Equity Investments formula sheet.

Where Value of position = market value of the shares held, Value of equity = the investor's own money in it, Initial margin = minimum equity fraction required at purchase.

The leverage ratio tells you how many times a price move is magnified in the return on your equity. Before interest and costs, equity return is about the leverage ratio times the share return, in both directions.

Exam tip A 40% initial margin gives at most 1 / 0.40 = 2.5x leverage, so a 10% price drop costs about 25% of the equity.

Lesson: Long, short and leveraged positions: leverage ratio, margin return and margin calls →All Market Organization and Structure formulas

Where Sale proceeds = shares x sale price, Loan = amount borrowed from the broker, Equity = investor's initial cash in the position; commissions and dividends are totals for the position.

This is the full margin-trade return the exam asks for: the numerator is the ending equity after repaying the loan and interest, the denominator is everything the investor put in at the start.

Exam tip Divide by the investor's initial equity plus the purchase commission, not by the total value of the shares bought.

Lesson: Long, short and leveraged positions: leverage ratio, margin return and margin calls →All Market Organization and Structure formulas

Where $P^*$ = price at which a margin call is triggered, $P_0$ = purchase price, Initial margin and Maintenance margin as decimals.

Below this price the investor's equity as a fraction of the position falls under the maintenance margin and the broker demands more cash. It is always below the purchase price for a long position.

Exam tip Check your answer: at $P^*$, (price minus loan per share) / price must equal the maintenance margin. For a short, use $P_0(1 + IM)/(1 + MM)$, which is above $P_0$.

Lesson: Long, short and leveraged positions: leverage ratio, margin return and margin calls →All Market Organization and Structure formulas

Where $V_{PRI,0}$, $V_{PRI,1}$ = price index value at the start and end of the period, $Inc_I$ = income (dividends) from all constituents over the period, in index points.

The price return captures only the change in constituent prices; the total return adds the income they paid. The gap between a total return index and its price return index widens every year that dividends are paid.

Exam tip Both returns divide by the beginning value of the price index. Over several periods, link returns geometrically: multiply the (1 + return) terms.

Lesson: What an index is: value, price return and total return →All Security Market Indexes formulas

Where $Q_i$ = shares outstanding, $P_i$ = share price, $f_i$ = fraction of shares in the market float (freely tradable), $N$ = number of constituents.

Each company's weight is its share of total market value, so the index tracks the value of the whole market. The float-adjusted version counts only shares available to the public, which is what most major indexes use.

Exam tip Shares held by governments, founders or other companies are excluded from the float, so $f_i$ is at most 1 and lowers closely held companies' weights.

Lesson: Building an index: target market, constituents and weighting →All Security Market Indexes formulas

Where $P_i$ = price of one share of security i, $N$ = number of constituents, $D$ = divisor (initially usually N), $w_i^{P}$ = price weight.

A price-weighted index holds one share of each constituent, so the highest-priced shares carry the most weight regardless of company size. Its return equals the return on a portfolio holding one share of each stock.

Exam tip A given percentage move in the highest-priced stock moves the index the most; a stock split cuts that stock's weight even though nothing economic changed.

Lesson: Price-weighted and equal-weighted indexes →All Security Market Indexes formulas

Where $D_{new}$ = adjusted divisor, $\sum P_i$ = sum of constituent prices using the post-split price, $V$ = index value just before the split.

The divisor is reset so the split (or a change of constituent) leaves the index value unchanged. Exam questions then ask for the index value or return on the next day using the new divisor.

Exam tip After a split the sum of prices falls, so the divisor falls too; if your new divisor is larger, you have inverted the ratio.

Lesson: Price-weighted and equal-weighted indexes →All Security Market Indexes formulas

Where $w_i^{E}$ = weight of each constituent, $N$ = number of constituents, $R_i$ = return on security i, $R_I$ = index return.

Every constituent counts the same, so the index return is the simple average of constituent returns. The method overweights small companies relative to their market value and needs frequent rebalancing.

Exam tip The simple average holds only for the first period after (re)weighting; once prices move, the weights drift away from 1/N.

Lesson: Price-weighted and equal-weighted indexes →All Security Market Indexes formulas

Where $NI_t$ = net income available to common shareholders in year t, $BVE_t$, $BVE_{t-1}$ = book value of equity at the end and start of the year.

ROE measures how much profit the company earns on the equity shareholders have invested at book value. Rising ROE is good news only if it comes from profitability rather than from shrinking equity or more debt.

Exam tip Use net income after preferred dividends, and use the average of beginning and ending equity unless the question says beginning equity.

Lesson: Book value, market value, ROE and the cost of equity →All Overview of Equity Securities formulas

Where NI/EBT = tax burden, EBT/EBIT = interest burden, EBIT/Revenue = EBIT margin, Revenue/Assets = asset turnover, Assets/Equity = equity multiplier (financial leverage).

Splitting ROE shows whether a change comes from taxes, interest, operating margin, asset efficiency or leverage. Exam questions ask which driver explains an ROE change and whether that source is sustainable or riskier.

Exam tip A higher tax burden ratio means a lower tax rate; more debt raises the equity multiplier but lowers the interest burden ratio, so the net effect on ROE can go either way.

Lesson: Capital investments and capital structure →All Company Analysis: Past and Present formulas

Where $s_i$ = market share of firm i as a whole number (25% is 25), $N$ = number of firms in the industry.

