Corporate Finance Flashcards
1
Q
Week 1 Risk Return - What has the highest return if invested $1 in 1900 and valued in 2007?
Portfolio of Treasury Bills
Portfolio of U.S government Bonds
Portfolio of U.S common stock
A
Portfolio of Treasury Bills: $71
Portfolio of U.S government Bonds: $242
Portfolio of U.S common stock: $14,276
2
Q
Week 1 Risk Return - Given the following portfolios:
Portfolio of Treasury Bills
Portfolio of U.S government Bonds
Portfolio of U.S common stock
What is can be said about the attributes of each?
A
Treasury Bills: No default risk and relatively stable prices.
U.S government Bonds: Prices fluctuate with interest rates to remain competitive (bond price down when interest rate up). Newly realeased bonds may have different coupon payments so the existing bonds adjust to remain competitive.
Portfolio of U.S common stock: Risk subject to interest rate changes and the volatile of the stocks.
The higher the risk, the higher the expected return required by investors.
3
Q
Week 1 Risk Return - r|p|?
A
The Expected Return from a portfolio of N securities, being the weighted average of expect returns from the single securities in the portfolio.
4
Q
Week 1 Risk Return - r|p| equation?
A
w|1| r|1| + w|2| r|2| + … + w|N| r|N|
= Σ w|i| r|i|
where w|i| is the weight of the security in the portfolio and will be the percentage (in decimal terms)
equally be 0.XX, where xx is the expected return.
5
Q
Week 1 Risk Return - What is the rate of return of a stock? (formula) - CHECK THIS
A
r = [ { p(t) - p(t - 1) } / p(t-1)] * 100
6
Q
Week 1 Risk Return - Aside from expected return, what are two possibly equivalent measures of risk?
A
Variance and Standard Deviation.
7
Q
Week 1 Risk Return - Variance Formula and interpretation?
A
σ² = 1/N [Σ (x|i| - μ)²]
The mean of the squared deviations from the mean.
It is a measure of volatility.
If 0, the portfolio is riskless.
8
Q
Week 1 Risk Return - When talking about the risk of a portfolio, what are we really talking about?
A
- Idiosyncratic Risk (Stock specific or unsystematic): The risk associated with each individual security.
Systematic Risk (Macro Risk): The degree to which the securities covary, being the covariance between securities.
9
Q
Week 1 Risk Return - Covariance In terms of the standard deviation and correlation coefficient of two stocks?
A
σ|12| = ρ|12| σ|1| σ|2|
σ|12|: the Covariance of the two securities.
σ|i|: the variance of security i.
ρ|12|: The correlation coefficient between security 1 and 2.
10
Q
Week 1 Risk Return - Given the covariance definition “ σ|12| = ρ|12| σ|1| σ|2| “, write the formula for risk (variance) of a portfolio.
A
σ|p|² =
Σ|i=1| Σ|j=1| w|i| w|j| σ|ij|
= Σ|i=1| Σ|j=1| w|i| w|j| ρ|ij| σ|i| σ|j|
σ|ij|: the Covariance of the two securities.
σ|i|: the variance of security i.
ρ|12|: The correlation coefficient between security 1 and 2.
11
Q
Week 1 Risk Return -What will the portfolio volatility of a two stock portfolio be?
A
BA 1.
σ|p|² =
Σ|i=1| Σ|j=1| w|i| w|j| σ|ij|
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| σ|12|
where σ|12| = ρ|12| σ|1| σ|2|
The following equation is therefore equivalent:
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| ρ|12| σ|1| σ|2|
12
Q
Week 1 Risk Return - Given the two security portfolio variance equation:
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| σ|12|,
What is the interpretation of each part?
A
w|1|²σ|1|²: Component due variance (idiosyncratic risk) of security 1.
w|2|²σ|2|²: Component due variance (idiosyncratic risk) of security 2.
2w|1| w|2| σ|12|: Component due to the covariance between security 1 and security 2 (systematic risk).
Each security contributes w|1| w|2| σ|12| worth of systematic risk.
13
Q
Week 2 Risk Return - Consider a portfolio of securities with expected return r|p| = 20% and standard deviation σ|p| = 50%. Suppose the composition of the portfolio is changed, such that the standard deviation reduces. What is this an example of?
A
Diversification.
14
Q
Week 2 Risk Return - What iii diversification with a portfolio?
A
To get at least the same return with lower risk, or lower risk and a lower return.
It is not diversification if the expected return falls though and the risk remains the same.
We need the expected return to stay the same (or improve) AND the portfolio risk to fall (So the standard deviation to fall.
15
Q
Week 2 Risk Return - Given the portfolio risk equation for two stocks:
σ|p|² = w|1|²σ|1|² + w|2|²σ|2|² + 2w|1| w|2| σ|12|,
What additions would be made if there were three stocks.
A
We would add
w|3|²σ|3|² + 2w|1| w|3| σ|23| + 2w|2| w|3| σ|23|
So the idiosyncratic risk associated with the additional stock and the systematic risk due to the covariance with the third stock with the other two stocks.
16
Q
Week 2 Risk Return - If you have calculated the portfolio variance of two stocks and want to calculate the standard deviation when adding a further stock, what would the process be?
A
You could start from scratch and calculate using the equation, or, given the knowledge of the first portfolio variance, use this to get the standard deviation and use the equation counting the portfolio as a solitary security.
17
Q
Week 2 Risk Return - When N securities are uncorrelated, what is the portfolio S.D?
