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--NOT the notion or probability of something bad happening - risk refers to uncertainty
--downside risk - chance of something bad happening
--upside risk - chance of something good happening



Usually shown as an annualized percentage
--should show the amt. you get over the amt. put in
--calculate the holding period return (return over any period)


Annualized return formula

((P1 - P0 + CF1) / P0) * 360 / holding period

P0 = price at the beg.
P1 = price at the end
CF = value of CF received from asset during the holding period
holding period = uses business month which is 30 day months = 360 day years

--purchased stock for $10 on Jan. 1 and to sold for $11 180 days later - stock paid div. of $.50 during holding period

annual return = ((11 - 10 + .50) / 10) * (360 / 180) = 30%

uses historical data (return based on past prices and cash flows) but in finance we use EXPECTATIONAL DATA
--A hypothesized or "best guess" estimate of future prices/returns under diff. scenarios

but should be able to assess risk and return with either historical or expectational data


Expected return

E(R) = Sum --> Pi*Ri
Pi = prob. of some state in the world occurring (probabilities are mutually exclusive and sum must be = 1)
Ri = return in state "I"
I = state of nature

ex. determine 60% chance that investment would return 10% and 40% chance it would return 2% nest year

expected return = (.6 * 10%) + (.4 * 2%) = 6.8%
--weighted average and .6 and .4 are the weights
--6.8% is an estimated Mu = estimated mean of pop.
--means expected return is ALSO EXPECTED MEAN/AVERAGE


nominal rate and real interest rate

rate advertised - interest rate without effect of inflation

nominal rate = real rate + inflation (fisher effect)

real interest rate = the inc. in purchasing power that results from investing (So earned 6% on savings is not good deal when inflation is 8%, means leasing 2% of purchasing power each year!!)

inflation = money loses its spending power over time

nominal rate = real rate + inflation
7% (APY) = 4% + 3%
---4% (is the 4% inc. in spending power)



the possibility that the realized or actual return will differ from our expected return - uncertainty in the distribution of possible outcomes


First way to measure total risk

To calc. the securities STANDARD DEVIATION of returns

st. dev = (on notecard) - radical( sum of (Ri - Rmean)^2 * Pi)

Pi = prob. of some state
Ri = return in state
Rmean = expected return (found in expected return formula - either with historical or expectational data0

the larger the st. dev. the more risky = more uncertainty


Example with risk and return

Economy. P. low tech firm. high tech firm
recession. .20. 4%. -10%
normal. .50 10%. 14%
boom. .30. 14%. 30%

expected returns for both firms:
LOW = (.2 * 4%) + (.5 * 10%) + (.3 * 14%) = 10% exp. return
HIGH = (.2 * -10%) + (.5 * 14%) + (.3 * 30%) = 14% exp. return

LOW = ((4 - 10)^2 * (.20)) + ((10 - 10)^2 * (.50)) + ((14 - 10)^2 * (.30)) = 12, radical 12 = st. dev. of 3.46%

HIGH - ((-10 - 14)^2 * (.20)) +.... = variance of 192
--radical 192 gives st. dev. of 13.86%


St. dev. measures...

a firms TOTAL RISK
--If you are measuring return by standard dev. always TOTAL RISK
---use normal curve to estimate percentages and spread


Decomposing risk

Market and firm specific risk
--risk and return are positively related in finance
--iNC. risk = INC. return
----but with st. dev. the correlation is not that strong


Two types of risk:

1. MARKET RISK (systematic risk)
---common to most securities and risk inherent in economy
--systematic risk cannot be diversified away
--EX. - unexpected changes in interest rates or I cash flows due to tax changes - or business cycle changes (most common)

---risk that can be reduced through diversification
--EX. company's labor force on strike, top mgmt. dies in place crash, oil tank bursts and floods comp. production area - lawsuits



process of "spreading" money over many diff. assets - spread wealth over more than one asset
--don't put all your offs in one basket
--premise of diversification is to spread an inv. over several securities to reduce risk

SO when combining assets into a portfolio, usually get somer risk reduction (st. dev. falls) but NOT total risk elimination (since corr. always > -1)
--but the lower the corr. among assets in portfolio (closer to -1) the greater the risk reduction possibilities for the portfolio
--lower corr. means greater diversification, or lower risk


Correlation (diversification)

--how related ones assets returns are to another assets returns - stocks moving together (stock goes up and other stock goes down = negative correlation)
--refers to the way 2 var. (the return on 2 stocks) co-move

1. corr. +1 ---variables move in perfect tandem (perfect positive corr.)
2. Corr. -1 ---variables move in exactly opposite directions (perfect neg. corr.)
3. imperfect positive corr., r = +.7 ---positive but less than +1

If perfect positive - no benefit to diversification - ex. buy one share of IBM stock then try to "diversify" by buying another share of IBM stock - vary exactly together so NO risk reduction
--if perf. negative corr. - we can eliminate ALL risk - cold combine 2 risky assets to form a riskless portfolio

However, corr. btwn 2 randomly selected large capitalization stocks is usually .3 to .4


How much risk reduction is possible?

