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business
theory of corporate finance

Questions and Answers of Theory Of Corporate Finance

How do shares disappear from the stock exchange?
What are the institutional mechanisms by which funds disappear from the public financial markets back into the pockets of investors?
What are the main mechanisms by which money flows from investors into firms?
What should happen if the holdings of an open-end fund are worth much more than what the shares of the fund are trading for? What should happen in a closed-end fund?
Describe some alternatives to trading on the main stock exchanges.
What is a specialist? What is a market maker? When trading, what advantage do the two have over you?
How does a crossing system differ from an electronic exchange?
Is your rate of return higher if you short a stock in the perfect world or in the real world?Why?
How does a prime broker differ from a retail broker?
What are the two main functions of brokerage firms?
What is the market beta of the market?
How do you graph a “market beta”? What should be on the x-axis, and what should be on the y-axis?What is an individual data point?
Is it possible for an investment to have a positive average rate of return, but still lose you every penny?
Is the average individual stock safer or riskier than the stock market?
Rank the following asset categories in terms of risk and reward: cash(money market), long-term bonds, the stock market, and a typical individual stock.
What is the annualized holding rate of return and the average rate of return for each of the following?(a) An asset that returns 5% each year.(b) An asset that returns 0% and 10% in alternate
What can you see in a compound return graph that is difficult to see in the time-series graph?
What can you see in a histogramthat is more difficult to see in the timeseries graph?
What can you see in a time-series graph that is lost in a histogram?
Assume that the correct future cash flow is$100 and the correct discount rate is 10%.Consider the value effect of a 5% error in cash flows and the effect of a 5% error in discount rates.(a) Graph the
Under risk neutrality, a factory can be worth$500,000 or $1,000,000 in 2 years, depending on product demand, each with equal probability.The appropriate cost of capital is 6% per year. The factory
Debt is usually safer than equity. Does the risk of the rate of return on equity go up if the firm takes on more debt, provided the debt is low enough to remain risk free? Illustrate with an example
A new project has the following success probabilities:Failure Success Buyout Prob 10% 85% 5%Payoff (in millions) $50 $200 $400 Assume risk neutrality. If a $100 bond collateralized by this project
Assume that the probability that the Patriots will win the Superbowl is 55%. A souvenir shop outside the stadium will earn net profits of $1.5 million if the Patriots win and $1.0 million if they
A project costs $19,000 and promises the following cash flows:Year 1 2 3 Cash Flows $12,500 $6,000 $3,000 The appropriate discount rate is 15% per annum. Should you invest in this project?
A bond promises to pay $12,000 and costs$10,000. The promised discount on equivalent bonds is 25% per annum. Is this bond a good deal?
How is a credit swap like an insurance contract?Who is the insurer in a credit swap?Why would anyone want to buy such insurance?
An IBM bond promising to pay $100,000 costs$90,090. Time-equivalent Treasuries offer 8%.(a) Setting aside the risk neutrality and perfect markets assumption for this question only, what can you say
What are the main bond rating agencies and categories? Roughly, what are the 10-year default rate differences between them?
Using information from a current newspaper or the WWW, what is the annualized yield on corporate bonds (high-quality, mediumquality, high-yield) today?
Return to the example on page 146, but assume that the probability of receiving full payment of $210 in 1 year is only 95%, the probability of receiving $100 is 4%, and the probability of receiving
Go to the Vanguard website. Look at funds by asset class, and answer this question for different bond fund durations.(a) What is the current yield-to-maturity of a taxable Vanguard bond fund invested
A Disney bond promises an investment rate of return of 7%. Time-equivalent Treasuries offer 7%. Is the Disney bond necessarily a bad investment? Explain.
An L.A. Lakers bond promises an investment rate of return of 9%. Time-equivalent Treasuries offer 6%. Is this necessarily a good investment? Explain.
A bond will pay off $100 with probability 99%and will pay off nothing with probability 1%.The equivalent risk-free rate of return is 5%.What is an appropriate promised yield on this bond?