A
σ|p| = [w|1|²σ|1|² + w|2|²σ|2|² + … + w|N|²σ|N|²]^1/2
SO the second part of the equation is removed (the systematic risk) leaving only the stock specific idiosyncratic risk.
18
Q
Week 2 Risk Return - How do we get to the risk pooling result in which variance is equal to 0 when N approaches infinity and what other axioms are required?
A
We assume stocks are uncorrelated (strong and unrealistic assumption) so
σ|p| = [w|1|²σ|1|² + w|2|²σ|2|² + … + w|N|²σ|N|²]^1/2
We then assume each share has the same variance and weighting, so w|I| become 1/N
The whole equation simplifies to:
(N * 1/N² σ²) ^1/2 =
(1/N σ²) ^1/2
As N approaches infinity, σ|p| approaches 0 (as this is what we were using the equation to find).
As more and more uncorrelated risks are pooled together, total risk is reduced.
19
Q
Week 2 Risk Return - Market Risk?
Graph?
A
The risk that cannot be eliminated through optimal diversifying the investment portfolio.
It is the risk driven by the economy as a whole.
See BA 2 for graph.
20
Q
Week 2 Risk Return - Total Risk?
A
Total Risk = Diversifiable risk + market risk.
It is the contribution of an individual security to the risk of a portfolio.
Diversifiable risk contributed to unique risk and can be eliminated through diversification.
Only market risk contributes towards risk of a well diversified portfolio.
21
Q
Week 2 Risk Return - What does risk pooling show?
A
That there is one type of risk that cannot be diversified away from, being market risk,
22
Q
Week 2 Risk Return - Beta (β)?
A
A measure of sensitivity of the stock, being how much the stock fluctuates given a change in the market (Purely Theoretical)
The market is made up of all stocks, so has a β=1 (this is an assumption)
Securities that move in the same direction but tend to amplify the movement of the market have β > 1.
Those that move in the same direction as the market but tend to reduce the movement have 0 < β < 1.
They will move up or down with the market.
Stocks that move opposite the market are very rare.
23
Q
Week 2 Risk Return - Beta (β)?
A
The systematic risk part.
The covariance of the asset with the market portfolio return divided by the variance of the market portfolio
A measure of sensitivity of the stock, being how much the stock fluctuates given a change in the market (Purely Theoretical)
The market is made up of all stocks, so has a β=1 (this is an assumption)
Securities that move in the same direction but tend to amplify the movement of the market have β > 1.
Those that move in the same direction as the market but tend to reduce the movement have 0 < β < 1.
They will move up or down with the market.
Stocks that move opposite the market are very rare.
24
Q
Week 2 Risk Return - How do we calculate β?
A
r|i| = α + β|i| r|m| + error|i|
r|m| : Return of market portfolio.
r|i| : Return on security
We use linear regression to calculate the slope of the line.
β|i| = σ|im| / σ|m|²
The beta is the covariance between stock and the market scaled by the variance of the market.
25
Week 2 Risk Return - What is a well diversified portfolio?
A portfolio that has low unique risk and mainly consists of market risk.
26
Week 2 Risk Return - Markowitz Portfolio Risk - Efficient Portfolios?
The combination of securities that create the OPTIMAL combination of expected returns and standard deviations.
Optimal means diversifying away specific risk.
On a graph showing risk and returns, these will be the points to the far left of the possible combination and then all the way to the greatest standard deviation in attainable.
The point will be dependent on the risk averseness/ love of the investor, but an point should be selected along the efficient frontier.
27
Week 2 Risk Return - See BA 3. What is this function representative of and when should it be used?
See BA 3.
28
Week 2 Risk Return - If the daily returns are distributed approximately by the normal distribution, what does this lead us to say?
The expected value and variance (or standard deviation) of a portfolio are the only measures an investor needs to consider.
This is because the normal distribution can be calculated using only these two, as shown in BA 3.
29
Week 2 Risk Return - When evaluating a two security portfolio, how would the variance and expected return vary with different weighting?
Only the idiosyncratic risk will be altered, being the first two additions in the equation.
The portfolio SD and r are functions of the amount invested in each company, when there is no perfect correlation (+ or -)
30
Function of meaning?
Something (such as a quality or measurement) that is related to and changes with (something else) Height is a function of age in children. It increases as their age increases.
So part of the equation that make sure the y.
31
Week 2 Risk Return - Explain the graph in BA 4.
A graph showing the resulting portfolio r and σ given different combination of w in a two stock portfolio.
The blue line represents that risk reward payoff.
32
Week 2 Risk Return - Efficient Portfolios?
Lie on the efficient frontier and offer the highest expected return for a given level of risk, or the lowest level of risk for a given expected return.
33
Week 2 Risk Return - r|f|?
The investors can borrow at the risk free rate, r|f|.
34
Week 2 Risk Return - With the introduction of lending money, how would this effect the S.D and expected returns ?
The expected returns would just the proportion of money in each tool multiplied by the expected return.
When lending, the S.D is 0. Therefore, the S.D of a combination of a portfolio and lending would just be the weighting of S that is in the portfolio multiplied by the S.D of the portfolio.
35
Week 2 Risk Return - With the introduction of borrowing money, how would this effect the S.D and expected returns ?
Expected returns: The amount of wealth compared to initial wealth due to borrowing * expected return of S minus the amount of wealth borrowed * interest rate
S.D: The amount of wealth compared to initial wealth due to borrowing * Standard deviation of S minus the amount of wealth borrowed * interest rate
36
Week 2 Risk Return - Looking at BA 5, Explain the graph.
BA 5.
