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130 Cards in this Set
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In words, how do you calculate the current stock price?

present value of all expected future dividends


In formula, how do you calculate the current stock price? (dividend growth model)

Sum from 1 to infinity of: DIVt/(1+r)^t


What's another way of representing the dividend growth model?

r = (DIV/P) + g


How do you calculate a dividend?

Div = (earnings/shares outstanding) x dividend payout rate


What are two things a firm can do that will increase its dividend?

1. increase its earnings
2. increase its dividend payout rate 

What are two things a firm can do with its earnings?

1. pay them to investors
2. retain them and invest them 

How do you calculate change in earnings from investments?

new investment x return on new investment


Wait a second, but how do you know the amount of new investments?

new investments = earnings x retention rate


And how do you calculate the earnings growth rate?

change in earnings / earnings


Putting that all together, how do you more simply calculate the earnings growth rate?

retention rate x return on new investments


Cutting a firm's dividend to increase investment will raise its stock price if and only if what?

the new investments have a positive NPV


The constant dividend growth model doesn't work if what is changing?

the growth rate (but we can make it work indirectly, using terminal value)


How is the P/E ratio of a stock calculated?

P/EPS


What is that also equal to? (after substituting in for P)

dividend payout rate / (rg)


How do you calculate the expected return of a portfolio from probabilities and returns?

r = p1r1 + p2r2 + p3r3....


How do you calculate the variance from probabilities, expected return and sample returns?

var = p(re1  r1)^2 + p(re2  r2)2 ...


What are the two components of realized return?

dividend yield + capital gain


What's the formula for annual realized return?

1 + Rannual = (1+Rq1)(1+Rq2)(1+Rq3)...


What's the formula for estimating the expected return from historical data?

T = sample size
sum of all returns / T 

What is the formula for estimating the variance from historical data?

[sum of (sample return  expected return)^2] / (T1)
this is the same as the previous probability one except it assumes equal weights for all of these 

How do you calculate the standard error of the estimate of the expected return?

SD(individual risk) / sqrt(# observations)


Is there a positive relationship between volatility and average returns for individual stocks?

no, because volatility may mean only idiosyncratic risk, which is not rewarded


What's the formula for covariance?

cov = sum of all p(r  re)(r  re)


How do you calculate the correlation?

cov / [SD(a)*SD(b)]


What is the covariance of a stock with itself equal to?

variance


What's the formula for the variance of a portfolio with two stocks?

var = (w^2)*var + (w^2)*var + 2*w*w*cov


How do you express that with correlation instead?

var = (w^2)*var + (w^2)*var + 2*w*w*SD*SD*corr


What's the formula for the variance of a very large portfolio?

(1/n)(avg var) + (1  1/n)(avg cov)
As this gets large, the variance disappears, as long as cov is small. 

What's an efficient portfolio?

no way to reduce its volatility without lowering its expected return


The graph with the curve. What's on the xaxis and what's on the yaxis?

xaxis: volatility
yaxis: return 

What variable makes this graph curve left more and more as the variable gets higher?

the correlation


When you add stocks to the portfolio, what does the curve do?

curves more to the left


What's the top left of the curve called?

efficient frontier


Assume you put in some rf. What's the formula for the expected return?

E[R] = (1x)rf + x*E(Rp)


How can you rewrite that formula?

E[R] = rf + x*(E(Rp)  rf)


What is the formula for the variance of a portfolio of two stocks, with one of them being at the risk free rate?

xSD(Rp)
remember the long equation, except plugging in 0s for the rf simplifies it lots 

In words, how is the sharpe ratio calculated?

portfolio excess return / portfolio volatility


What's the equation for the sharpe ratio?

(E[Rp]  rf) / SD(Rp)


What's the CAPM formula?

r = rf + B(E[Rm]  rf)


Use the market premium in a formula for expected return

expected return = rf + market premium


How is B defined in a formula? What's the other way of writing that?

(SD of stock x correlation with the market) / SD of market
cov between the stock and market / var of market 

How the hell do you calculate the beta of a portfolio?

just the weighted average of the betas of each stock in the portfolio


What the hell is the alpha?? in words

the difference between a stock's expected return and its required return according to the security market line


What's on the axes of the security market line?

beta and return
they're directly correlated (if not, there's alpha) 

What is a firm's market capitalization?

# of outstanding shares x share price


What is a valueweighted portfolio?

a portfolio in which each security is held in proportion to its market capitalization
examples are S&P500 etc 

In words, what is beta?

the expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio


When we talk about estimating beta using linear regression, what's on the axes of the graph?

xaxis has market excess return
yaxis has stock excess return remember the definition of beta! 

What is the expected return of a bond equal to (use its YTM and incorporate default probability)

r = YTM  (prob of default)(expected loss rate)


How does the real world calculate debt betas?

they look it up based on the rating of the bond and its maturity


What does unlevered mean?

