Equity Investments — Formula Sheet

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M01: Market Organization and Structure

Leverage Ratio

$\text{Leverage Ratio}=\frac{\text{Asset Value}}{\text{Equity Value}}=\frac{1}{\text{Margin Percentage}}$

where Margin Percentage = Initial Margin / Asset Value.

Margin Return (Return on Leveraged Position)

Long position:

$r_{\text{margin}}=\frac{P_1-P_0+D-\text{Interest on Borrowed Funds}}{P_0\times \text{Initial Margin \%}}$

where:

• $P_0$ = purchase price
• $P_1$ = selling price
• $D$ = dividends received
• Initial Margin % = equity as fraction of total position

Short position:

$r_{\text{short}}=\frac{P_0-P_1-D-\text{Interest on Borrowed Shares}}{P_0\times \text{Initial Margin \%}}$

Margin Call Price

Long position — margin call triggered when equity falls to maintenance margin:

$P_{\text{margin call}}=P_0\times \frac{1-\text{Initial Margin \%}}{1-\text{Maintenance Margin \%}}$

where:

• $P_0$ = original purchase price
• Initial Margin % = fraction of equity deposited initially
• Maintenance Margin % = minimum equity fraction before margin call

Short position:

$P_{\text{margin call}}=P_0\times \frac{1+\text{Initial Margin \%}}{1+\text{Maintenance Margin \%}}$

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M02: Security Market Indexes

Price Return Index

$\text{Price Return}=\frac{V_1-V_0}{V_0}$

${\text{Price Return Index}}_t={\text{Index}}_{t-1}\times (1+{\text{PR}}_t)$

where $V$ = index value, $\text{PR}$ = price return for the period.

Total Return Index

${\text{Total Return Index}}_t={\text{Total Return Index}}_{t-1}\times (1+{\text{TR}}_t)$

where:

${\text{TR}}_t=\frac{V_1-V_0+{\text{Income}}_t}{V_0}$

${\text{Income}}_t$ includes dividends, interest, and other distributions.

Price-Weighted Index Return

$R=\frac{{\sum }_{i=1}^N{P}_{i,1}-{\sum }_{i=1}^N{P}_{i,0}}{{\sum }_{i=1}^N{P}_{i,0}}$

where $P_{i,t}$ = price of stock $i$ at time $t$, $N$ = number of stocks.

Market-Cap-Weighted Index Return

$R=\frac{{\sum }_{i=1}^N{w}_i\times R_i}{{\sum }_{i=1}^N{w}_i}$

where $w_i=P_i\times Q_i$ (market cap weight).

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M04: Overview of Equity Securities

Book Value per Share

$\text{BVPS}=\frac{\text{Total Shareholders’ Equity}-\text{Preferred Equity}}{\text{Common Shares Outstanding}}$

Return on Equity (ROE)

$\text{ROE}=\frac{\text{Net Income}}{\text{Average Total Equity}}$

DuPont Decomposition (3-factor)

$\text{ROE}=\underset{\text{Profit Margin}}{\underbrace{\frac{\text{Net Income}}{\text{Revenue}}}}\times \underset{\text{Asset Turnover}}{\underbrace{\frac{\text{Revenue}}{\text{Total Assets}}}}\times \underset{\text{Financial Leverage}}{\underbrace{\frac{\text{Total Assets}}{\text{Equity}}}}$

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M05: Company Analysis — Past and Present

Gross Margin

$\text{Gross Margin}=\frac{\text{Revenue}-\text{COGS}}{\text{Revenue}}$

Operating Margin

$\text{Operating Margin}=\frac{\text{Operating Income}}{\text{Revenue}}$

EBITDA Margin

$\text{EBITDA Margin}=\frac{\text{EBITDA}}{\text{Revenue}}$

Cash Conversion Cycle

$\text{CCC}=\text{DSO}+\text{DIO}-\text{DPO}$

where:

• $\text{DSO}=\frac{\text{Accounts Receivable}}{\text{Revenue}}\times 365$
• $\text{DIO}=\frac{\text{Inventory}}{\text{COGS}}\times 365$
• $\text{DPO}=\frac{\text{Accounts Payable}}{\text{COGS}}\times 365$

Return on Invested Capital (ROIC)

$\text{ROIC}=\frac{\text{NOPAT}}{\text{Invested Capital}}$

where $\text{NOPAT}=\text{EBIT}\times (1-\text{Tax Rate})$ and $\text{Invested Capital}=\text{Debt}+\text{Equity}-\text{Cash}$.

