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144 Cards in this Set
- Front
- Back
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Full price of a bond
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Full price = Clean price + Accrued interest
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Duration
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-%change bond price/%change bond yield
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Value of Callable Bond
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=Value of option free bond - Value of the call
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TIPS coupon payment
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=Inflation adjusted Par Value X (Stated coupon rate/2)
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Absolute Yield spread
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=Yield on bond with Higher yield - Yield on bond with lower yield
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Relative Yield spread
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=(Higher yield/Lower yield)-1
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Yield Ratio
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=Higher yield/lower yield
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After-tax yield
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=Taxable yield X (1-marginal tax rate)
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Tax equivalent yield
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=Tax free yield/(1-Marginal tax rate)
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Bond equivalent yield
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=[{(1+monthly CFY)^6}-1] X 2
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Spot rate at time 3
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[(1 + one year forward rate at time 0)(1 + one year forward rate at time 1)(1 + one year forward rate at time 2)^1/3] - 1
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1 year forward rate at time 2
and 7 year forward rate at time 3 |
=[(Spot rate at time 3)^3 / (Spot rate at time 2)^2] - 1
and ={[(1 + 10 year spot rate)^10 / (1 + 3 year spot rate)^3]^1/7} - 1 = |
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Effective Duration
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=(Bond price when yield falls - bond price when yield rise) / 2 X initial price X % change in yield as decimal
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Percentage change in bond price
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=-effective duration X % change in yield
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Portfolio duration
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=W1D1 X W2D2 X ... X WnDn
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% change in bond price
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=Duration effect + convexity effect = [(-duration x change in yield)+ (convexity X change in yield^2)] X 100
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Price Value of basis point
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=duration X .0001 X bond value
Note: if rates increase, bond value must fall. After calculation, use this information for come up with final answer |
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Value of long FRA at settlement
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=notional principal X [(floating rate-forward rate)X(days to maturity/360) / (1 + floating rate)X(days to maturity/360)
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Intrinsic value of Call and Put
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Call = max[0, S-X]
Put = max[0, X-S] |
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Option value
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=intrinsic value + time value
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Lower/Upper bound European Call Option
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Lower = Max[0, S - (X/(1+RFR)^T-t]
Upper = S |
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Lower/Upper bound American Call Option
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Lower = Max[0, S - (X/(1+RFR)^T-t]
Upper = S |
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Lower/Upper bound European Put Option
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Lower = Max[0,(X/(1+RFR)^T-t) - S]
Upper = (X/(1+RFR)^T-t) |
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Lower/Upper bound American Put Option
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Lower = Max[0,(X - S)]
Upper = X |
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Put-Call Parity
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c + (X/(1+RFR)^T) = S + p
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Net fixed rate payment on fixed/floating swap
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= (SWAP fixed rate - LIBOR) X (Days to maturity/360) X (Notional Principal)
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WACC
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=Wd[(Kd)(1-t) + WpsKps + WeKe
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CAPM (Ke)
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= RFR + B[(E(rm)-RFR]
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Ke
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=CAPM or D1/P0 + g or Bond yield + Risk premium
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RFRreal
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= [(1+RFRnominal)/(1+IP)]-1
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After tax cost of debt
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=Kd(1-t)
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Cost of Preferred Stock (Kps)
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=Dps/Pnet
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Correlation
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= Cov1,2/SD1 X SD2
Indicates strength and direction in which two random variables move together. |
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Total Risk
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=Systematic Risk + Unsystematic Risk
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Beta (B)
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= Cov1,mkt/SDmkt^2
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Equation for CML
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=RFR + SDportfolio[(E(Rm)-RFR)/SDmarket]
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Straight line depreciation
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=Cost-Salvage/useful life
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Double Declining Balance Depreciation
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=(2/Useful life)(Cost-Accumulated depreciation)
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Sum of Years Digits Depreciation
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Depreciation in year X = (original cost-salvage value)(n-x+1)/SYD
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Free Cash flow
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=Operating Cashflow-Net Capital Expenditures
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Common Size income statement ratios
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=Income statement account/Sales
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Common Size Balance Sheet ratios
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=Balance Sheet account/Total Assets
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Current Ratio
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=Current Assets/Current Liabilities
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Quick Ratio
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=Current assets - inventories/Current Liabilities
or =Cash + mkt. Securities + receivables / current liabilities |
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Cash ratio
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=Cash + Mkt. Securities / current liabilities
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Receivables Turnover
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=Net annual sales / Average Receivables
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Average Receivables collection period
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=365 / Receivables turnover
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Inventory Turnover
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=Cogs / Avg. Inventory
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Average inventory processing period
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=365 / Inventory turnover
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Payables turnover
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=Cogs / Avg. payables
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Payables Payment period
