### 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

### economic income ?

cash flow + (ending market value - beginning market value) OR cash flow - economic depreciation

### 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

### expected dividend

Previous dividend + ((Expected increase in EPS)**(target payout rate)**(adjustment factor))

### 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

### 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

### return on total invested capital ratio

net income + interest expense / interst bearing debt + shareholders equity

### 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)]

### Effect of inflation on leading PE

P0/E1 = 1 / (real required return +((1-inflation flow through rate)*inflation rate))

### Gordon Growth Model equity risk premium

(one year forecasted dividend yield on market index) + (consensus LT earnings growth rate+ - (LT gov bond yield)

### Present value of grwoth opportunities (PVGO)

E/r + PVGO

E=no growth earnings level

R= required return on equity

### 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

### PB ratio

Market value of equity / book value of equity

which equals

market price per share / book value 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

### 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

### 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

### 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

### favorable income difference per share

coupon interest - (conversion ratio*dividends per share) / conversion ratio

### Mortgage prepayment

prepaymentm = SMMm *(mortgage balance at beginning of month m - scheduled principal payment for month m)

###
Commercial MBS credit analysis:

loan to value ratio

current mortgage amount / current appraised value

### 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:

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 = (S0**e^(-cont comp div yield**T))**e^(Rfc**T)

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

### expiration value of floorlet

max(0,((floor rate - one year rate)*notional principal)) / 1+one year rate

### 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))

### 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;

### Return on Total Capital

Earnings before interest and taxes ÷ (Interest bearing debt + Shareholders' equity)

### Fixed Charge Coverage Ratio

(Earnings before interest and taxes + Lease payments) ÷ (Interest payments + Lease payments)