"an unlevered firm is fully equity financed and does not have any debt, so that all cash flows are paid to shareholders"


What is levered equity?

equity in a firm that has debt outstanding


What rate do firms borrow at? Why?

risk free, because the project's cash flows will always (i guess) be enough to repay the debt (the slides says verbatim)


Levered equity sells at a lower price. Why?

because the cash flows of levered equity are smaller than those of unlevered equity.
if you have debt, the equity doesn't have to be as high to achieve the same financing 

Does leverage increase the risk of the equity of a firm?

ya (so investors require a higher return)


Does debt increase the overall risk of a firm?

no, the WACC stays the same, only the cost of equity increases


When finding an arbitrage opportunity, what should you do?

find permutations of the securities (multiply by something, including a negative) to set the cash flows equal to zero. the present value difference is all yours to keep


What is a market value balance sheet?

a balance sheet where all assets and liabilities of the firm are included (even intangible assets such as reputation, brand name, or human capital)
the values are current market values rather than historical costs 

What's equal to what when it comes to the value of a firm?

total value of all securities issued by the firm = the total value of the firm's assets


What's the equation on the balance sheet?

market value of assets = market value of equity + market value of debt and other liabilities
or equity = assets  liability 

What is a leveraged recapitalization?

when a firm uses borrowed funds to pay a large special dividend or repurchase a significant amount of outstanding shares


What does leveraged recapitalization have to maintain constant?

assets = liabilities
and the share price 

Terminology. What's E, D, U and A?

E = market value of equity in a levered firm
U = market value of equity in an unlevered firm D = market value of debt (in a levered firm, obviously) A = market value of the firm's assets 

What is MM I?

E + D = U = A
that is all. the two parts are in there. E+D = U, and E+D = A 

What is the relationship between the returns of unlevered equity, debt and levered equity?

(E/(E+D))(Re) + (D/(E+D))(Rd) = RU = RA
same as above, except returns, and weighted 

If you play around with that equation (for the relation between levered, unlevered equity, as well as debt), what do you get?

Re = Ru + D/E(Ru  Rd)


What does that equation essentially say?

that the COC of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the debtequity ratio


What is the debttovalue ratio?

the fraction of a firm's enterprise value that corresponds to debt
D/(E+D) 

What happens to the WACC as you add more debt?

it doesn't change, doesn't care


What happens to the equity cost of capital as you add more debt?

it goes up, fast


What happens to the debt cost of capital when you add more debt?

it stays the same, unless you get to 80%, 100% of debt, in which case it goes up fast


How does the WACC stay constant despite changes in debt/equity? (in my own words)

The WACC is a weighted average of the two. Let's say you start with all equity. As you add debt, two things happen.
1. the equity COC goes up 2. the weight of debt goes up These two cancel each other, and keep the WACC the same 

What is the beta for a riskless security?

0


What is the affect of leverage on the risk of a firm's securities?

Ba = (E/(E+D))Be + (D/(E+D))Bd
just do the weight, yo 

Clarify A, D, E and U for me.

E and D make up A
U is like A, except without debt 

What does holding cash do to risk and return? What's an equation for net debt?

it has the opposite effect on risk and return. it can be viewed as negative debt
Net debt = debt  cash and riskfree securities 

What can leverage do to a firm's EPS?

increase it


Does the fact that leverage can increase a firm's EPS mean it can also increase its stock price?

nope


Why is it that when firms use leverage to increase their EPS, shareholders aren't better off?

because the risk of its EPS also increases. the increase in EPS is necessary to compensate shareholders for the additional risk


What can you say EPS equals?

a dividend payment


Explain via formula how the price of a share remains the same despite leveraged recapitalization.

P = Div / Re
EPS goes up. That increases the numerator. Re goes up. That's because there's more debt. Remember: more debt means a higher cost of equity. You're taking on more risk! Need to be compensated for that. So EPS goes up but the price is the same. 

Does issuing more shares of a stock increase the firm's EPS?

nope. EPS = earnings/share
assets increase, shares increase 

Does capital structure matter in a perfect market?

nope


What is tax deductible, and thus screwing with the assumption of perfect markets?

interest payments! that makes debt attractive. cuz you save money


Is income higher or lower with debt?

Per the example, it can be lower. Cuz you have to pay interest expense. But that goes to those who hold bonds. The total dispersed to stockholders and debtholders is greater, because you're saving on tax.


What does the interest tax shield equal to?

corporate tax rate x interest payments


To get EBIT to become net income, what do you have to subtract?

interest and taxes (must be in that order)


What's the difference between cash flows to investors with leverage and cash flows to investors without leverage?

interest tax shield


What did MMI say about the relationship between the value of a firm with and without leverage?

they're equal


Okay. So now that we have taxes, how's that relationship look?

VL = VU + PV(interest tax shields)


Is repayment of the principal on debt tax deductible?

nope


What are the three components multiplied by each other to get the interest tax shield?

debt * interest rate * tax rate


What is the present value of a stream of tax shields that go on in perpetuity? (assume the interest rate is riskfree)

T x D
from: (T x rf x D) / rf 

If a firm has a certain number of shares and a certain share price, and then it borrows money to repurchase shares, what happens?

Tax shield! Leads to higher total assets. Which leads to a higher price given the same number of shares.
BUT... the number of shares decreases, because you're purchasing them back. AND, equity goes down because you're buying shares, so that decreases the numerator (total value to be divided by the number of shares). 

