexity definition above. Δy must be in decimals (0.01 for 1%), so (Δy)^2 = 0.0001 for a 1% move. The result is a fraction; multiply by 100 for a percentage.
Zero-coupon bond duration: D = Maturity in years; Single cash flow at maturity.

Quick revision

Intrinsic value is what analysis says a security is worth. Compare it with market price to decide buy, sell or hold.
Fundamental analysis moves from economy to industry to company (top-down).
Technical analysis uses past price and volume to predict direction. It assumes trends tend to continue.
Weak form: prices reflect past price data. Semi-strong: all public information. Strong: all information, including private.
If markets are weak-form efficient, technical analysis should not give consistent excess returns.
Constant growth model: P₀ = D₁ ÷ (ke − g), valid only when ke > g.
D₁ = D₀ × (1 + g). Do not use D₀ in place of D₁.
P/E-based value = expected EPS × appropriate P/E multiple.
Bond price = present value of coupons + present value of redemption value, discounted at the required yield.
Bond price and yield move in opposite directions.
Current yield = annual coupon ÷ current market price.
A bond selling below face value has a yield to maturity above its coupon rate.

Common mistakes

Writing the framework as a list of definitions without applying it to the case facts. Fix: Pull at least one fact per level from the scenario and say how it affects value.
Confusing fundamental and technical analysis, for example saying fundamental analysis uses charts. Fix: Remember: fundamental uses economic and financial data to find value; technical uses price and volume history to find trends.
Treating technical and fundamental analysis as the same thing, or saying technical analysis finds intrinsic value. Fix: Remember: fundamental analysis finds value; technical analysis reads price and volume to time the trade.
Using a negative number for average loss in the RS formula. Fix: Take the size of each loss as a positive figure, then divide average gain by average loss.
Saying weak form means fundamental analysis is useless. Fix: Weak form rules out only technical analysis. Fundamental analysis is ruled out from semi-strong onwards.
Treating the three forms as separate, unrelated ideas. Fix: Remember they are cumulative. Each higher form includes the information of the lower forms.
Using D0 in the Gordon formula as if it were D1. Fix: If D0 is given, compute D1 = D0 × (1 + g) first. If 'expected dividend next year' is given, that is D1.
Applying Gordon when g is equal to or more than ke. Fix: Check ke > g before using the formula. For a high-growth phase, use multi-stage and apply Gordon only to the stable phase.
Calculating coupon as a percentage of market price instead of face value. Fix: Coupon = coupon rate × face value. Market price is used only in current yield and YTM.
Using current yield as YTM. Fix: Current yield ignores redemption gain or loss and the time value. Use it only when the question asks for it. It equals YTM for a perpetual bond. For a bond trading at par, current yield equals the coupon rate and the YTM.

Exam tips

Theory questions on EIC reward structure: use the three headings and tie each to the case facts given.
In numerical cases, show the formula, the substitution and the final comparison with market price in separate lines.
Always write the word undervalued or overvalued and a recommendation; markers look for this conclusion.
For the fundamental vs technical question, give four or five contrasts: basis, data, time horizon, objective, tools.
Read the dividend carefully: latest paid dividend means D₀, expected next-year dividend means D₁.
For numerical questions, show the formula, the working and a one-line signal. Marks are given for all three.
In theory answers, write the difference between technical and fundamental analysis in two columns of points: basis, data used, time horizon and objective.
Learn Dow Theory as a short list: three trends, three phases of a bull market, and confirmation by averages and volume.