Own a stock on NYSE or NASDAQ are diversified
--as INC. # assets in portfolio, Risk level DEC.
--BUT eventually reaches horizontal axis (market risk) and adding # stocks makes no diff. on risk (Graph)

some risks can be diversified away but others can't


TOTAL RISK, as measured by st. dev. can be divided into 2 parts

1. easily diversified by adding more assets to portfolio (firm-specific, diversifiable risk)

2. systematic risk (market/non-diversifiabl risk) cannot be


Systematic risk principle

the size of risk premium is based on the market risk
--bc can't be diversified away...it is the MARKET (systematic risk) that is important in risk/return relationship



Beta - measures the systematic/market/beta/non-diversifiable risk

diff. firms have diff. amt. of systematic risk - don't all decrease by same amt.
--Apple has high systematic risk - when market INC. sodas Apple's stock returns, if market DEC. apple DEC.
--utility is much less dramatic - LOW systematic risk - market moves up or down = utility firms move up and down but not dramatic
--BOTH exposed to market risk but diff. degrees
--LUXURY goods = lots more market risk (vary lots if small market changes)


Beta with regression line

BETA - measure of systematic risk determined by a REGRESSION LINE
--specifically measures how an individual stock return varies with market returns
--regression analysis to find line of best fit
--positiv relationship btwn market and company

--shows BOTH systematic and firm-specific risk for XYZ
--line of best fit = "average" relationship of data set

SLOPE = systematic risk in XYZ (in ex. Beta - 1.2)
--so if market INC. by 10%, XYZ INC. 12%
--firm specific risk shown in dispersion around line 0 diversification reduces a distribution about line --- as add # securities = closer to line of best fit
--if market INC. by 1%, XYZ's risk will INC. by 1.2% -- shows XYZ I swore volatile than the market (more sensitive to changes)


Beta facts

Beta < 1 --- less sensitive/volatile the market
HIGH beta (luxury) firms are more volatile (fluctuate more) than market

--comp. or securities with Beta > 1

--company or securities with Beta < 1

if hear stock market will crash, as investor want stocks with LOW beta securities bc less impact if crashes
--but if own high Beta security and falls into recession...your portfolio would lose more than the market

Beta measures risk and st. dev. represents non-systematic (total) risk


Return on equity

(Req. rate of return by equity holders) - allows compensation for risk
--the return on an inv. req. by investors given the investment's risk

--allows us to assign a level of return we should get for a certain level of systematic risk
--what should be the expected return? lead to asset pricing


Req. rate of return =

req. rate of return = RISK FREE RATE + RISK PREMIUM

Risk free rate - compensation for time the investor is w/o her money
--U.S. treasury bills (T-bill) - no fluctuations so beta = 0 = risk free
--for T-Bills risk premium = 0 (but all others besides treasury carry some risk and will have a risk premium

--More diff. to determine (how large to compensate for a securities risk level)

Size of risk premium based on MARKET RISK (systematic)


SML (Security market line)

re. return as function of risk free rate and risk premium as determined by BETA - Quantifies the risk return trade-off in terms of the assets BETA

--SML crosses the vertical at RISK FREE RATE (Beta = 0) (risk free)
--any security with Beta = 1 will earn the market return
--low beta = DEC. return, high Beta = INC return

STRAIGHT LINE - linear relationship btw risk and return called CAPITAL ASSET PRICING MODEL
--SML is graphical representation of the CAPM

SML tells us how to price risk



Ri = Rrf + Beta(Rm - Rrf)
--most influential model in 50 years - bc gives closed-form solution for an inv. req. rate of return

Ri = return on "I"th security
Rrf = risk free rate
Rm = return on market
Betai = security's beta


Ex. of CAPM

Treasury bond (proxy for risk free rate) is yielding 6% - expected return on S&P 500 index is 12% and google has beta = 1.7

CAPM - what is Google's req. rate of return?

E(R(google)) = .06 + 1.7*(.12 - .06) = 16.2%


CAPM and small firms

CAPM struggles pricing for small firms - usually earn higher than CAPM's calc.
--Used to understanding the risk/return relationship

in equilibrium, all securities should lie on SML - if lies on line, means inv. is fairly compensated for risk and it is properly priced
--CAPM is an equilibrium model, but market not always in equilibrium
--so can also use CAPM to determine if over/under priced

ABOVE SML = return > risk level = price to low = undervalued
--So bUY - if buy underpriced = earn return > req. return

BELOW SML = over priced - not enough return for risk if bought = sell


EX. over/under value with CAPM

Rrf = 4%, Rm = 12%, Beta = 1.8 - today stock trades at $150 per share
--an analysis estimates stock will be selling at $170 in one year - is Hammer's stock correctly priced given analyst must first determine if over-valued, under-valued, or estimate correct?

