25 formulas that show up in financial exams and client work, each with a worked example and a calculator you can change.
Current yield = Annual interest / Market price
Example: with annual interest of $60 and market price of $1,200, the result is 5.00%.
Ignores the gain or loss to maturity, so it differs from yield to maturity whenever a bond trades away from par. About Current Yield
YTM ~ (Annual interest + (Par - Price) / Years) / ((Par + Price) / 2)
Example: with annual interest of $50, par value of $1,000, market price of $900 and years to maturity of 10 yrs, the result is 6.32%.
A shortcut, close enough for exam answers. The exact figure needs a financial calculator. About Yield to Maturity (YTM)
Tax-equivalent yield = Municipal yield / (1 - Marginal tax rate)
Example: with municipal bond yield of 3.6% and marginal tax rate of 32%, the result is 5.29%.
The taxable yield needed to match a tax-free one. The higher the bracket, the more a muni is worth. About Municipal Bond Tax Treatment
Price change ~ -Duration x Change in yield
Example: with duration of 8 yrs and change in yield of 0.5%, the result is -4.00%.
Rates up, prices down. Accurate for small moves; less so for large ones. About Duration
Conversion ratio = Par value / Conversion price
Example: with par value of $1,000 and conversion price of $50, the result is 20.00 shares.
How many common shares one convertible bond exchanges into. About Convertible Bond / Preferred
Conversion value = (Par value / Conversion price) x Stock price
Example: with par value of $1,000, conversion price of $50 and common stock price of $55, the result is $1,100.00.
What the bond is worth if converted today. At parity, bond and shares are worth the same. About Convertible Bond / Preferred
HPR = (Ending value - Beginning value + Income) / Beginning value
Example: with beginning value of $40, ending value of $46 and income received of $2, the result is 20.00%.
Total return over the whole holding period - not annualized. About Holding Period Return
Annualized return = (1 + Holding period return)^(1 / Years) - 1
Example: with holding period return of 28% and years held of 3 yrs, the result is 8.58%.
Makes returns over different lengths of time comparable. About Annualized Return
CAGR = (Ending value / Beginning value)^(1 / Years) - 1
Example: with beginning value of $100, ending value of $75 and years of 2 yrs, the result is -13.40%.
The example is +50% then -50%: the average is 0%, but the money shrank. About Compound Annual Growth Rate (CAGR)
Real return = (1 + Nominal return) / (1 + Inflation) - 1
Example: with nominal return of 7% and inflation of 3%, the result is +3.88%.
The quick version, nominal minus inflation, gives 4% here - close, and fine for most exam questions. About Real vs. Nominal Return
After-tax return = Pre-tax return x (1 - Tax rate)
Example: with pre-tax return of 6% and tax rate of 35%, the result is 3.90%.
For fully taxable income. The mirror image of tax-equivalent yield. About After-Tax Return
Sharpe ratio = (Portfolio return - Risk-free rate) / Standard deviation
Example: with portfolio return of 10%, risk-free rate of 2% and standard deviation of 10%, the result is 0.80.
Excess return per unit of total risk. Higher is better. About Sharpe Ratio
Expected return = Risk-free rate + Beta x (Market return - Risk-free rate)
Example: with risk-free rate of 3%, beta of 1.5 and expected market return of 9%, the result is 12.00%.
A common mistake is multiplying beta by the whole market return instead of the premium over the risk-free rate. About Capital Asset Pricing Model (CAPM)
Future value = Present value x (1 + Rate)^Years
Example: with present value of $10,000, annual rate of 6% and years of 12 yrs, the result is $20,121.96.
Annual compounding. More frequent compounding gives a slightly higher result. About Future Value & the Rule of 72
Present value = Future value / (1 + Rate)^Years
Example: with future value of $20,000, annual rate of 6% and years of 12 yrs, the result is $9,939.39.
What a future sum is worth today. The basis of discounted cash flow and NPV. About Time Value of Money
Years to double ~ 72 / Annual rate (as a whole number)
Example: with annual rate of 6%, the result is 12.0 years.
A mental-math estimate, most accurate for rates between about 6% and 10%. About Future Value & the Rule of 72
Value = Current dividend x (1 + Growth) / (Required return - Growth)
Example: with current annual dividend of $2, dividend growth rate of 3% and required return of 8%, the result is $41.20.
Only works when the required return is above the growth rate. With no growth, value is dividend / required return. About Dividend Discount Model
Dividend yield = Annual dividends per share / Share price
Example: with annual dividend per share of $2 and share price of $50, the result is 4.00%.
A rising yield can mean a bigger payout - or a falling price. Check which. About Dividend Yield
P/E = Share price / Earnings per share
Example: with share price of $60 and earnings per share of $4, the result is 15.00.
Dollars paid per dollar of annual earnings. Meaningless when earnings are negative. About Price-to-Earnings (P/E) Ratio
P/B = Share price / Book value per share
Example: with share price of $60 and book value per share of $30, the result is 2.00.
A classic value screen. Most useful for asset-heavy businesses like banks. About Price-to-Book (P/B) Ratio
Current ratio = Current assets / Current liabilities
Example: with current assets of $600,000 and current liabilities of $300,000, the result is 2.00.
Short-term liquidity. Above 1.0 means current assets cover current liabilities. About Current Ratio
Quick ratio = (Current assets - Inventory) / Current liabilities
Example: with current assets of $600,000, inventory of $200,000 and current liabilities of $300,000, the result is 1.33.
Stricter than the current ratio because inventory may not sell quickly. About Quick Ratio (Acid-Test Ratio)
Debt-to-equity = Total liabilities / Shareholders' equity
Example: with total liabilities of $3,000,000 and shareholders' equity of $2,000,000, the result is 1.50.
Leverage. Normal levels vary widely by industry. About Debt-to-Equity Ratio
Market value at a margin call = Debit balance / (1 - Maintenance requirement)
Example: with debit balance (amount borrowed) of $10,000 and maintenance requirement of 25%, the result is $13,333.33.
If the account's market value falls below this, equity is under the maintenance level. FINRA's minimum is 25%; many firms require 30% or more. About Margin Call
NIIT = 3.8% x the lesser of (Net investment income) or (MAGI - Threshold)
Example: with modified adjusted gross income of $320,000, net investment income of $100,000 and threshold ($250,000 joint, $200,000 single) of $250,000, the result is $2,660.00.
The thresholds are set by statute and are not adjusted for inflation. About Net Investment Income Tax (NIIT)
Calculators are for study and illustration only. They are not financial, tax or investment advice. See the disclaimer.