37
Week 2 Risk Return - If you have a graph of efficient portfolios, and know the risk free rate r|f|, how would you add the borrowing and lending line?
Start at r|f| and draw the steepest line that touches the efficient frontier.
38
Week 2 Risk Return - Sharpe Ratio?
The ratio of risk premium to standard deviation:
Sharpe Ratio =
Risk Premium/ S.D =
(r - r|f|) / σ
39
Week 2 Risk Return - What are the shortcomings of the Markowitz Approach?
Zero taxes and transaction costs false.
Fractional securities are not available.
Credit limits constrain investors
Investors seem to have an influence on the market (large institutional investors)
Correlations between assets are never stable and fixed.
Past performance is not a good indicator of future performance.
40
Week 3 Asset Pricing - Why do Treasury Bills have a Beta value of 0?
Return is flex, so they are unaffected by the market, giving them a Beta value of 0.
41
Week 3 Asset Pricing - How do we get from Markowitz to the CAPM model?
Previously we looked at a market portfolio with Beta = 1 and treasury bills beta = 0/
What about when the Beta of the portfolio is not 1?
42
Week 3 Asset Pricing - What underpinning of the CAPM model?
In a Competitive Market, the expected risk premium varies in direct proportion to beta.
The risk premium is r|p| - r|f|, as at the risk free rate, the risk is 0.
This leads all investments to lie on the SECURITY MARKET LINE, being the line that is drawn from the r|f| on the y axis to the market portfolio r|m| and associated beta = 1.
e.g. the expected risk premium of an investment with beta of .4, will have .4 * the expected market risk premium.
43
Week 3 Asset Pricing - How do we get from Markowitz to the CAPM model?
Previously we looked at a market portfolio with Beta = 1 and treasury bills beta = 0.
What about when the Beta of the portfolio is not 1?
44
Week 3 Asset Pricing - What underpinning of the CAPM model?
In a Competitive Market, the expected risk premium varies in direct proportion to beta.
The risk premium is r|p| - r|f|, as at the risk free rate, the risk is 0.
This leads all investments to lie on the SECURITY MARKET LINE, being the line that is drawn from the r|f| on the y axis to the market portfolio r|m| and associated beta = 1.
e.g. the expected risk premium of an investment with beta of .4, will have .4 * the expected market risk premium.
CAPM assumed that investors are only concerned about the expected return and the risk of an investment strategy.
45
Week 3 Asset Pricing - CAPM - Expected risk premium on stock formula?
Expected risk premium on stock =
beta x expected risk premium on market
r - r|f| = β(r|m| - r|f|)
46
Week 3 Asset Pricing - What are the 5 basic principle of the CAPM model?
1. Investors like high expected return and low standard deviation. Common stock
portfolios that offer the highest expected return for a given standard deviation are
known as efficient portfolios.
2. If the investor can lend or borrow at the risk-free rate of interest, one efficient
portfolio is better than all the others: the portfolio that offers the highest ratio of risk
premium to standard deviation.
A risk-averse investor will put part of his money in this efficient portfolio and part in the risk-free asset.
A risk-tolerant investor may put all her money in this portfolio or she may borrow
and put in even more.
3. The composition of this best efficient portfolio depends on the investor’s assessments of expected returns, standard deviations, and correlations. But suppose everybody has the same information and the same assessments. If there is no superior information, each investor should hold the same portfolio as everybody else; in other words,
everyone should hold the market portfolio.
Now let us go back to the risk of individual stocks:
4. Do not look at the risk of a stock in isolation but at its contribution to portfolio risk.
This contribution depends on the stock’s sensitivity to changes in the value of the
portfolio.
5. A stock’s sensitivity to changes in the value of the market portfolio is known as beta.
Beta, therefore, measures the marginal contribution of a stock to the risk of the market
portfolio.
Now if everyone holds the market portfolio, and if beta measures each security’s contribution to the market portfolio risk, then it is no surprise that the risk
47
Week 3 Asset Pricing - CAPM - What if a stock does not lie on the security market line.
If a stock is below the line, the investor can attain higher return for that level of risk.
The price of A will have to fall until the expected return matches what you could get elsewhere.
Nobody will hold a stock with a lower return than β(r|m| - r|f|)
As no stocks can lie below the line, it must equally be the case that none lie above the line, as the market line is the average of all the securities in the market portfolio.
48
Week 3 Asset Pricing - What would the expected return be of a portfolio made up of a risk free asset and the market portfolio?
Show how we get the final equation using the expected return.
= w|m| r|m| + (1- w|f|) r|f|
Rearranging:
w|m| = (r|p| - r|f|) /
(r|m| - r|f|)
So the weight dedicated the market portfolio is the premium of the selected portfolio divided by the market premium.
49
Week 3 Asset Pricing - CAPM meaning?
Capital Asset Pricing Model.
An approach to establishing the reward for baring the systematic risk of a portfolio.
50
Week 3 Asset Pricing - Week 3 Asset Pricing - What would the S.D be of a portfolio made up of a risk free asset and the market portfolio?
What can this be simplified to?
σ|p| = √(w|m| x σ|m|)²
= w|m| x σ|m|
As the risk free asset has no standard deviation.
We then attain
w|m| = σ|p| / σ|m|
To find the proportion of investment in the market portfolio.
51
Week 3 Asset Pricing - Derive the Capital Market Line Equation.