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=365 / Payables turnover
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Cash Conversion Cycle
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=(Avg. Rec. collection period) + (Avg. Inventory processing period) - (Payables payment period)
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Total Asset Turnover
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=Net Sales / Avg. Total Assets
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Fixed Asset Turnover
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=Net Sales / Avg. Fixed Assets
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Equity Turnover
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=Net Sales / Avg. Equity
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Gross Profit Margin
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=Gross Profit / Net Sales
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Operating Profit Margin
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=Operating Profit / Net Sales
or EBIT / Net Sales |
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Net Profit Margin
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=Net Income / Net sales
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Return on Total Capital
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=Net Income + Interest Exp. / Avg. Total Capital
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Return on Total Equity
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=Net Income / Avg. Total Equity
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Return on Common Equity
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=Net Income - Preferred Dividends / Avg. Common equity
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Business Risk
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=SD of EBIT / Mean of EBIT
or SD of Operating Income / Mean of operating income |
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Debt to Equity Ratio
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=Total long term debt / Total Equity
or Long term liabilities + Deferred Tax + PV of lease obligations / Common + Preferred Equity |
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Long Term Debt to Long Term Capital ratio
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=Total Long Term debt / Total long term capital
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Total Debt Ratio
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=Current Liabilities + Long term debt / Total Debt + Total Equity
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Interest Coverage AKA Times interest earned
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=EBIT / interest expense
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Fixed Financial Cost Ratio
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=EBIT + ELIE / gross interest expense + ELIE
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Cash flow coverage to fixed financial costs
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=CFO + Interest expense + ELIE / Interest Expense + ELIE
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Cash flow to long term debt
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=CFO / BV long term debt + PV operating leases
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Cash flow to total interest bearing debt
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=CFO / Total long term debt + current interest bearing liabilities
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Original DuPont
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=Total Asset Turnover X Equity Multiplier X Net profit Margin
or =Sales/Total Assets X Net Income/Sales X Assets/Equity |
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Extended DuPont (ROE)
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=[(EBIT/Sales)(Sales/Assets)-(Int. Exp/Assets)](assets/equity)(1-t)
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Basic EPS
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=(Net Income - Preferred Dividend) / (Weighted Avg. # common shares outstanding)
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Diluted EPS
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=(Net Income - Pref Div)+(Conv. Pref. Div.)+(Conv. Debt int.)(1-t) / (Weighted Avg. # Common)+(Conv. Pref Shares)+(Conv. debt shares)+(shares issued for Stock Options)
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Ending Inventory
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=Begenning Inventory + Purchases - COGS
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Current Cost of FIFO inventory
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=LIFO inventory + LIFO Reserve
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FIFO COGS
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=LIFO COGS - (Ending LIFO Reserve - Beg. LIFO Reserve)
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Average Age in years
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=Accumulated Depreciation / Depreciation Expense
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Average Age as % (Relative Age)
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=Accumulated Depreciation / Ending Gross Investment
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Average Depreciable Life
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=Ending Gross investment / Depreciation Expense
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Income Tax Expense
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=Taxes Payable + (Change DTL - Change DTA)
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Interest Expense
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=(Market rate @ issuance) X (Balance Sheet Value of Liability at begenning of period)
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Nominal Risk Free Rate
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=Real Risk Free Rate + Expected inflation
or =(1+RFRreal)X(1+inflation premium)-1 |
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Required Rate of return on a security
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=(Real Risk Free Rate + Expected inflation) + Default risk premium + Liquidity premium + Maturity Risk Premium
or =[(1+RFR)(1+IP)(1+RP)]-1 |
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EAR
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=[(1 + Periodic Rate)^n] - 1
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Continuous EAR
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=(e^r)-1
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PV of Perpetuity
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=PMT / i
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Future Value
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=PV(1+i)^n
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Bank Discount Yield
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=(Face Value-Purchase Price/Face Value) X (360/t)
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Holding Period Return (HPY)
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=(P1 - P0 + D1) / P0
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Effective Annual Yield (EAY)
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=[(1+HPY)^(365/t)]-1
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Money Market Yield
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=(360+BDY) / [360-(t X BDY)]
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Geometric Mean
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=[(1+r1)(1+r2)...(1+rn)]^(1/n)
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SemiVariance
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=Sum of (X-Avg)^2 / (#obs below Avg - 1)
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Coefficient of Variation
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=SD of X / Mean of X
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Sharpe Ratio
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=Rportfolio - RFR / SDportfolio
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Excess Kurtosis
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=Sample kurtosis - 3
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Harmonic Mean
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= N / Sum(1/x)
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Mean Absolute Deviation (MAD)
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= Sum |(X-obs)| / n
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Joint Probability P(AB)
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=P(A|B) X P(B)
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P(A or B)
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=P(A) + P(B) - P(AB)
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nCr
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= n! / (n-r)! X r!