1. Use CAPM to estimate req. return
E(Rhammer) = .04 + 1.8*(.12 - .04) = 18.4 %

18.4% is req. return on its SYSTEMATIC risk - now decide if misplaced

2 options:
1.) Discount expected future cash flows back to today with 18.4% req. return
FV = 170, N = 1, I = 18.4, PV - -143.58
--if 1701 yr. from now = expect price today to be $143.58 - but it is trading at $150 - so OVER valued

or 2.) Calc. HPR (holding period return) and compare to req. return from CAPM

HPR = (P1 - P0) / P0 = 13.33%
-inv. at $150 today and can sell at $170 next yr. with 13.33% buys return on inv.
--but CAPM says should get 18.4% return on market risk
--bc 18.4 > 13.33, comp. os OVER valued


Alternate to CAPM

How to assess riskiness of comp. w/o public traded stock - if PRIVATE COMP.
--cannot diversity? small - CAPM assumes only risk is market risk...but CAPM is not good model for poorly diversified investors, such as young entrepreneurs (can't eliminate firm-specific risk)

--alternate to CAPM - used to estimate cost of equity - used in small businesses
--"build up" req. return by adding risk premiums



estimates comp. req. rate of return on equity
1. usually used for small firms with no stock return (so cannot estimate Beta)
2. or for undiversified investor

Bond yield (Estimate)
+ Equity risk premium (given)
+ micro-cap risk premium (if small firm)
+ start-up risk premium (for ventures)
= req. rate of return

BY and ERP = called "Base equity rate" - IBM's equity return = add bond yield and equity risk premium to find CAPM for security with Beta almost = 1

BY + ERP + MCRP = called micro-cap equity rate
--add microchip for small comp. ( < $1 billion in sales)
--can't compare to IBM bc not same market penetration, asset base or recognition
--also not fully integrated supply chain

all 4 = start up comp. - risky

IF don't give bond yield - look at debt ratio or look at what similar companies are doing


Ex. build up

bond yield = 6%
equity risk premium = 5%
micro-cap risk = 4%
start up risk = 4%

for LARGE cap stock = req. rate return = 11% ( 6 + 5)

for small, well-established form = req. return (11 + 4) = 15%

start up = 15% + 4 = 19% (usually btw 17-25% or HIGHER)


Ch. 8 measurements

Beta = measures systematic risk
--measure how an ind. asset return varies from market returns - sensitivity to market changes

st. dev. = measures total risk

return = put in / get out

firm specific risk = Can be reduced through diversification

use CAPM - well -diversified investors


Return =

= What you get out / was you put in

= (capital gains - (P1 - P0)) +div. / P0

= [(P1 - P0 + DIV) / P0] * 360 / holding period DAYS

360 = bankers year - an estimate - 12 mo. in year and 30 days in each month

Buy for $10 and sell for $11 - Div = $1, had for 3 months

= [(11 - 10 + 1) / 10)] * 360 / 90 = 80% return (Crazy return but he will use crazy #s on test even though doesn't make sense - not realistic but right in problem

--ignoring TVM in these problems


Inferior good

Expected return ex.
= 6% E(R)
--In BOOM period - does bad and in recession does well


RISK - Efficient frontier

Rational expectations
--assume want HIGHEST return for a given level of risk
--also assume loses risk for a given level of return
(every model in finance based on these premises)
--risk is NOT just downside


Total risk (class) (var. and st. dev)

--want to know total amt. separated from the mean - volatility - fluctuations (variance and st. dev.)

sum of squared deviations - SSD

st. dev.^2 = sum of [(Ri - Rmean)^2 * Pi]
--Pi is the WEIGHT
--capture below and above - separation from mean

Rmean is the expected return (found in prev. problem of expected return = sum Ri*Pi)


Total risk formula class ex.

Pi. Ri
BUST. 15%. -10%
Normal80%. 3%
BOOM 5%. 15%
Rmean = 1.65%

Var. = (-10 - 1.65)^2 *.15) + (3 - 1.65)^2 * .8) + ...
var. = 30.72
radical 30.72 = 5.54 st. dev.

more volatility - can easily switch btwn high and low return

the HIGHER the st. dev./variance the MORE risky it is (be more volatile - subject to change)



Return (portfolio) - Rf / st. dev.

= Rp - Rf / st. dev.
--Rp = return on portfolio
--Rf = risk free rate (Treasury bill or bond)
--st. dev. = total risk
--Rp - Rf (numerator) = abnormal return

Deciding where to invest -most attractive option
Rp st. dev.p = SR
TECH 15% 3% = 15/3 = 5
UTIL 10%. 1%. = 10/1 = 10!!
---utility is double the better investment bc tech is sooo much riskier and more volatile
(There was no Rf in these ex. so just delete in formula)

it tells us the return for tech. is higher...so think it is a better inv. (15 vs. 10)...but can't decide until know risk - bc total res (st. dev.) is higher in tech - utility is better inv.


Treynor's ratio = TR
(and risk types)

Rp - Rf / Betap --->
--Betap = Beta risk/market risk on portfolio

1. Diversifiable risk
--firm specific risk
--unsystematic risk
--Idiosyncratic risk

2. Market risk
--systematic risk
--Beta risk
--nondiversifiable risk

(remember TOTAL RISK measured by st. dev.)

rational thinking
--most models in finance ONLY price 2nd beta risk...bc assume most ppl would choose the beta (smaller) risk and NOT pay the 1st diversifiable risk if have choice (but small comp. usually can't diversify so pay price)


Beta = (Class notes)

how strongly the asset correlates (moves with) the market
--for every 1% change in the market, stock changes Beta%

Beta APPLE = 1.26
--means is stock market INC 10% Apple INC 12.6% - or if market DEC 20%, Apple DEC. 25.2%
--smaller BETA is LESS risky

Beta > 1 (means riskier than the market)
m/Beta > 1 ("growth" mutual fund

Beta < 1 = "value" mutual fund
m/Beta < 1 = " "

market capitalization = total # shares * price per share


Can Beta be negative??