From the standard deviation equation we found attained:
w|m| = σ|p| / σ|m|
From the expected return equation we attained:
w|m| = (r|p| - r|f|) /
(r|m| - r|f|)
We now make the above to equal and write in terms of r|p|:
σ|p| / σ|m| = (r|p| - r|f|) /
(r|m| - r|f|)
r|p| = r|f|) +σ|p| / σ|m| (r|m| - r|f|)
See BA 6 for a clearer representation.
52
Week 3 Asset Pricing - Explain the Capital Market Line Equation:
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] σ|p|
What will the graph be?
The slope of the line [(r|m| - r|f|)/ σ|m|] shows the rate at which risk σ|p| and return r|p| can be traded against each other on a portfolio as a combination fo the market portfolio and the risk free asset.
It shows how the return of a portfolio increases above the risk free amount and the assorted risk to attain the extra return.
See BA 7 for the graph.
53
Week 3 Asset Pricing - Given that portfolios on the capital market line are efficient, what can be said about the combinations and the correlation?
Portfolios on the capital market line are efficient portfolios.
This is because they are obtained as a combination of the market portfolio and the risk free asset: therefore, they are perfectly positively correlated with the market portfolio.
Formally, this means
that the correlation coefficient between a portfolio on the capital market line and the market portfolio is equal to ρ|pm| = 1.
54
Week 3 Asset Pricing - How do we derive the equation for a security market line, given that the capital market line is
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] σ|p|
We know that ρ|pm| = 1 for the capital market line and the portfolio as the portfolio is made up of a proportion of the market portfolio.
In general, it can be shown that:
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] σ|p|ρ|pm|
since σ|pm| = ρ|pm| σ|p|σ|m|,
we rewrite the CAPM line to be:
r|p| = r|f| +[(r|m| - r|f|)/ σ|m|] [σ|pm|/
σ|m|]
By analogy, a security:
r|i| = r|f| +[(r|m| - r|f|)/ σ|m|] [σ|im|/
σ|m|]
The β for security I is:
β|i| = σ|im|/
σ|m|²
{from OLS regression]
The Security Market Line is therefore:
r|i| = r|f| + β|i|(r|m| - r|f|)
55
Week 3 Asset Pricing - How does the graph for CAPM change when we swap from the capital market line to the security market line?
See BA 8.
56
Week 3 Asset Pricing - Interpret the security market line equation:
r|i| = r|f| + β|i|(r|m| - r|f|)
r|i| = r|f| + β|i|(r|m| - r|f|)
The expected risk premium (r|I| - r|f|) varies in direct proportion to the security beta β|i|. β|i| measures how sensitive security I is to market movements.
Therefore, the market only rewards market risk, because unique risk can be diversified away.
57
Week 3 Asset Pricing - ABT?
The arbitrage pricing theory.
58
Week 3 Asset Pricing - What does CAPM attempt to answer?
How returns on assets are determined.
You are required for bearing the systematic risk of the asset.
59
Week 3 Asset Pricing - What does the APT assume?
Each stock's return depends on two components: some macroeconomic composes "factors", and a "noise" component.
Return = a + b|1|(r|factor1|) + b|2|(r|factor2|) + ...+ ε
Where:
r|factor1| is the return on the first factor, etc. b1, b2 etc measure the securities sensitivity to each factor.
ε: the noise.
The APT does not say what the factors are
60
Week 3 Asset Pricing - APT - What could some examples of the factors and what are they?
Market portfolios
Market capitalisation
GDP
Interest Rates
(anything macro economic)
The factors must be common factors across all securities, so they move the entire market, not just idiosyncratic (so they are only looking at systematic sources of risk).
61
Week 3 Asset Pricing - Why could unique risk be ignored when buying a stock?
Because the risk can be diversified away.
62
Week 3 Asset Pricing - What is a key difference between CAPM and the APT?
CAPM and the use of Betas of a security or portfolio simply shows how much the portfolio or stock moves relative to the market.
APT sheds some light on what these factors could be.
63
Week 3 Asset Pricing - APT - According to the APT, what does the risk premium (r - r|f|) depend on?
1. The expected risk premium associated with each factor (r|factor1| - r|f|), (r|factor2| - r|f|) etc.
2. The security's sensticitiy to each factor b1, b2 etc.
64
Week 3 Asset Pricing - APT - What is the formula for the expected risk premium on a security?
r - r|f| = b|1|(r|factor1| - r|f|) + b|2|(r|factor2| - r|f|) + ...
65
Week 3 Asset Pricing - APT -What does the expected risk premium formula tell us:
r - r|f| = b|1|(r|factor1| - r|f|) + b|2|(r|factor2| - r|f|) + ...
1. If b1 = b2 = 0, the risk premium (r -r|f|) = 0. This implies that a diversified portfolio contracted to have zero sensitivity to each macroeconomic factor is risk free and is priced to offer zero risk premium. If this were the case but r - r|f| > 0, a risk free arbitrage profit could be made by borrowing at rate r:f: to buy the asset that offer a rate r. If r - r|f| < 0, you could sell the asset offering rate r and make a risk free profit by lending at rate r|f|.
2. A portfolio constructed to be exposed to only factor (factor 2, 3 ... =0) offers a risk premium that varies proportionally with the portfolio's sensitivity to that factor (b1). i.e. if you have portfolios A and B, with portfolio A being twice as sensitive to factor 1, then must portfolio A must offer twice the risk premium of portfolio B.
66
Week 3 Asset Pricing - How could we compare CAPM and APT?
Both stress that expected returns only depend upon economy wide market risk and should not be influenced by unique risk.
CAPM relies on the notion of market portfolio, and it may not always be possible to measure this. APT does not require this.