Now assume that the financial instrument from Q6.33 costs $100.(a) What is its expected rate of return?(b) If the prevailing interest rate on timeequivalent Treasuries is 10%, and if financial
A financial instrument will pay off as follows:Probability 50% 25% 12.5%Payoff $100 $110 $130 Probability 6.25% 3.125% 3.125%Payoff $170 $250 $500(a) What price today would make this a fair bet?(b)
Would a single individual be effectively more, equally, or less risk averse than a pool of such investors?
Does a higher reward (expected rate of return)always come with more risk?
Is this morning’s CNN forecast of tomorrow’s temperature a random variable? Is tomorrow’s temperature a random variable?
Discount rate uncertainty is relatively more problematic for long-term projects. For short-term projects, the exponents limit the damage.
Although the relative importance depends on the exact interest rate, here 100 years is so long that cost of capital errors almost surely matter for any reasonable interest rates now. Cash flow errors
To assess relative error importance, consider a project that earns $100 in 10 years and where the correct interest rate is 10%.The correct PV is $100/1.1010 ≈ $38.55.If the cash flow is incorrectly
Once you reach above $20,000 + 0.8 . $20,000 = $36,000 in expected value, you fall into the third piece of the function, where you receive only 60% on the dollar. Thus, you can set Formula 6.1 on
For promised payoffs between $60,000 and $80,000, solve E(Payoff of Loan if $60,000 ≤ Loan Promise ≤$80,000) = $20,000 + 80% . $20,000 + 60% . $20,000 + 40% . (Loan − $60,000).
With 20% probability, the loan will pay off $20,000; with 80% probability, the loan will pay off the full promised $40,000. Therefore, the loan’s expected payoff is 20% . $20,000 + 80% . $40,000 =
Given the now unequal probabilities,(a)(b) The exact expected payoff is 1/8 . $20,000 + 3/8 . $40,000 + 1/2 . $50,000 = $42,500. The 1/2 is the probability that you will receive the $50,000 that you
Visually, from the graph, if the expected payoff is $45,000, the promised payoff is around $55,000. The correct value can be obtained by setting Formula 6.1 on page 163 equal to $45,000 and solving
Visually, from the graph, for a promised payoff of $45,000, the expected payoff is around $40,000. The correct value can be obtained by plugging into Formula 6.1 on page 163:E(Payoff(Loan Promise =
With infinitely many possible outcomes, the function of expected payoffs would be a smooth increasing function. For the mathematical nitpickers: [a] We really should not allow a normal distribution,
This risk-free loan pays off $20,000 for certain. The levered ownership pays either $0 or $80,000, and costs$64,000/1.10 ≈ $58,182. Therefore, the rate of return is either −100% or +37.50%. You
For the loan that promises to pay off $25,000 (instead of providing it): In the tornado state, the creditor gets all $20,000. In the sunshine state, the creditor receives the promise of $25,000.
Taking rent into account:(a) In the sun state, the value is $120,000 + $11,000 = $131,000. In the tornado state, the value is$11,000 + $20,000 = $31,000. Therefore, the expected building value is
The 80% mortgage would finance 0.8 . $76,363.64 ≈ $61,090.91 today.Event Prob Building Value Mortgage Value Levered Ownership Tornado 20% $20,000 $20,000 $0 Sunshine 80% $100,000 $79,000 a $21,000
No! Partners would share payoffs proportionally, not according to “debt comes first.” For example, in the tornado state, the 32.74% partner would receive only about $6,500, not the entire $20,000
For the dynamite/dud project:(a) The expected payoff is E(P) = 20% . $20,000 + 70% . $40,000 + 10% . $80,000 = $40,000.(b) The present value of the expected payoff is $40,000/1.08 ≈ $37,037.(c) The
The factory’s expected value is E(Value at Time 2) = [0.5 . $500,000 + 0.5 . $1,000,000] = $750,000. Its present value is therefore $750,000/1.062 ≈ $667,497.33.
The actual cash flow is replaced by the expected cash flow, and the actual rate of return is replaced by the expected rate of return.
Both. The historical evidence is that lower-grade borrowers both default more often and pay less upon default.
No, the expected default premium is zero by definition.
