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200 terms

formulas CFA 2

STUDY
PLAY
Annualized Forward premium/discount
(forward rate - spot rate / spot rate)(360/#of days forward)
Interest Rate Parity
F/S = (1+rate D) / (1+rate F)
relative PPP
S (1+inflation D / 1+inflation F)^t = E(St)
International Fisher relation
(1+Rnominal D / 1+Rnominal F) = (1+inflation D / 1+inflation F)
Fisher Linear Approximation
R nominal D - R nominal F = E inflation D - E inflation F
Uncovered interest rate parity
E(S1) / S = (1+Rate domestic / 1+Rate foreign)
ending inventory
beginning inventory + purchases - COGS
FIFO inventory
LIFO inventory +LIFO reserve
FIFO COGS
LIFO COGS - (ending LIFO reserve - beginning LIFO reserve)
funded status of the plan
fair value of plan assets - PBO
average age
accumulated depreciation / depreciation expense
average depreciable life
ending gross investment / depreciation expense
remaining useful life
ending net investment / depreciation expense
net pension expense summary
current service cost
+interest cost
-Expected return on assets
+/- Amortization of actuarial (G) and L
+ Amortization of past service costs
= Net penion expense
current ratio
Current assets / current liabilities
quick ratio
cash + marketable securities + receivables / current liabilities
Cash ratio
Cash + ST marketable securities / current liabilities
receivables turnover
net annual sales / average receivables
average receivable collection period
365 / receivables turnover
Inventory turnover
COGS / average inventory
**make sure to use average**
average inventory processing period
365 / inventory turnover
Payables turnover
Purchases / average payables
**make sure to use average**
average payables payment period
365 / payables turnover
total asset turnover
net sales / average total net assets
fixed asset turnover
net sales / average net fixed assets
equity turnover
net sales / average equity
**make sure to use average**
Corporate finance initial outlay
FCInv + NWCinv
Corporate finance after-tax operating cash flow
(S-C-D)(1-T)+D
TNOCF
Sales amount + NWCInv - T (Sale amount - BV)
economic income ?
cash flow + (ending market value - beginning market value) OR cash flow - economic depreciation
Economic Profit ?
EP = NOPAT - $WACC
Market value added ?
NPV = MVA = EP(t) / (1+WACC)^t
Residual income ?
net income - equity charge
Project cost of equity
Rf + beta of project (equity risk premium - Rf)
Weighted average cost of capital WACC
rate on debt(1-t)(debt/assets) + rate on equity*equity/assets
MM Proposition I (no taxes)
Value levered = value unlevered

Capital structure has no effect on firm valuation
MM Proposition II (no taxes)
Re = R0 + D/E (R0-Rd)

Cost of equity is a linear function of its debt to equity ratio. Main risks are business risk and financial leverage risk

D=market value of debt
E=market value of equity
Rd=after tax marginal cost of debt. Or before tax because assumption is for no tax
R0= cost of capital for company financed 100% by equity
MM Propositon I (with taxes)
value levered = value unlevered + (T*D)

T=marginal tax rate
T*D= debt tax shield

For same level of operating income a company with debt WACC must be lower then that of a company financed with all equity
MM Proposition II (with taxes)
Re = R0 + D/E(R0-Rd)(1-T)

the cost of equity becomes greater as the company increases the amount of debt in its capital structure, but the cost of equity does not rise as fast as it does in the no-tax case. Equivalently, the slope coefficient is (r0 -rd )(1 - t ), which is smaller than the slope coefficient (r0 -rd ) in the case of no taxes. As a consequence, the WACC for the leveraged company falls as debt increases, and overall company value increases. Therefore, if taxes are consid- ered but financial distress and bankruptcy costs are not, debt financing is highly advantageous, and in the extreme, a company's optimal capital structure is all debt
static trade off theory
value levered = value unlevered + (t*d) - PV
PV= cost of financial distress

static trade-off theory of capital structure is based on balancing the expected costs from financial distress against the tax benefits of debt service pay ments
**unlike mm this states there s an optimal capital structure
effective tax rate
corporate tax rate + (1-corporate tax rate)(Individual tax rate)
expected dividend
Previous dividend + ((Expected increase in EPS)(target payout rate)(adjustment factor))
FCFE coverage ratio
FCFE / (dividends+sahre repurchases)
Herfindahl-Hirschman Index
(market share i * 100)^2