CAPM condenses all macroeconomic factors into one factor (the expected returns on the market portfolio). APT does not tell us the underlying factors.
67
Week 3 Asset Pricing - What are the a priori guidelines to the characteristics required of potential factors for the APT?
1. Their impact on asset prices manifests in their unexpected movements
2. They should represent un-diversifiable influences (these are, clearly, more likely to be macroeconomic rather than firm-specific in nature)
3. Timely and accurate information on these variables is required
4. The relationship should be theoretically justifiable on economic
grounds
68
Week 3 Asset Pricing - How are APT factor specific betas found?
As with the CAPM, the factor specific betas are found via a linear regression of historical security returns on the factor in question.
69
Week 3 Asset Pricing - What factors for APT were identified by Chen, Roll and Ross in the Journal of Business (1986) to be significant in explaining security returns?
1. Surprises in inflation;
2. Surprises in GNP as indicated by an industrial production index;
3. Surprises in investor confidence due to changes in default premium in
corporate bonds;
4. Surprise shifts in the yield curve.
Note : surpise = (expectation - realisation)
70
Week 3 Asset Pricing - APT - Why must unexpected movements be a characteristic of potential factors?
The price at time t of a stock reflects all the available information.
We factor in surprises (when the outcome goes against the consensus).
Say we have a consensus that the interest rate will increase by .5%. If in fact it increases by 0.75%, the model will need to be updated to reflect of difference, being 0.25%, which is the news.
The difference is the noise and the aim of a model is to minimise the noise and maximise what is explained by a model≥
71
Week 3 Asset Pricing - APT - What can we do to address macro-economic factors that are reported at low frequency and often with significant estimation errors?
We can use indices, spot or futures market prices as a reflection of the underlying factor. Multiple different variables can be attributed to one macro economic factor.
72
Week 3 Asset Pricing - Other than factor analysis, what other indices might be used in place of macro-economic factors?
1. Short-term interest rates;
2. The difference in long-term and short-term interest rates;
3. A diversified stock index such as the SP 500 or NYSE Composite;
4. Oil prices
5. Gold or other precious metal prices
6. Currency exchange rates
73
Week 4 Capital Structure: Terms and Taxes - Capital Structure?
A company's mix of debt and equity financing. Refers to the decision about how to raise funds to conduct the business, specifically the decision between debt (borrowing) and equity (bringing in new partners).
Retained earnings are a first choice to raise funds and do not tend to be included.
74
Week 4 Capital Structure: Terms and Taxes - What are the three main ways to raise funds?
1. Keep the profits in the firm rather than paying back to the owners. (AKA Plowback or retained earning)
2. Borrow the cash.
3. Bring in new partners (sources of cash)
75
Week 4 Capital Structure: Terms and Taxes - Debt implications?
Debt = Principal + accrued interest.
Debts are a cost to the firm, not the owners, and the company has a legal obligation to pay the debts. Failure to do so enables to the lender to seize assets of the company or force the company into liquidation.
Lenders do not own the company
76
Week 4 Capital Structure: Terms and Taxes - How can debt be incurred by a company?
The main two ways are:
1. loans from a bank/ private investor.
2. Issuing bonds, being a debt security that is (generally) traded on the market.
77
Week 4 Capital Structure: Terms and Taxes - Bond issuing information?
The issue of bonds by a firm is known as a primary issue, and they are sold on the primary market.
The initial creditor can sell on the bond to someone else without the company's approval: these are known as secondary transactions, and take place in the secondary market.
78
Week 4 Capital Structure: Terms and Taxes - What is the effect of share buybacks or repurchases?
A company can purchase its shares back from the secondary market. The shares do not raise money but instead just distribute money back to the owners.
79
Week 4 Capital Structure: Terms and Taxes - Key differences between debt and equity?
Debt is a legally enforceable promise to pay the providers of capital. Lenders are not owners of the company. Payments generally consist of periodic interests followed by the repayment of the principal.
Equity promises only part ownership of the company, no specific cash claims are legally enforceable. Payments to shareholders generally consist of periodic dividends (although the company is not legally required to pay dividends) and any liquidation value of the company if it ceases to operate.
80
Week 4 Capital Structure: Terms and Taxes - Firm Market Value?
Value = Debt + Equity
V = D + E
V: The firms market value
D: The market value of the firm's outstanding debt.
E:The market value of the
81
Week 4 Capital Structure: Terms and Taxes - Financial Leverage?
FE = Debt / Equity
It is the proportion of debt relative to the equity of the company. The higher this number, the more risky a firm is.
82
Week 4 Capital Structure: Terms and Taxes - Financial Deficit?
The difference between cash that a company needs and the cash that the company generates (though plowback)
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Week 4 Capital Structure: Terms and Taxes - Payout Policy?
The decision by a firm as to how much of the profits should be retained and how much should be payed to the shareholders.
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Week 4 Capital Structure: Terms and Taxes - How are taxes involved in the capital structure decision of a company?
In most countries, the tax system creates distortions in the capital structure decision, being the allocation of debt and equity. The capital structure thus depends on the tax system, not just the private-sector fundamentals.
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Week 4 Capital Structure: Terms and Taxes - How does the tax system effect equity and debt?
Equity: Income tax is levied on corporate and personal income. Income is taxed at the company level and to the shareholders when they receive income as dividends.
So dividends get taxed twice.
Debt: No double taxation generally exists, only the lender gets taxed, being the interest.
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Week 4 Capital Structure: Terms and Taxes - In summary, interlink the concepts of payout policy, debt, equity, financial deficit and capital structure.