Betagold = -.5 ---means it is negatively correlated
--market DEC 10%, Gold INC. by 5%
--Does opposite of market


Nominal return formula

nominal return = real return + inflation

1 + nominal = (1 + real) * (1 + inflation)
==fisher effect!!!


Graph to estimate Beta - OLS

Discussed in earlier cards but this is class notes
--measures how well Apple did compared to the market

OLS = ordinary least sq. regression - measures line of best fit with LEAST amt. of variation (Distance btwn point and line - firm-specific risk)

slope of line is BETA - called CML (Characteristic capital market line)

two ways to find return for Apple
1. new - old / old (121 - 120 / 120) = .0083
2. (new / old) - 1 = (121 / 120) - 1 = .0083


Asset Pricer

Assign values to assets
--single asset pricing model

RRR = RF + risk premium (if buy risky asset...should get risk free rate and risk premium)
---(RRR = req. rate return)

Ri + Rf + Beta(Rm - Rf)
--Rm = expected return on market
--Beta * (Rm - Rf) = the entire risk premium
--Rm - Rf = market risk premium


BUILD up questions!!

only main 4 on test
--for bigger, established company only need the first 2 (bond yield and equity risk premium)
--always ignore beta if in problem bc not possible to add - just add them together and ignore extra info.


Sharpes ratio example

Comparing A and B
A - SR = 2
B E(R) = 12%, Beta = 1.2, Var. = 16% (var. = st. dev^2), so st. dev. = 4%

what is SR of security B?

SR = Ri - Rf / st. dev. = .12/.04 = 3 (didn't give risk free rate so do not worry about it)
--going 50% better return with B

bc. SR is better - want to invest in security B
--we are comparing the risk-adjusted returns


Cost of capital =

= rate of return - return req. by those who provide the capital
= cost of debt + cost of equity
--add together = total cost of capital (called weighted ave. cost of capital (WACC))

--prev. ch. discount rate (cost of capital) was given
--but in solving for cost...depends on which sources of financing used - calc. cost of equity debt and combine to find WACC


Capital budgeting

Goal of any cap. budgeting analysis is to determine whether or not the project we are considering will INC value of firm - first have to understand the cost of capital
--Va of firm is PV ion its future cash flows discounted back to present
--cost of capital is capital budgeting and can't know value of firm unless know capital costs

EX. bank - cost for bank to hold money is interest rate to its depositors (our rate of return as consumers)
--when comp. borrows from bank, charges higher rate than int. rate paid to Indiv. depositors
--cost to bring funds into a business - cost based on HOW FUNDS ARE OBTAINED (stocks, loans, bonds) and level of RISK
--cost of funds is "Cost of capital" - must compare w/ earnings from using funds
--earnings measured by ROA (Return on assets) - compare ROA with cost of capital to see if we are creating value in a company


Comparing ROA and cost of capital

ROA > cost of capital ---> inc. firm value
ROA < cost of capital ---> dec. firm value


Investment decision
vs. financing decision

LEFT side of balance sheet = INVESTMENT decision
--how a firm builds the asset side of the balance sheet by allocating funds, time and other resources
--deciding in what we should invest and how to use funds, time resources

RIGHT of Balance sheet = FINANCING decision
--how we will fin. our assets and operations (what proportions of debt and equity will we use)
--cost of capital - what it costs to finance our assets on the left

WACC - weighted ave. cost of capital - "on ave. how much does it cost this firm to keep $1 of capital for one year?"


Capital sources and costs

--when buying securities (stocks and bonds) as consumers think of returns as income or source of revenue - the return is amt. of money that we require in order to lend or give our money to the comp. issuing the stock or bond
--but managers of corp. see returns req. by stock and bond holders as a COST - amt. paid to investors to encourage them to lend or invest their $

stockholders (Residual claim) -what makes firm valuable is possibility of earning more than req. return (when economic value is added)


EVA formula (economic value added)

EVA = NOPAT - [WACC * Costly capital]
--NOPAT = net operating profit after taxes
--NOPAT = EBIT - cash taxes
--EBIT = earnings before interest and taxes

costly capital = sum of all interest bearing debt and all equity

Earn positive EVA (economic profits) by earning return > cost of capital
--if return = WACC, the EVA = 0, ---> NO economic profits
--must earn more than opp. cost of costly capital


Sources to raise capital in firms

3 basic sources:
--borrowing (Debt), common stock (equity), pref. stock (hybrid)
--each req. a rate (cost to comp.) - determined by terms and risk
--weights based on mix of debt, CS and PS

weighted average - ave. where each element has a spec. weight assigned


thinking about cost of capital

--it is req. return on an asset - benefit from investing
--that same rate of return is cost of raising funds needed to operate the firm
FOR YOU (stockholder)
--an INC in firm value over what is req .comes for the diff. in the cost of capital and the req. rate of return


1. Cost of DEBT

Three components to calculate
---explicit int. rate you pay on debt (10% int. rate)
--on bond the YTM (including CPN and final pmt.)