Under 1000 if fine
1000-1800 may be some push back
Over 1800 big concern
Free Cash flow
Net income
+Net interst after tax
=Unlevered net income
+/- Change in deferred taxes
=Net operating profit less adjusted taxes (NOPLAT)
+net noncash charges
+/-Change in net working capital
-Capex
=FCF
Terminal value
FCF*(1+g) / (WACCadj - g)
OR
FCF * (P/FCF)
takeover premium
DP - SP / SP

DP=deal price per share of the target company
SP=stock price of the target company

The analyst must be careful to note any pre-deal jump in the price that may have occurred because of takeover speculation in the market. In these cases, the analyst should apply the takeover premium to a selected representative price from before any speculative influences on the stock price.
post merger value of an acquirer
Vat = Va + Vt + S - C

VA= pre-merger value of the acquirer
C= cash paid to target shareholders
S= synergies created by the business combination
VT= pre-merger value of the target company
Gain to target
TP = Pt - Vt

PT=price paid for the target company
VT= pre-merger value of the target company
Gain to acquirer
S - TP = S - (PT - VT)

S= synergies created by the business
TP= gain to target
PT=price paid for the target company
VT= pre-merger value of the target company
Price of target in stock deal
Pt = (N*Pat)
gross profit margin
gross profit / net sales
operating profit margin
EBIT / sales
net profit margin
net income / net sales
return on assets
net income / average total assets
return on total invested capital ratio
net income + interest expense / interst bearing debt + shareholders equity
return on total equity
Net income / average total equity
interst burden rate
interest expense / total assets
tax retention rate
1- (dividends declared / operating income after taxes)
Financial leverage ratio
total assets / total equity
long term debt to equity ratio
total long term debt / total equity
debt to equity ratio
total debt / total equity
debt to capital ratio
ST+LT debt / ST +LT debt + total equity
interest coverage
EBIT / interest expense
payout ratio
dividends paid / net income
retention ratio
1 - payout ratio
earnings per share
net income - preferred dividends / average common shares outstanding
book value per share
common stockholders equity / total number of common shares outstanding
NOA
net operating assets (NOA) as the differ- ence between operating assets (total assets less cash) and operating liabilities (total liabilities less total debt):
NOAt = [(Total assetst - cash) - (Total liabilitiest- Total debtt)]
Balance Sheet based accruals ratio
(NOA end - NOA beg) / (NOA end + NOA beg)/2)
Cash Flow Based Accruals Ratio
(NI - CFO - CFI) / ((NOA end + NOA beg)/2)
core operating margin
sales - COGS - SG&A / Sales
Measure of industry concentration
Herfindahl index = MSi^2
DuPont
ROE = NI/equity EBT/EBIT EBIT/Sales Sales/assets assets/equity
Intrinsic PE
tangible PE + franchinse PE
OR
P0/E1 = (1/r) + (FF*G)
Franchise Factor (FF) ?
(1/r)-(1/ROE)
Sustainable growth rate (g)
ROE*b
Growth factor (G)
g / r-g
Effect of inflation on leading PE
P0/E1 = 1 / (real required return +((1-inflation flow through rate)*inflation rate))
Holding period return
r = P1-P0+CF1 / P0
Adjusted beta
2/3 regression beta + 1/3 (1)
Gordon Growth Model equity risk premium
(one year forecasted dividend yield on market index) + (consensus LT earnings growth rate+ - (LT gov bond yield)
Gordon growth model
D0*(1+g) / r-g
or
D1 / r-g
Value of perpetual preferred shares
VP = Dp / rp
Present value of grwoth opportunities (PVGO)
E/r + PVGO

