# formulas CFA 2

### 200 terms by Pnolan20

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### 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**

FCInv + NWCinv

(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)

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

Pt = (N*Pat)

### gross profit margin

gross profit / net sales

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

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)

(1/r)-(1/ROE)

ROE*b

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

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)

D0*(1+g) / r-g
or
D1 / r-g

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

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

NOI / MV

### RO(BOI)

(mortgage weight mortgage costs)+(equity weight equity cost)

### gross income multiplier (M)

sale price / gross income

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

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