2. FLOTATION COSTS - ex. transaction fees
--rent house, not only pay 10% int. but also additional closing fees and others - firms pay IB to issue bonds - ALWAYS exist in external funding unless internal (ONLY in case of Retained earnings)

--decrease borrowing cost bc create tax shield
--int. tax shield - (savings a firm gets by using debt to write off the interest expense) - (ex. in note cards)
--tax deductible - subtracted from income BEFORE tax rate is applied - lowers total taxable income (so dec. tax expense)


after tax cost of debt =

after tax cost of debt = pretax cost of debt - tax savings (from int. tax shield)
= before tax cost of debt * (1 - tax rate)

Ex. mortgage - 5% pretax mortgage pmts. and tax = 40%
5% * (1 - .40) = 3% (pay 3% on house bc gov. picks up 40% of interest expense) - gov. rewards bc wants us to own home and inc. economic stability in nation

ex. 10% int. 34% tax bracket - what is after tax cost of debt?
10% (1 - .34) = 6.6%


cost of debt ex. problem

comp. issues $1000 par value 20 yr. bond paying market rate of 10% annual CPN - bond will sell for par since it pays market rate, but flotation costs are $50 per bond - marginal tax rate = 34%
what are the pre-tax and after-tax costs of debts?
--explicit borrowing cost is the 10% int. on loan ea. yr.
--flotation costs of $50 mean that FV is 1000 but buy for $950 today - but in 20 yrs. when matures will be 1000

1. PRETAX cost - consider flotation costs
--find YTM (req. rate of return, or pre-tax cost of bond)
N = 20, PV = -950, pmt. = 100, FV = 1000, YTM = 10.61%
= Pre tax cost of borrowing = 10.61%

after tax = 10.61 * (1 - .34) = 7%

10% nominal int. rate bonds issued - flotation costs INC rate to 10.61% pre-tax, tax shield lowered I to 7% after-tax cost of boring

DO QUIZ 9.2 #1


2. Cost of EQUITY

rate of return required by shareholders
--two sources of common equity:
1. retained earnings - INTERNAL - firm keeps all profits not paid out in dividends - simple - fund with own money so no flotation costs
2. external common equity - new common stock (req. firms to hire IB or 3rd parties to issue) - flotation costs

3 methods to compute cost of CS: CAPM, Build-up, GGM


2) cost equity, 1. CAPM method

Kcs = Rrf + Beta(Rm - Rrf)
Kcs = req. return (cost of CS)
return is equal to risk free rate + beta times the market risk premium

Rrf = if we could inv. in security that had GUARANTEED rate of return with NO risk, be risk free rate - use gov. t-bill as proxy - many analysis's say to use 3.mo t-bill for (market risk premium) bc least risky..but many say 30 yr. t-bill bc long term

Beta - relationship comp. has with entire market - shows how stock returns of firm relate to contemporaneous market returns

Rm - our estimate of returns general stock market will gain over time

--bc Rrf and Rm are same for all companies (Determined by economy and general market) - most IMP. to determine is beta risk


2.) cost equity, 2. Build up method

Internal already know - gives. req. rate of return for internal funding (retained earnings) - small businesses where beta cannot be found

Take build up internal cost of equity and do (1 + FC)
internal cost = 19%, FC = 10%

19% * (1 + .10) = 20.9%


3.) cost equity, 3. GGM method

V0 = D1 / (kcs - g)

rearrange: (bc V0 is current value (which is price) so change V0 to P0)
kcs = (ANNUAL D1 / P0) + g
--D1 / P0 is the dividend yield
--G = capital gains yield = growth

Ex. recently rec. $1 quarterly div. - value is $40 per share,
g = 10%
--DON'T do 1/40 (quarterly) or 4/40 (bc it was D0 not D1)
--multiply ANNUAL div. by (1 + g)

Kcs = (4 * (1.1) / 40) + .10 = 21%


2.) Cost external equity, 1.) CAPM method

-take cost of internal equity (Result from CAPM) and multiply by (1 = flotation cost %)

Ex. internal = 8.9%, flot. cost = 10%
external cost = 8.9% * (1 + .10) = 9.97%

---But GGM can have cash or %


2.) Cost external equity, 2. GGM method

two options bc can give FC as cash or percentages
1. adjust price by FC, substitute NP (NET PRICE) for P (price)
Kcs = (D1 / NP0) + g

ex. 10% FC, D0 = 4, g = 10%, PV = $40
= [4*(1.1) / (40*(1 - .10)] + .10 = 22.2%

2. if know dollar cost of FC
ex. FC = $5 - then take off from issued value

(4*(1.1) / 35) + .10

the FC takes from profit bc it is costs to IB, attorneys, CPAs, printers, and anyone externally involved


Cost of Preferred stock

Vps = D / Kps
--D = ANNUAL fixed div.
--Kps = discount rate or req. rate of return
--replace K with P (price)

Kps = D / NPps

ex. 5000 shares at $20 per share - FC = $3 per share

Kps = 2 / (20 - 3) = 2 / 17 = 11.8%



formula on notecard
--when we say "common stock" mean "TOTAL ASSETS - TOTAL LIABILITIES - PREFERRED STOCK"
--includes all common equity summed together (commons tock account, additional paid capital, treasury stock)

for C, P, D in equation - prefer market values if available - bc want to know what CURRENT cost of capital is
--if unavailable use book values (historical #s) and ask if had to rebuild identical cap. structure today, what would be our WACC?