A firm decided how much is will return to shareholders or plowback, which related to payout policy.
Plowback does not generally cover cash needs for a firm. The difference between what cash the firm needs and what the firm raises internally is the financial deficit.
The firm must decide what proportion of the financial deficit to fund though borrowing and though issuing equity. the mixture of these issues called the capital structure.
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Week 4 Capital Structure: Terms and Taxes - EXTRA
EXTRA
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Week 4 Capital Structure: Terms and Taxes - EXTRA
EXTRA
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Week 5 Capital Structure: When Capital Structure Does Not Matter - What does MM stand for?
Modigliani and Miller.
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Week 4 Capital Structure: Terms and Taxes - Simple MM intuition?
A firms value is determined by its real assets, not by its capital structure.
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Week 4 Capital Structure: Terms and Taxes - MM Propostion 1?
Company value is dictated by the company's assets. The capital structure simply alters the risk.In a world with perfect capital markets, no risk of default and no informational issues, capital structure does not matter, so the market value of a firm is independent of its capital structure and is determined by real assets when the firm's investment decisions are taken as a given.
Specifically, a firm cannot change the total value of its securities just by splitting its cash flows into different streams (debt or equity streams). Whether all financing is attained through equity, or just 50%, the cost of financing will be exactly the same.
Thus, we are able to completely separate the investment and financing decisions.
Although in practice capital structure does matter, we must understand understand under what conditions the the MM theory holds to fully understand what capital structure is better than another given specific market imperfections.
It relies upon the assumption that by maximising the Total value of the firm, financial managers maximise the wealth of the shareholders.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - What is financial leverage?
When equity of a company is leveraged though debt, increasing its value.
It is also known as gearing.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - How could we show the second key part of MM one, that when maximising total value of the firm, shareholder wealth is also maximised?
See BA 9.
In general, a policy that maximises the market value of a firm also maximises the wealth of shareholders:
Max(W) = Mac(V)
THIS RELIES ON the assumptions that:
- Firms can ignore payout policy (i.e. dividend policy)
- The value of the existing debt stock is not affected.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Show using the sample of an unleveraged and leveraged firm that the expected payoffs of two equal investments would amount to equal payoffs.
See BA 10.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Value Additivity?
If we have two streams of cash flow, A and B, then the present value of A + B is equal to the present value of A plus the present value of B.
We are not combining assets but splitting them up.
With perfect capital markets, combining or splitting will not affect values as long as they do not affect an investor's choice.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Law of conservation of value?
How is this applicable?
The value of an asset is preserved regardless of the nature of the claims against it.
This can be used to show how the value of a leveraged firm and unleveraged firm are equal given the MM assumption (perfect capital markets).
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Why is it the case that individuals do not care about a firm's capital structure they are investing in?
With perfect capital markets where companies and individuals can borrow and lend at the same risk free rate, individuals can undo the effect of any changes in the firm's capital structure.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Show that V|l| = V|u| by investing in debt and a company.
See BA 1.
First invest in a leveraged company, paying the interest.
Then an unleveraged, and borrowing an amount to account for the interest payment.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - What are the restrictive consumption of the MM proposition 1?
No Personal or Corporate Taxes (or at least not distortions, so a tax system that taxes debt and equity equally)
Perfect Capital Market: People can borrow and lend at the same rate that companies do.
No Informational issues: So individuals do not infer anything about a firms capital structure.
No costs of financial distress: So no costs when a company is in poor health.
No Effects On Management: No issues such as leverage affecting values of executive stock options, which in turn would affect executive incentives. (or if a company is doing bad, effort going down etc)
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Week 5 Capital Structure: When Capital Structure Does Not Matter - MM Proposition 2?
As a firm takes on more debt, the equity becomes riskier and must be priced to earn a higher return. This is balanced out exactly by the fact that more of the capital structure is (cheaper) debt.
The expected return on equity r|E| of a levered firm increases in proportion to the debt-equity ratio D /E , and the rate of increase depends on (rA − rD).
Remember that D / E will increase at an increases rate with rises in D (or equally, falls in equity)
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Expected Return on Assets Equation?
r|A| = expected operating income / market value of all securities.
So it is the yearly expected income that will be generated by the assets divided by the value of all securities.
This is constant according to MM proposition 1, as the MARKET VALUE OF ALL SECURITIES IS CONSTANT.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - What is the return on assets equation?
What could this formula be turned into.
r|A| = (r|D| * D / D+E ) + (r|E| * E / D+E )
Expected return on assets = proportion in debt x expected return on debt + the proportion of equity x expected return on equity.
w|D| = D / (D + E)
w|E| = E / (D + E)
This is the expected return on a portfolio of all the firms securities.
We can change this to be in terms of the return on equity:
r|E| = r|A| + D/E(r|A| - r|D|)
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Week 5 Capital Structure: When Capital Structure Does Not Matter - Given the return of debt calculation previously calculated:
r|E| = r|A| + D/E(r|A| - r|D|)
How can we explain this and link to MM 2?
D\E is the leverage.
When there is no debt, r|E| = r|A|
Then the firm is leverered, they require a premium of D/E(r|A| - r|D|) to compensate them for the extra risk.
```
MM 2 states that as a firm takes on more debt, the
equity becomes riskier and so must be priced to earn a higher return. But this is balanced out exactly by the fact that more of the capital
structure is (cheaper) debt.
```
More capital structure is composed of cheaper debt.