Do original share holders of a firm get the benefits of the increase in share price that results from a leveraged recapitalization?

yep


When a firm wants to purchase some of its shares back, how does the repurchase affect the new share price? Given a constant amount its willing to commit to doing this.

the higher the share repurchase price, the fewer shares it can buy back and the more shares are left. that means a lower new share price


If a firm has a certain number of shares and a certain share price, and then it borrows money to repurchase shares, what happens?

Tax shield! Leads to higher total assets. Which leads to a higher price given the same number of shares.
BUT... the number of shares decreases, because you're purchasing them back. AND, equity goes down because you're buying shares, so that decreases the numerator (total value to be divided by the number of shares). 

How do you calculate the WACC now that there is an interest tax shield (based on MMII)?

(E/(E+D))rE + (D/(E+D))rD(1T)


Do original share holders of a firm get the benefits of the increase in share price that results from a leveraged recapitalization?

yep


Given that equation, it's clear the existence of taxes decreases the WACC. By how much?

(D/(E+D))*rD*T


When a firm wants to purchase some of its shares back, how does the repurchase affect the new share price? Given a constant amount its willing to commit to doing this.

the higher the share repurchase price, the fewer shares it can buy back and the more shares are left. that means a lower new share price


How do you calculate the WACC now that there is an interest tax shield (based on MMII)?

(E/(E+D))rE + (D/(E+D))rD(1T)


Given that equation, it's clear the existence of taxes decreases the WACC. By how much?

(D/(E+D))*rD*T


Tell me again, what happens to the equity cost of capital, equity cost of debt and WACC as the debttovalue ratio increases?

debt COC: flat, except rapid increase at end
equity COC: rapidly rises (more debt means more risk for the equity holders) WACC: stays the same (MMI) 

Now that we have taxes, how are those three COCs changed as the debttoequity ratio rises?

debt COC: goes down a bit (debt is better because of the interest tax shield, so the COC goes down)
equity COC: stays the same WACC: goes down gradually (more debt helps with the interest tax shield) 

What's one way of finding the present value of the interest tax shield?

PV(Ts) = VL  VU
take the value of the firm with taxes and subtract the value of the firm without taxes 

What are the three adjustments made to unlevered net income in order to get FCFs?

add depreciation, subtract capex, subtract inc. in NWC


What's the equation for the WACC again?

(D/(D+E))(1T)rD + (E/(E+D))rE


What's the hardest part of calculating the WACC?

getting the rE
D/E, T, rD are usually given 

What's the hard variable to get that helps you calculate rE (via CAPM)?

Be


How do you convert from the asset beta to the equity beta?

Be = Ba(1 + D/E)  Bd(D/E)
I DONT KNOW WHY 

What are the three steps to the WACC method of valuing a project?

1. determine FCFs
2. determine the WACC 3. determine the value of the investment by discounting 

What are the two requirements for using a WACC for a project?

1. must be of comparable risk to the rest of the firm
2. must not alter the firm's debtequity ratio 

What are the two ways to add debt?

increase debt or decrease cash


Suppose a firm wants to undertake a project that will increase its assets. If it wants to maintain its debttoequity ratio, what does it have to do?

increase debt


What happens if the funds it raises through debt is more than the amount needed to fund the project?

issue dividends with the surplus
that, added to the increase in equity, equals the NPV of the project apparently 

What is the definition of the debt capacity?

the amount of debt at a particular date that is required to maintain a firm's target debttovalue ratio


How do you calculate the debt capacity in a formula?

D = d x VL
d = firm's target debttovalue ratio VL = levered continuation value 

How do you find VL for time t?

(FCF for t+1) + (VL continuation value for t+2 and beyond) / (1+WACC)


What happens if after issuing debt to keep a constant debt/equity ratio, the debt isn't enough to fund the project?

issue more stocks!


What does APV do to value an investment?

first calculate the unlevered value
then adding the value of the interest tax shield (and deducting any costs that arise from other market imperfections) 

What's the formula for the APV method?

VL = VU + PV(interest tax shields)


What COC do you use for the APV method?

the unlevered COC


How do you calculate it??

Well, it's the same as the RA, as long as you calculate it without the interest tax shield
RU = (E/(E+D))(rE) + (D/(E+D))rD 

How do you calculate the interest tax shield for the APV method, through the debt capacity?

debt capacity x rD (interest rate) x T


What COC should be used to get the present value of all those interest tax shields?

unlevered COC


Do the WACC and APV methods get the same answer?

yep


What are the three steps of the APV method?

1. determine the investment's value without leverage
2. determine the present value of the interest tax shield (a. determine the expected interest tax shield, b. get the present value) 3. add those to get the investment with leverage 

What are two advantages of the APV method over the WACC method?

1. it can be easier if a firm doesn't want to maintain a constant debtequity ratio
2. it explicitly values market imperfections and therefore allows managers to measure their contribution to value 

What does the APV method simplify to if a firm has permanent fixed debt (maintains same level of debt forever)?

VL = VU + T*D