V is totally capitalization of the firm (means ALL int. bearing liabilities and ALL equity)

--the weights should always sum to one
--also can be adjusted if have both internal and external equity
--or if have two types of debt: notes and bonds (both have tax shield)


Limitations of WACC

WACC is for extensions, now NEW projects
--may not be able to acct. for the risk involved

can change the Value formula to compute FCFF (Free cash flow for the firm)

Vo = sum of FCF / (1 + k)^t

change to V0 = sum of FCFF / (1 + WACC)^t


to use WACC instead of k

New project must be an EXTENSION of existing firm (Pizza Hut opening new restaurant or Microsoft launch new version of windows)
--otherwise not an appropriate discount rate (bc diff. risk level)

so NO WACC - then analyze firms already in the market where we are moving - called PURE PLAY (looks at their costs and infer from theirs how to adjust ours)


WACC goals and optimal capital structure

GOAL: Maximize owner wealth

Optimal capital structure:
1. best possible mix of debt and equity
2. minimize discount rate (which will give us the best)

two sides of balance sheet
LEFT - assets
--accountants record - finance: decide which to buy and how to fund

RIGHT - debt and equity
--which should we use to finance for OPTIMAL CAPITAL STRUCTURE?

Optimal is best mix of debt and equity with minimum r value (discount rate)


In which cases does the CAPM not accurately determine whether a security is under/ overvalued?

When portfolios are concentrated and investors are undiversified
--The CAPM is not accurate for concentrated portfolios. Undiversified investors cannot eliminate firm-specific risk, therefore the cost of equity may be much higher for investors in this situation


Goals and optimal capital structure

GOAL: Maximize owner wealth

1. best possible mix of debt and equity
2. minimize discount rate

--LEFT - assets - acc. record and fin. decide which to buy and how to fund
--RIGHT - Debt and equity - which should we use to fin. for optimal capital structure

optimal is best mix of D and E w. minimum R



Midigliani and Miller (WATCH HIS NOTES ON YOUTUBE)
--basis of corporate finance


Cost of debt - Yield to maturity

1. after flotation costs (for bonds about 2.5%)
2. has to be after tax

2 ways they could issue bond:
A.) FC = $30/Bond @ Par
--PV = Price - $FC = 1000 - 30 = 970 (PV in calc!)
B.) FC = 5% bond @ Par
--PV = Price * (1 - FC %) = 1000* (1 - .05) = 950

solve and find YTM = 6.72%
--then after tax = 6.72(1 - .34) = 4.43%



Ex. bond FC

Bond - 10 yrs. to maturity, FV = 1000, CPN = 5% semi annual pmt.
--quoted at 96% face value
Solve for YTM, n = 20, PV = -960, PMT = 25 FV = 1000
Y = 5.53% (BEFORE TAX)

A. FC = $50/ Bond
NP = PV - FC = 960 - 50 = $910

B. FC = 5%/ Bond
NP = 960*(1 - .05) = $912

T = 21% (Tax rate)
After tax Kd ---> 5.53* (1 - .21) = 4.37%

to find after tax = Kd* (1 - t)


4 ways to call internal equity and 3 for external equity

internal equity
--retained earnings
--plowback (profits)

external equity
--outside shareholders


capital gains yield

also called growth rate - in GGM model for finding cost of CS


what are we finding with CAPM?

Market price/ market rates
--price today to restructure capital structure of firm

WACC - what would it be today, at market rates, to rebuild this cost of capital?
Ex. sell firm for $23.60 to Goldman, then they sell it to market for $26.60 - FC is what is paying the IB

--adjust for FC - makes it more expensive
--makes the Kcs INCREASE


WACC Meanings

V = total capitalization
--Market capitalization = the value of a company that is traded on the stock market, calculated by multiplying the total number of shares by the present share price.

E = dollar market value of equity
D = dollar market value of debt
--need market value - want to know what it sells for today

E / V = weight of equity
D / V = weight of debt

market cap = publicly traded common shares

WACC - used for dinging value of a FIRM (rework the VA FCF equation to show value of CF and chance k to WACC)
--shows that value a firm should trade for = stock (what Amazon should trade for)


In WACC problem..