E=no growth earnings level
R= required return on equity
H-model
D0(1+GL)/r-GL + D0H*(GS-GL)/R-GL
sustainable growth rate
g= (net income -dividends / net income)(net income/sales)(sales/total assets)*(total assets/equity)
Value wit FCF models
Firm value = FCFF discounted at the WACC
Equity value = FCFE discounted at the required return on equity
FCFF from NI
NI + NCC + (Int*(1-tax rate)) - FCInv - WCInv
FCFF from EBIT
(EBIT*(1-tax rate))+depreciation - FCInv -WCInv
FCFF from EBITDA
(EBITDA(1-tax rate))+(depreciationtax rate)-FCInv-WCInv
FCFF from CFO
CFO + (Int*(1-tax rate))-FCInv
FCFE from FCFF
FCFF - (Int*(1-tax rate)) + net borrowings
FCFE from NI
NI + NCC - FCInv - WCInv + net borrowing
FCFE from CFO
CFO - FCInv + net borrowing
FCFE from NI
NI - ((1-DR)(FCInv-Dep) - ((1-DR)WCInv)
Single stage FCFF model
value of the firm = FCFF1 / WACC-g
which equals
FCFF0*(1+g) / WACC-g
Single stage FCFE model
value of equity = FCFE1 / r-g
which equals
FCFE0*(1+g) / r-g
Trailing PE
Market price per share / EPS over previous 12 months
Leading PE
Market price per share / forecasted EPS over next 12 months
PB ratio
Market value of equity / book value of equity
which equals
market price per share / book value per share
PS ratio
market value of equity / Total sales
which equals
Market price per share / sales per share
P/CF ratio
Market value of equity / cash flow
which equals
market price per share / cash flow per share
where:
Cash flow = CF, adjusted CFO, FCFE or EBITDA
Income taxes payable
(NOI-depreciation-interest)*tax rate
CFAT
NOI-debt service-taxes payable
ERAT
selling price - selling costs - mortgage balance - taxes on sale
MV0
NOI1 / r-g = NOI1 / R0
Ro(ME)
NOI / MV
RO(BOI)
(mortgage weight mortgage costs)+(equity weight equity cost)
R0(Bu)
pure rate + liquidity premium+recapture premium+risk premium
gross income multiplier (M)
sale price / gross income
MV
gross income * M
exit value
investment cost + earnings growth + increase in price multiple + reduction in debt = exit value
NAV before distributions
NAV after distributions in prior year + capital called down - managemetn fees + operating results
NAV after distribution
NAV before distributions - carried interest - distributions
Venture capital method: the post money portion of a firm purchased by an ivnestment is
F1 = investment 1 / PV1(exit value)
Venture capital method: the new shares issued are
shares(equity) (F1 / 1-F1)
where sahres(equity) is the pre-investment number of shares, and share price is:
Price 1 = investment 1 / shares vc
long-term debt to cap ratio
long term debt / LT debt+minority interst+shareholders common and preferred equity
total debt to cap ratio
current liabilities + long term debt / current liabilities +LT debt+minority interst+shareholders common and preferred equity
coverage ratios
EBIT / annual interst expense
OR
EBITDA / annual interest expense
S&P cash flow ratios
funds from operations / total debt
funds from operations / capital spending requirements
free operating cash flow + interest / interst
Free operating cash flow + interest / interest + annual principal repayment =debt service coverage
Total debt/discretionary cash flow = debt payback period
SD of daily yield changes
SD annual = SD daily * (number of trading days in the year)^.5
value of embedded call option
Vcall = Vnoncallable - Vcallable
Value of embedded put option
Vput = Vputable - Vnonputable
effective duration
ED = BV-chgy - BC+chgy / 2 BV0 chg y
effective convexity
EC = BV-chgy + BV+chgy - (2BV0) / 2 BV0 *chgy^2
convertible bonds conversion value
market price of stock * conversion ratio
convertible bonds market conversion price
Market price of convertible bond / conversion ratio
Market conversion premium per share
market conversion price - market price
Market conversion premium ratio
market conversion premium per share / market price of common stock
premium payback period
market conversion premium per share / favorable income difference per share
favorable income difference per share
coupon interest - (conversion ratio*dividends per share) / conversion ratio
premium over straight value
(market price of convertible bond / straight value) - 1
Mortgage prepayment speed
single monthly mortality rate = 1 - (1-conditional prepayment rate)^1/12
Mortgage prepayment
prepaymentm = SMMm *(mortgage balance at beginning of month m - scheduled principal payment for month m)
Commercial MBS credit analysis:
debt to service coverage ratio
net operating income / debt service
Commercial MBS credit analysis:
loan to value ratio
current mortgage amount / current appraised value
bond equivalent yield
2((1+monthly cash flow yield)^6 - 1)
Futures price
spot price * (1+r)^(T-t)
forward contract price
FP = S0 * (1+Rf)^T