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M07: Company Analysis — Forecasting

Degree of Operating Leverage (DOL)

$\text{DOL}=\frac{\%\Delta \text{Operating Income}}{\%\Delta \text{Revenue}}$

Sustainable Growth Rate

$g=\text{ROE}\times b$

where $b$ = retention ratio = $1-\text{Payout Ratio}$.

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M08: Equity Valuation — Concepts and Basic Tools

Gordon Growth Model (GGM)

$\boxed{V_0=\frac{D_1}{r-g}}$

where:

• $D_1=D_0\times (1+g)$ = expected next dividend
• $r$ = required rate of return (must be $>g$)
• $g$ = constant dividend growth rate

Implied Required Return (from GGM)

$r=\frac{D_1}{P_0}+g=\text{Dividend Yield}+\text{Capital Gains Yield}$

One-Period DDM

$V_0=\frac{D_1+P_1}{1+r}$

Multi-Period DDM

$V_0={\sum }_{t=1}^n\frac{D_t}{(1+r{)}^t}+\frac{P_n}{(1+r{)}^n}$

Price-to-Earnings (P/E)

Trailing P/E:

$\text{Trailing P/E}=\frac{P_0}{E_0}$

Leading (Forward) P/E:

$\text{Leading P/E}=\frac{P_0}{E_1}$

Justified Leading P/E (from GGM):

$\frac{P_0}{E_1}=\frac{1-b}{r-g}$

where $(1-b)$ = dividend payout ratio.

Price-to-Book (P/B)

$\text{P/B}=\frac{P_0}{\text{BVPS}}$

Justified P/B:

$\frac{P_0}{B_0}=\frac{\text{ROE}-g}{r-g}$

Price-to-Sales (P/S)

$\text{P/S}=\frac{P_0}{\text{Sales per Share}}$

Price-to-Cash Flow (P/CF)

$\text{P/CF}=\frac{P_0}{\text{Cash Flow per Share}}$

Enterprise Value (EV)

$\text{EV}=\text{Market Cap}+\text{Total Debt}-\text{Cash \& Equivalents}$

EV/EBITDA

$\text{EV/EBITDA}=\frac{\text{Enterprise Value}}{\text{EBITDA}}$

Net Asset Value (NAV)

$\text{NAV per Share}=\frac{\text{Market Value of Assets}-\text{Market Value of Liabilities}}{\text{Shares Outstanding}}$

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Quick Reference Table

Formula	Module	Key Variables
Leverage Ratio = $1/\text{Margin \%}$	M01	Margin percentage
Margin Call (Long) = $P_0\times \frac{1-IM}{1-MM}$	M01	Initial/maintenance margin
Total Return = $\frac{V_1-V_0+\text{Inc}}{V_0}$	M02	Price change + income
ROE = Net Income / Equity	M04	Profitability
BVPS = (Equity - Pref) / Shares	M04	Book value
CCC = DSO + DIO - DPO	M05	Working capital efficiency
GGM: $V_0=D_1/(r-g)$	M08	Dividend, return, growth
Justified P/E = $(1-b)/(r-g)$	M08	Payout, return, growth
EV = MCap + Debt - Cash	M08	Enterprise value

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Related Pages

• M01: Market Organization and Structure
• M02: Security Market Indexes
• M04: Overview of Equity Securities
• M05: Company Analysis — Past and Present
• M08: Equity Valuation