If the overall r|A| is determined by the weighted average of the return on debt and return on equity. r|E| increases with risk (which will lead to r|D| increasing), this is offset by he fact that the weight the debt is increasing (which has a lower return), which moves in the opposite direction, keeping r|A| constant.
r|E| increases, and w|E| falls, given that w|D| rises.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - MM’s proposition 1 says that financial leverage has no effect on shareholders’ wealth.
Proposition 2 says that the rate of return they can expect to receive on their shares increases as the firm’s debt–equity ratio increases. How can shareholders be indifferent to increased
leverage when it increases expected return?
Any increase in expected
| return is exactly offset by an increase in risk and therefore in shareholders’ required rate of return.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - How does leverage (capital structure) relate to CAMP?
MM proposition 1: financial leverage has no effect on shareholders’ expected wealth (since it does not change the market value of the
firm).
MM proposition 2: the rate of return on equity rE increases as the firm’s leverage increases.
An increase in rE is exactly offset by an increase in risk, and therefore in shareholders’ required rate of return. Leverage can then be seen as a way to move outward the risk-return trade-off. In this
sense, MM is very similar to the CAPM.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - How would one find the r|A| in a question?
r|a| is consistent under MM and will equal r|e| when w|e| = 100.
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Week 5 Capital Structure: When Capital Structure Does Not Matter - What would a firm's asset Beta be?
Beta's measure the return of a company (dependent on its risk).
The beta of a firm's asset is equal to the beta of a portfolio of the firm's debt and its equity.
The beta of this hypothetical portfolio is the weighted average of the debt and equity ratios (the weight of each)
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Week 5 Capital Structure: When Capital Structure Does Not Matter - β|A| equation?
What about β|E|?
β|portfolio| = β|A|
= β|D|*D/(D + E) + β|E|*E/(D + E)
β|E| = β|A| + D/E(β|A| - β|D|)
Where β|E| is the r|E|
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Week 5 Capital Structure: When Capital Structure Does Not Matter - EXTRA
EXTRA
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Week 5 Capital Structure: When Capital Structure Does Not Matter - EXTRA
EXTRA
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Week 6 Capital Structure: When Capital Structure Does Matter - Are interest payments a cost to the firm? ...expand on the implications for tax
Yes. As lenders are not the owners of the firm, interest rates are considered a cost and are therefore tax-deductible.
This means debt financing is tax deductible as the cost can be taken away from corporation tax.
This is known as the tax shield for debt.
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Week 6 Capital Structure: When Capital Structure Does Matter - Tax Shield?
Relies on the fact that debt financing (interest) is tax deductible.
It is the amount saved due to debt financing.
Tax Shield: Interest x Corporate Tax Rate
: r|D| x D x T|c|
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Week 6 Capital Structure: When Capital Structure Does Matter - When assessing tax shields, what are the three assumptions we make?
```
Assumption 1 (D constant): The company’s debt D is fixed and permanent (that
is, the company commits to refinance its present obligations when
they mature, and to keep rolling over its debt obligations indefinitely).
```
Assumption 2 (T|c| constant): The corporate tax rate T|c| is (reasonably) stable over time: therefore, T|c| can be treated as constant.
Assumption 3 (r|D| = interest rate payment amount): The risk on the tax shields is the same as the risk of the interest payments that generate them. This assumption is equivalent to saying that capital markets are perfect. The interest rate that is paid on the debt is the same as the interest rate used to discount.
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Week 6 Capital Structure: When Capital Structure Does Matter - PV of tax shield?
PV(tax shield): tax shield/ discount rate = tax shield/ expected return
= [(r|D| x D) x T|c|] /r|D|
= D x T|c|
So the PV(tax shield) is independent of expected return on debt r|D|
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Week 6 Capital Structure: When Capital Structure Does Matter - How can equity earners receive incomes?
(3)
1. Dividends from profits.
2. Retained earnings increasing firm value.
3. Share buybacks increases the value of the remaining shares on the market.
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Week 6 Capital Structure: When Capital Structure Does Matter - Why would companies care about double taxation (for equity)?
Maximising the wealth of investors is the same as maximising the value of the company.
If investors are taxed more, they receive less from a firm and therefore the risk to reward payoff if altered, leading to the company being less valued than if investors were only being taxed once.
The firms new aim is to minimise all taxes, meaning those of the firm, bondholders and shareholders, thereby maximising after-tax income.
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Week 6 Capital Structure: When Capital Structure Does Matter - How do we include the effect of personal taxes (notation)?
T|p|: personal tax rate on interest (debt income)
T|pE|: The effective tax rate on equity income (dividends and capital gains).
T|c|: Corporate tax rate.
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Week 6 Capital Structure: When Capital Structure Does Matter - In general, why is
T|p| < T|pE|?
(2)
1. Statutory Rates (rates fixed by law) applicable to equity income may be lower.
2. Capital gains are not taxed until the shares are sold, so there is a tax deferral advantage, lowering the present value of the tax.
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Week 6 Capital Structure: When Capital Structure Does Matter - What would the after tax income of £1 be for:
1. A debt investor
2. An equity investor
1. Debt investor:
£(1-T|p|)
Remember, these interest payments are tax deductible from corporation tax, so that tax is not included.
2. Equity investor:
£(1-T|c|)(1-T|pE|)
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Week 6 Capital Structure: When Capital Structure Does Matter - Relative tax advantage of debt equation and explanation?
RA= (1-T|p|) / [(1-T|c|)(1-T|pE|)]
So this is the post tax income of debt investors compared to the income of equity investors as a ratio.
When RA goes up, the more of an advantage there is to debt financing rather than equity financing.