Book value and face value = SAME


Diff. goals entrepreneurial finance

Corp. finance - GOAL to MAXIMIZE OSHareholder wealth - return - profits of firm

Entrepreneurial fin. - goal to maximize the lifestyle that the person wants to live
--dentist - run a lifestyle business and max. his UTILITY function (things that make him happy), not max his wealth function

in entrepreneurship - need to know the END goal: stable lifestyle or high-growth venture you can hopefully quickly harvest


lifestyle firm vs. new venture

lifestyle firm
--owners desire to hang on to the bus. and run for many years - focus on max. utility instead of max. wealth

new venture
--focus on bus. that hopefully w/in 5 years will either be bought out or go public via INITIAL PUBLIC OFFERING - liquidating event for founders known as the harvest


5 major business ENTITY structures

1. Sole Proprietor
--TAX/FILING - single taxation
--LIABILITY PROTECTION - none (unlimited - can sue for personal assets)
--# of OWNERS = one

2. Partnership
--TAX/FILING - Single
--EQUITY UNITS - Capital
--LIABILITY PROTECTION - none (unlimited - same as SP)
--# of OWNERS - 2+

--TAX/FILING - Articles of INCORPORATION - single taxation
--EQUITY UNITS - common shares (no PS)
--LIABILITY PROTECTION - Yes (limited liability)
--# owners - 100 MAX (Called shareholders) - if go public have to become a C-Corp. bc too many shareholders

--TAX/FILING - only entity that pays corporate taxes - double taxation
--EQUITY UNITS - Pref., CS, - diff. classes of shares ok
--LIABILITY PROTECTION - Yes (limited liability)
--# Owners - unlimited (called shareholders)

5. LLC (Limited liability company)
--TAX/FILING - Articles of ORGANIZATION - very pop. structure - can tax as a sole prop. and get protection as a C-Corp. - can choose to be taxes as S-Corp. to avoid SE taxes - single member LLC ok - have MEMBERS, not share holders or partners (means can have single or double taxation)
--only the assets labeled in LLC (Ex. $50) can be sued in accident - not personal assets
--EQUITY UNITS - Member % units
--LIABILITY PROTECTION - Yes (limited liability)
--# OWNERS - Unlimited - called MEMBERS - own a (membership) but no shares


Filing/tax requirements 1. sole prop.

1. sole prop.
--cheapest to start, easiest, lightest filing req. - starts on own and at tax time filled out IRS Sched. C (profit or loss from Bus. - sole prop.) and that profit or loss is reported on IRS 1040 tax filing doc. as ordinary income


filing/ tax req. 2. partner

2. partner - use IRS 1065 (U.S. return for partnership income)
---IRS Sched. K-1 - reports how much income or loss each partner is responsible for - partners must pay taxes on any K-1 form whether they actually re.c it or not

--if income is not paid out to the partners (ex. invested in the partnership), this income called PHANTOM INCOME - declared as income for tax purposes but after taxes are paid on it, do not need to be paid again when income is actually distributed to partner
--then take K-1 info. and report to IRS schedule. 1 - report on form 1040 as ordinary income

for sole prop. and partnership --- no paperwork to "begin" company - did not file with state or any regulatory body - started to work then dealt with income taxes come tax time


filing/tax req. 3. 4. S-corp, C-Corp.

both req. ARTICLES OF CORPORATION - filed with the state and pay a filing fee (varies each state - range from low 100s to mid 1000s

Tax purposes: Scorps. file IRS form 1120S (US income returns for an S-Corp.) at corp level and firm issues K-1 to owners reporting income and losses (like partnership)
--C-Corp. use IRS 1120 (US Corp. income tax return)

--like partnerships, owners of S-Corp. take K-1 info., complete Schedule. E and report data on IRS 1040
--But C-Corp. rec. dividends, reported on Sched. D (not E) - owners rec. div. from C-Corp. have no tax break


tax/filing 5. LLC

register firm before beg. operations - Articles of Organization
--quick and cheap to form (Utah $70, Texas $200) - can be formed online
--in single member LLC, LLCs are taxed as sole prop. - entrepreneur walks through IRS schedule. C - then 1040
--multiple member LLCs. entrepreneur uses schedule. E route, then some process Inc.


C-CORP. income statement

C-Corps. are ONLY ones with DOUBLE TAXATION - bc corp. income tax paid before distribution to owners, then personal income tax paid on distributions (div.)

Gross profit expenses
EBIT (Earnings before int. and taxes)
- interest
= EBT (Earnings before taxes)
- corp. taxes (1st part of double taxation)
(then 1 of two operations flowing form NI)
1. used as retained earnings (balance sheet)
2. pay as dividends - then shareholders pay personal income taxes on them (double taxation)


tax strategies

income and losses can offset each other
--two types: ordinary and capital
---with any except C-Corp. can claim any gains and losses on personal income tax return (1040) and net these gain/losses with the income
ex. - positive cash flows but say depreciation of equipment as a loss = reduces tax burden

also way to reduce social security and medicare taxes - 14.2 my educator


equity units

SP - Owner owns everything so not equity units
P - each partner rec. capital % of ownership
SCORP - common share - divided to owners based on % ownership
CCORP - common, pref, class A or B shares
LLC - expressed as member % or a # of units ownerd