FP=forward price
S0= spot price
RF= risk free rate
T= expiration time (if months or days do x/12 or x/365)

Or

S0 = FP / (1+RF)^T
Forward contract value of long position:
At initiation
Zero, because priced to prevent arbitrage
Forward contract value of long position:
During life of contract
St - (FP / (1+Rf)^T-t)

St= current spot at particular time in the future
FP= forward price
RF= Risk free rate
T-t = # of periods before contract expiration
Forward contract value of long position:
at expiration
St - FP

St= market price
FP= our forward price
Equity forward contract price
FP(on an equity security) = (S0-PVD)*(1+Rf)^T

Same equation from above but we have to subtract out dividends (PVD) from spot price
**in all these formula's, always use 365 days for basis
equity forward contract value
Vt(long position) = (St - PVDt) - (FP/(1+Rf)^(T-t))

St= current spot at some future point in time
PVDt= PV of the remaining expected discrete dividends at time t

This is the same as above, the "spot price minus PV of forward price" but now spot price has to be adjusted by subtracting out PV of the dividends.
Equity index forward contract price (continuous dividends)
FP (on an equity index) = S0 e^(Rfc-continuously compounded dividend yield)T
OR
FP = (S0e^(-cont comp div yieldT))e^(RfcT)

Rfc= continuously compounded risk free rate
gama c = continuously compounded dividend yield

make calculation as if dividends are paid continuously (rather then discrete times like above equations)

relationship with RF and the continuously compounded RFc is RFc = ln(1+RF)

exp: SPX is 1140. RFc rate is 4.6% and cont div yield is 2.1%. calculate no art prie of 140-day forward contract?
FP = 1,140 e^(.046-.021)(140/365) = 1,151
Equity index forward contract value
Vt = (St / e^(cont comp div yield)(T-t)) - (FP / e^RFc*(T-t))

exp: after 96 days, value of index is 1025. calcite value o long assuming RFc is 4.6% and cont div filed is 2.1%?
After 95 days there are 45 days remaining from original forward contract
V95 = (1025/e^.021(45/365))-(1151/e^.046(45/365)) = -122.14
fixed income forward contract price
(S0-PVC)*(1+Rf)^T

same formula for equity paying dividend except subbing PVD for the expected coupon payment (PVC) over the life of the contract.

exp: 250-d forward on 7% US treasury bond with spot of 1050 and will make a coupon payment in 182 days. RF is 6%?
C = 1000*7% / 2 =$35 (semiannual coupon payment)
PVC = $35 / 1.06^182/365 = $34
FP = (1050-34)*1.06^250/365 = 1057.37
fixed income forward contract value
(St - PVCt) - (FP / (1+Rf)^(T-t))

exp: after 100 days, value of bond s 1090. calculate vale of forward assuming Rf 6%?
coupon remaining in 82 days before contract matures in 150 days.
PVC=$35 / 1.06^82/365 = $34.54
V100 = 1090 - 34.54 - (1057.37/1.06^150/365) = $23.11
Currency forward contract price
S0 * ((1+Rdc)^T) / (1+Rfc)^T

Rdc= rate domestic
Rfc= rate foreign
S0= spot price
T= use 365 day basis for FX contracts

exp: RF 6% in US and 8% in mexico. spot ecahnge rate is .0845 USD/peso. forward rate for a 180-day contract?
FT = .0845 * (1.06^180/365 / 1.08^180/365 = .0837
Currency forward contract value
(St / (1+Rfc)^(T-t)) - (Ft / (1+Rdc)^(T-t))