The HHI measures industry concentration: the higher it is, the fewer and larger the competitors and the greater the pricing power is likely to be. A monopoly scores 10,000.

Exam tip 10,000 / HHI gives the equivalent number of equal-sized firms; if two firms merge and keep their customers, HHI rises by $2 s_a s_b$.

Lesson: Profitability, market share trends and concentration (HHI) →All Industry and Competitive Analysis formulas

Where $CFO$ = cash flow from operations, $FCInv$ = investment in fixed capital, Net borrowing = new borrowing minus debt repaid (can be negative).

FCFE is the cash that could be paid to common shareholders after operating needs, capital spending and debt flows. Discounting it at the required return on equity values the equity, which is useful when a company pays little or no dividend.

Exam tip Net borrowing is added and repayments are subtracted; discount FCFE at the cost of equity, never at the WACC.

Lesson: Present value models: DDM and FCFE →All Equity Valuation: Concepts and Basic Tools formulas

Where $V_0$ = value today, $D$ = level annual preferred dividend, $r$ = required return on the preferred share.

A non-callable, non-convertible preferred share with a fixed dividend and no maturity is valued as a perpetuity. A higher required return lowers its value, just as for a perpetual bond.

Exam tip D is the dividend amount (dividend rate x par), not the par value; if dividends are quarterly, use the annual dividend with the annual rate or match both per quarter.

Lesson: Preferred stock and the Gordon growth model →All Equity Valuation: Concepts and Basic Tools formulas

Where $D_0$ = dividend just paid, $D_1$ = dividend expected next year, $r$ = required return on equity, $g$ = constant dividend growth rate forever.

Values a mature, dividend-paying company whose dividends grow at a stable rate forever. The value is very sensitive to the gap between r and g, and the model fails when g is at or above r.

Exam tip Grow the last dividend first: the numerator is $D_1$, not $D_0$. The value you get is dated one period before $D_1$.

Lesson: Preferred stock and the Gordon growth model →All Equity Valuation: Concepts and Basic Tools formulas

Where $g$ = sustainable growth rate of earnings and dividends, $b$ = earnings retention rate, $ROE$ = return on equity.

Growth funded only by retained earnings, with ROE unchanged, equals the share of earnings reinvested times the return earned on it. It is the usual source of g for the Gordon model and the justified P/E.

Exam tip Use the retention rate, not the payout ratio: a company paying out 40% of earnings with ROE of 15% grows at 0.60 x 15% = 9%.

Lesson: Preferred stock and the Gordon growth model →All Equity Valuation: Concepts and Basic Tools formulas

Where $g_S$ = high short-term growth rate for years 1 to n, $V_n$ = terminal value at the end of year n, $r$ = required return, $D_0$ = current dividend.

Used when a company grows fast for a few years before settling to a stable rate. Value = present value of the high-growth dividends plus the present value of the Gordon value at the end of that phase.

Exam tip Write out each dividend year by year and discount each one separately; then add the terminal value discounted by $(1+r)^n$.

Lesson: Multistage dividend discount models →All Equity Valuation: Concepts and Basic Tools formulas

Where $V_n$ = value at the end of year n, $D_{n+1}$ = first dividend of the stable phase, $g_L$ = long-term growth rate, $g_S$ = high-growth rate, $r$ = required return.

The terminal value is a Gordon growth value placed at time n, once growth has stabilised. It often makes up most of the total value, so small changes in $g_L$ or r move the answer a lot.

Exam tip The classic trap: $V_n$ uses $D_{n+1}$ but is discounted back n years, not n + 1.

Lesson: Multistage dividend discount models →All Equity Valuation: Concepts and Basic Tools formulas

Where $P_0$ = price today, $E_1$ = next year's EPS, $D_1$ = next year's dividend, $p$ = dividend payout ratio, $r$ = required return, $g$ = growth rate.

This is the Gordon model divided by next year's earnings: the P/E a stock deserves given its payout, risk and growth. Compare it with the actual P/E to judge over- or undervaluation; it rises with payout and growth and falls as r rises.

Exam tip For the justified trailing P/E ($P_0/E_0$), multiply by $(1+g)$: $p(1+g)/(r-g)$.

Lesson: Price multiples and the method of comparables →All Equity Valuation: Concepts and Basic Tools formulas

Where Market cap = share price x shares outstanding, Preferred = value of preferred stock, $\text{Debt}_{\text{market}}$ = market value of debt, Cash and ST investments = cash and short-term investments.

EV is the value of the whole operating business to all capital providers, net of cash. EV/EBITDA lets you compare companies with different capital structures and is useful when earnings are negative but EBITDA is positive.

Exam tip Subtract cash, do not add it; and pair EV with pre-interest measures such as EBITDA, never with net income.

Lesson: Enterprise value multiples, asset-based valuation and choosing a model →All Equity Valuation: Concepts and Basic Tools formulas

Where $EV/EBITDA$ = benchmark (peer) multiple, $EBITDA$ = the company's EBITDA, Debt, Preferred and Cash = the company's own balances.

Apply a peer EV/EBITDA multiple to the company's EBITDA to get its enterprise value, then remove the claims of debt and preferred holders and add back cash to reach the value of common equity.

Exam tip Finish by dividing by shares outstanding if the question asks for a value per share.

Lesson: Enterprise value multiples, asset-based valuation and choosing a model →All Equity Valuation: Concepts and Basic Tools formulas