Liability protection

SP and P have unlimited liability - no insurance and can be sued for personal assets and forced into bankruptcy
CORP. and LLC - only have business assets at risk (personal assets protected)
--but often sign personal collateral to fin. bus. - then corp./LLC's protection worthless
--UNDO protection by personal commitments in loans


"give birth" to business

1. LLC - file Articles of ORGANIZATION and pay fee
2. open commercial bank acct. in home of bus


Financing a new venture

1. fin. projections ar made as demonstrated in forecasting
2. decide how to finance the firm


1. bootstrapping

1. bootstrapping - self-funding a venture - using inventive ways to limit expenses and fund a new venture
--minimize costs by buying used equip. work in garage
--inventive ways to fin. w/o external investors - trade credit - owe accts. payable to your suppliers - factoring - sell acct. receivable at a discount to rec. immediate cash - credit cards
--adv. is don't sell ownership in firm to others

or go to family/friends - but must either structure inc. as debt or make sure they are ACCREDITED INVESTORS
--need $200,000 Indiv. or $300,000 joint annual income or $1M net worth as an div. or joint wit spouse
--structure as a loan!!

--own funds
--trade credits - accts. payables ($ owe ppl for service/goods)
--factoring (Accts. receivable) - Christmas ex. with guy who couldn't pay employees


seed financing

loans are seed financing - initial funds used to start up a venture
--but most loans will not loan to a bus. unless it has a 3-yr. operating history with profits - for this reason, many firs compromise persona collateral to secure a loan - destroys liability protection


2. instead of bootstrapping use outside equity investors

1. angels - wealthy ind. - invest in new ventures for return and thrill - help entrepreneurs - usually lead very early stage ventures

2. venture capitalists - 2nd level - usually invest much more than angels and D large share of ownership in venture and 1/2 board seats
--look for huge returns -VC fund set up as limited partnership of up to a 10 yr. life - very high risk
--if have 10 comp. in fund - 3/4 = total fail, 4-5 living dead (alive but barely break even), 1-2 homers

3. PE - make larger investments and usually buy entire comp. using combo of debt and equity

PE and VC called, "2 and 20 shops" - bc firm gets 2% of size of fund for admin. fees - then 20% career (amt. of profits the shops get to keep)


capital call

VC fund calls accredited investors and solicit inc. in the fund
--Ex. VC fund raises a $100M fund - each yr. fund gets $2 M (2% of $100M) for admin fees
--has a firm that does an IPO and earn $300M on the dial - t


Harvesting a new venture

1. LIFESTYLE - firms exp. PERPETUAL harvest- - dentist - rec. nice income for rest of life

2. SELL - in M&A market - ex. dentist turns 55 and retires - sells practice to another dentist and exp. final harvest on top of lifestyle harvest

3.. Venture - an IPO - files with SEC and becomes publicly traded comp. - founders can then sell shares of stocks in open


3 main areas in finance

1. corporate finance
2. investments
3. institutions (IB)
--all trying to get highest return for group they work for - maximize wealth

diff. of firms
--wealth maximization - corporate finance
--utility maximization - entrepreneurship


Diff. types of firms within entrepreneurship

1. lifestyle business - get into bc want a certain lifestyle
2. salary replacement - buy and own their own business
3. new venture - closest to wealth max. goal bc want to harvest
--harvest (or called "Exit") - prof. investors (VC and angels)


LLC strategy

taxes have to pay
--FICA ("payroll") taxes
--social security
= approx. 15%

LLC $70 - say want to be taxed as an S-Corp. (no double taxation)
--summer sales ---> $50,000 sales
--write check to LLC (not personal acct.)
Pay yourself from LLC
--$10,000 in wages (have to pay .15% in FICA, S.S., and medicaid taxes)
--then $40,000 distribution (if give self as distributions = NO taxes (Except later income tax, but no FICA or others))

40,000 * .15 = 6000 = means you SAVE $6000 from not paying those taxes and giving to self as distribution from LC


How to "give birth" to a company? (class notes)

1. File articles
---hire lawyer or fill out articles
--LLC called "Articles of Organization"
--Corp. called "Articles of Incorporation"
2. Open a bank acct. in the firms name

Don't peirce the veil
--mingle funds - using LLC funds for personal reasons - any attorney could come sue you for your personal asset


Order of financing a new venture by inc. time it is in the market

1.personal capital
2. FFF (friends, family, fools)
--must be accredited investors - can go to jail if not, called "solicitation"
--acc. inv. means 1. invest institution or 2. individual makes more than $200,000 income for 3 years or 3. worth greater than 1M in assets

3. ANGELS - shark tank
4. VCs - buy a portion of company
5. PE shops - buy whole company

if you are staying in business you are succeeding - INC. time = success


Venture capital notes

on notecard


3 ways to harvest

1. lifestyle perpetual harvest
2. sell-out (M&A)
3. IPO - go public


discount rates of VC

use about 40-50% - REASONS
1. very risky
2. adequate - deal flows - history on side - S & D
3. VC provide more than $ - strategy, mentor, sit on board
4. Cash flows are overly optimistic - "haircut"

venture startup - (formula for value of firm)
--bc overestimate future cash flows, make r really high in the denominator