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nPr
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= n! / (n-r)!
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90%, 95%, 99% Confidence Intervals
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= 90% CI = -1.65
= 95% CI = -1.96 = 99% CI = -2.58 |
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Z score
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=Observation-population mean / Standard Deviation
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SFRatio
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=E(rp)-RFR / SDmarket
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Continuous compounded Rate of Return
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=ln(1+HPR)
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Rate of inflation
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=CPI this year - CPI last year / CPI last year
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Potential deposit expansion multiplier
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= 1 / Required reserve ratio
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Potential increase in money supply
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= Potential deposit expansion multiplier X Increase in excess reserves
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Equation of Exchange
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= Money Supply X Velocity = GDP = PRICE X Real Output
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Price Elasticity of Demand
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= % change in Qunatity Demanded / % change in Price
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Income Elasticity
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= % change in Quantity demanded / % change in income
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Cost Minimizing condition
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= [(MP of A)/Price A] = [(MP of B)/Price B] = [(MP of C)/Price C]
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Interest rate parity
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Forward(DC/FC) = Spot(DC/FC) X [(1+Rd)/(1+Rf)]
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Annualized Forward discount or premium
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=[(forward rate/spot rate)-1] X (360/t)
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Balance of Payment equation
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=Current Account + Financial Account + Reserve Account = 0
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Relative PPP
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=Expected future exchange rate = Spot Rate X [((1+inflation domestic)^t) / ((1+inflation foreign)^t)]
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CF
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=Net income + Depreciation + Amortization
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Adjusted CFO
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=CFO + [(net cash interest outflow)X(1-t)]
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P/CF
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=Market price per share / CF per share
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P/BV
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=Market price per share / BV per share
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P/S
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=Market price per share / Sales per share
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Short interest ratio (SIR)
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=Outstanding short interest / Avg daily volume on exchange
note: ratio high (6 or above), potential demand, bullish - ratio low (4 or below), potential for short sales. bearish sign. |
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Uptick/downtick
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=# block uptick transactions / # block downtick transactions
note: Bullish if ratio close to .7. Bearish if ratio close to 1.1 |
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Confidence Index (CI)
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=Quality bond yield / average bond yields
note: Periods of confidence yield spreads narrow, CI GETS BIGGER - Periods of pessimism yield spreads widen, CI GETS SMALLER |
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Smart money technician ratios
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Confidence index
Tbill-Eurodollar spread Specialist short sales Debit balances in brokerage accounts |
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Specialist short sales
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=Short sales by specialists / Total short sales on NYSE
note: below 30% bullish - above 50% bearish |
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Mutual fund ratio
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=Mutual fund cash / total fund assets
note: greater than 13%, funds holding cash and market is bearish, CONTRARY BULLISH - Vice versa if less than 5% |
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Contrarian technician ratios
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Mutual fund ratio
Investor credit balances in brokerage accounts Investment advisor opinions OTC vs. NYSE volume CBOE Put/call ratio Stock index futures |
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Investment advisor ratio
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=Bullish opinions / total opinions
note: Greater than 60%, mkt bearish, CONTRARIAN BULLISH - Less than 20%, mkt bullish, CONTRARIAN BEARISH |
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Volume ratio
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=OTC volume / NYSE volume
note: Greater than 112%, speculation high, CONTRARIAN BEARISH - less than 87%, investors bearish, CONTRARIAN BULLISH |
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Put call ratio
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=Puts/Calls
note: Greater than .5, mkt bearish, CONTRARIAN BULLISH - less than .35, mkt bullish, CONTRARIAN BEARISH |
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Expected growth rate (g)
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=Retention rate X ROE
or (1-dividend payout) X ROE |
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Preferred stock valuation
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=Price at time 0 = Dps / Kps
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One-period stock valuation
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=Price at time 0 = [(D1 / Ke) + (P1 / Ke)]
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Infinite Period Stock valuation
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=Price at time 0 = D1 / (Ke - g)
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Earnings Multiplier
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=P/E = (D1/E) / (Ke - g)
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Negative Skew
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Tail points toward negative number/origin. If median is higher than mean, distribution is negatively skewed
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Platykurtic
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Distribution with negative excess kurtosis
Distribution is less peaked than normal distribution |
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Bid-Ask spread percentage
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=(Ask-Bid / Ask) X 100
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Things to consider in determining DTL treated as equity
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1. Likelihood of reversal
2. Growth rate of entity 3. Time Value of money |
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Firms optimal Capital Structure
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Ratio fo debt and comm0n/preferred equity that creates lowest possible WACC and maximizes the value of the firms stock
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Financial leverage multiplier
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=A/E
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