exp: calculate value of forward if after 15 days spot is .0980?
V15 = (.0980 / 1.08^165/365) - (.0837/1.06^165/365) = .0131
generalized no-arbitrage futures price
FP = S0 *(1+Rf)^T + FV(NC)
FP = S0 *(1+Rf)^T - FV(NB)
Treasury bond futures contract price
FP = (bond price (1+Rf)^T - FVC) 1/CF
put-call parity of european options
C0 + (X / (1+Rf)^T)
=
P0 + S0
Put call parity for European options with cash flows
C0 + X / (1+Rf)^T
=
P0 + (S0 - PVCF)
Binomial model
D = 1 /U
pieU = 1+Rf -D / U-D
pieD = 1-pieU
expiration value of caplet
max(0,((one year rate-cap rate)*notional principal)) / 1+ one year rate
expiration value of floorlet
max(0,((floor rate - one year rate)*notional principal)) / 1+one year rate
Delta and dynamic hedging
Delta(call) = C1 - C0 / S1 - S0
Forward put-call parity
C0 + ((X-Ft) / (1+Rf)^T) - P0 = 0
Fixed swap rate (with four payments)
C = 1- Z4 / Z1+Z2+Z3+Z4
payoff to cap buyer
periodic payment = max(0,(notional principal)(index rate - cap strike)(actual days/360))
payoff to floor buyer
periodic payment = max(0,(notional principal)(floor strike - index rate)(actual days/360))
expected portfolio return (two assets)
E(Rp) = W1(E(R1)) + W2(E(R2))
portfolio variance (two assets)
(weight 1^2SD1^2) + (weight 2^2SD2^2) + 2weight1weight2*cov1,2
correlation
COV1,2 / SD1*SD2
reward to risk ratio
E(Rt) - Rf / SD(T)
CAL
Rf + (E(Rt) -Rf / SD(T)) SD(c)
CML
Rf + (E(Rm) - Rf / SD(M)) SD(c)
SML
Rf + beta (E(Rm) - Rf))
at page 21 of formula notes..need to finish!!!
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Justified leading P/E
1-b / r-g

1-b= dividend payout ratio
G= dividend growth rate
Justified trailing P/E
(1-b)*(1+g) / r-g
CAGR
(ending value/beginning value)^(1/# of yrs) - 1
Income Property- Direct income capitalization approach
Market value = NOI / capitalization rate
Income Property- Gross income multiplier approach
Market value = gross income * GIM

GIM=gross income multiplier =
comparable property sales price / grow income
Direct income cap approach vs gross income multiplier approach
GIM approach considers only income, not costs. Also, sales of some properties occur infrequently, thus the derivation of a market GIM must be based on is limited info.
Direct cap limitation lies in the selection of the cap rate. it must accurately reflect the behavior of investors in the marketplace
Debt payback period
Total debt / discretionary cash flow
Or
Total debt ( ie total liabilities) / (operating cash flow - capex - cash dividends)
Defensive Interval Ratio
(Cash + Short-term marketable investments + Receivables) ÷ Daily cash expenditures;
Receivables Turnover Ratio
Total revenue ÷ Average receivables
Days of Sales outstanding (DSO)
Number of days in period ÷ Receivables turnover ratio;
Inventory Turnover Ratio
Cost of goods sold ÷ Average inventory
Days of Inventory on Hand (DOH)
Number of days in period ÷ Inventory turnover ratio
Payables Turnover Ratio
Purchases ÷ Average trade payables
Number of Days of Payables
Number of days in period ÷ Payables turnover ratio
Cash conversion Cycle
DOH + DSO - Number of days of payables
Working Capital Turnover Ratio
Total revenue ÷ Average working capital
Fixed Asset Turnover Ratio
Total revenue ÷ Average net fixed assets
Total Asset Turnover Ratio
Total revenue ÷ Average total assets
Operating Return on Assets
Operating income ÷ Average total assets
Return on Assets
Net income ÷ Average total assets
Return on Equity
Net income ÷ Average shareholders' equity
Return on Total Capital
Earnings before interest and taxes ÷ (Interest bearing debt + Shareholders' equity)
Return on Common Equity
(Net income - Preferred dividends) ÷ Average common shareholders' equity
Tax Burden
Net income ÷ Earnings before taxes
Interest Burden
Earnings before taxes ÷ Earnings before interest and taxes
EBIT Margin
Earnings before interest and taxes ÷ Total revenue
Financial leverage ratio (equity multiplier)
Average total assets ÷ Average shareholders' equity
Fixed Charge Coverage Ratio
(Earnings before interest and taxes + Lease payments) ÷ (Interest payments + Lease payments)
Retention Rate
(Net income attributable to common shares - Common share dividends) ÷ Net income;