RA = 1 when there is no advantage.
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Week 6 Capital Structure: When Capital Structure Does Matter - Given the RA of debt formula:
(1-T|p|) / [(1-T|c|)(1-T|pE|)]
What is the outcome when:
1. T|p| = T|pE|
2. RA = 1
See BA 13.
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Week 6 Capital Structure: When Capital Structure Does Matter - What was the idea put forward by Merton Miller?
Question: Is there an economy-wide debt-equity ratio (macro)?
People de factor have different tax rates.
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Week 6 Capital Structure: When Capital Structure Does Matter - What are the assumptions used by Merton Miller?
1. T|pE| = 0
2. All companies have the same marginal T|c|
3. Different investors have different T|p|, ranging on both sides of T|p|:
T|pL| < T|c| < T|pH|
With L and H being Low and High respectively.
124
Week 6 Capital Structure: When Capital Structure Does Matter - Given the Merton Miller assumptions, when is debt and when is equity cheaper to sell?
What are the implications?
1. T|pE| = 0
2. All companies have the same marginal T|c|
3. Different investors have different T|p|, ranging on both sides of T|p|:
When T|p| < T|c|, It is cheaper to sell debt.
When T|c| < T|p|, it is cheaper to sell equity.
The Relative Advantage is simplified to
(1-T|p|) / (1-T|c|)
The economy wide capital structure is then equal to the relative wealth of the two types of investors. There is no optimal debt-equity ratio for a single firm as it depends on the specific investors each firm has to deal with, it is only for the economy as a whole.
125
Week 6 Capital Structure: When Capital Structure Does Matter - What is the value of a firm analytical formula given the tradeoff between the tax shield and debt-equity ratio?
Value of Firm = Value if all-equity financed + PV(tax shield) - PV (costs of financial distress)
The last two are due to the tradeoff that the more a firm is leveraged, the more problems are exacerbated should it enter financial distress.
126
Week 6 Capital Structure: When Capital Structure Does Matter - Trade-off theory?
A theoretical optimum reached when the present value of tax savings due to further borrowing is just offset by increases in the present value of costs of distress.
Remember that V = Value if all equity financed + PV(Tax Shield) - PV (Costs of financial distress)
The costs of financial distress are not necessarily going to happen, but it is an expectation.
Costs of distress increase at an increasing rate value of a firm increases at a decreasing rate. We find when the marginal unit of each is equal.
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Week 6 Capital Structure: When Capital Structure Does Matter - Graph for Trade-off Theory of capital structure?
BA 14.
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Week 6 Capital Structure: When Capital Structure Does Matter - How can trade-off theory be different for different firms?
The optimal debt ratio will be different for different companies.a
Companies will have a different change of incurring financial distress.
For instance, a start-up may have a higher probability of financial distress, so the less debt can be taken on.
Companies with a large number of tangible assets (higher liquidity) and plenty of taxable income to shield should aim at relatively high debt rations.
The chance of financial distress will fall as businesses get less risky.
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Week 6 Capital Structure: When Capital Structure Does Matter - Aside from maximising value, what else may effect the debt-equity tradeoff?
Asymmetric information.
Manager taking the decision have superior information about the firm's health condition and might reveal this information through their debt-equity choice.
A firm that believes their stock is under valued will favour debts. Issuing shares at the current price would be to financially beneficial to investors, not to the company that is showing it is valued at this level or lower.
If a firm that believes the stock is overvalued issues shares at the current price, the market instantly assumes that the shares are overvalued, so investors will stop investing. So the firm may in fact issue bonds to avoid the market responding negatively.
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Week 6 Capital Structure: When Capital Structure Does Matter - What is the result of asymmetric information?
+ 2 remarks?
Asymmetric Information favours debt over equity. If managers are better informed than investors, then any company that can borrow will do so rather than issuing new equity.
Remark 1: It does not rule out issuing equity, as there are other forces outside of capital structure.
Remark 2: Asymetric information and costs of financial distress imply that issue of new debt may affect the price of outstanding shares.
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Week 6 Capital Structure: When Capital Structure Does Matter - Pecking order theory?
A theory on how firms raise funds.
Firms prefer internal finance (retained earnings)
Target levels of dividends are selected and firm stick to this as much as possible. They have STICKY POLICIES.
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Week 6 Capital Structure: When Capital Structure Does Matter - How do intangible and tangible assets effect the debt to equity ratio?
Natural fluctuations in year to year cash flow can lead to deficits of cash. One solution would be to change the debt to equity amount and take on more of either.
Firms prefer to finance internally though so selling assets to cover a shortfall is preferable.
Intangible assets are harder to liquidate, which provides more of an incentive to take on debt.
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Week 6 Pecking Order Theory - Zeidan et al (2018) Paper - What does the paper address?
Looking at SME in Brazil and studies the sources of capital ( D/E greater and less than 50%.
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Week 6 Pecking Order Theory - Zeidan et al (2018) Paper - What are the findings of the paper?
Companies prefer retained earnings over external sources of financing and that the preferences do not change with D/E ratios.
They conclude that pecking order theory holds.
1) Retained Earnings
2) Debt
3) Equity
Debt is still preferred over equity even with high D/E ratios.
They prefer to keep control of the company, and debt owners do not attain control of a company.
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Week 6 Pecking Order Theory - Zeidan et al (2018) Paper - Econometric methodology?
Propensity Score Matching algorithm (PSM)
Their conjecture was that firms with low D/E ratio should leverage more and those with high D/E should deleverage.