With the revised probabilities:(a) The expected payoff is now 95% . $210 + 1% . $100 + 4% . $0 = $200.50. Therefore, the expected rate of return is $200.50/$200 = 0.25%.(b) You require an expected
Expected and promised rates are the same only for government bonds.Most other bonds have some kind of default risk.
Individual investors are more risk averse than investors in the aggregate.
Investors are more risk averse for large bets relative to their wealth.
The variance of the P+1 stock investment is Var = 5% . ($41 − $52)2 + 10% . ($42 − $52)2 + 20% .($45 − $52)2 + 30% . ($48 − $52)2 + 20% . ($58 − $52)2 + 10% . ($70 − $52)2 + 5% . ($75
The expected value of the stock investment is 5% . ($41) + 10% . ($42) + 20% . ($45) + 30% . ($48) +20% . ($58) + 10% . ($70) + 5% . ($75) = $52. Therefore, purchasing the stock at $50 is not a fair
If the random variable is the number of dots on the die, then the expected outcome is 1/6 . (1) + 1/6 . (2) + 1/6 . (3) + 1/6 . (4) + 1/6 . (5) + 1/6 . (6) = 3.5. The realization was 6.
If you do not know the exact bet, you may not know the expected value, which means that even the expected value is unknown. This may be the case for stocks, where you are often forced to guess what
No! The expected outcome (value) is assumed to be known—at least for an untampered die throw. The following is almost philosophy and beyond what you are supposed to know or answer here: It might,
Is discount rate uncertainty relatively more problematic for long-term or for short-term projects?
What is the relative importance of cash flow and cost of capital errors for a 100-year project?
What is the relative importance of cash flow and cost of capital errors for a 10-year project?
ADVANCED: Can you work out the exact required promised payoff for the$45,000 loan for which a creditor would expect a payoff of $38,500?
ADVANCED: What is the formula equivalent to Formula 6.1 on page 163 for promised payoffs between $60,000 and $80,000?
A new product may be a dud (20% probability), an average seller (70%probability), or dynamite (10% probability). If it is a dud, the payoff will be $20,000; if it is an average seller, the payoff
Assume that the probabilities are not equal: $20,000 with probability 1/8, $40,000 with probability 3/8, $60,000 with probability 3/8, and$80,000 with probability 1/8.(a) Draw a graph equivalent to
In the example with 5 possible outcomes, what is the promised payoff if the expected payoff is $45,000?
In the example with 5 possible outcomes, what is the expected payoff if the promised payoff is $45,000?
If there were infinitely many possible outcomes (e.g., if the building value followed a statistical normal distribution), what would the graph of expected payoffs of the loan as a function of
Repeat the example if the loan promises to pay off $20,000. Such a loan is risk free. How does the riskiness of the project “Full Building Ownership” compare to the riskiness of the project
Assume now that the loan does not provide $25,000, but rather promises to pay off $25,000.(a) Repeat the table in the text that summarizes all the information.(b) How much money do you get for this
ADVANCED: For illustration, we assumed that the sample building was not occupied. It consisted purely of capital amounts. But in the real world, part of the return earned by a building owner is rent.
Buildings are frequently financed with a mortgage that pays 80% of the price, not just 32.7% ($25,000 of $76,364). Produce a table similar to Table 6.3 for this case.
In the example, the building was worth $76,364, the mortgage was worth $25,000, and the equity was worth $51,364. The mortgage thus financed 32.74% of the cost of the building, and the equity
A new product may be a dud (20% probability), an average seller (70%probability), or dynamite (10% probability). If it is a dud, the payoff will be $20,000; if it is an average seller, the payoff
A factory can be worth $500,000 or $1,000,000 in 2 years, depending on product demand, each with equal probability. The appropriate cost of capital is 6% per year.What is the present value of the
What changes have to be made to the NPV formula to handle an uncertain future?
Does the historical evidence show that lower-grade borrowers default more often or that they pay less upon default?
Recompute the example from the text, but assume now that the probability of receiving full payment in 1 year on a $200 investment of $210 is only 95%, the probability of receiving $100 is 1%, and the
For what kind of bonds are expected interest rates and promised interest rates the same?
Are individual investors or investors in the aggregate more risk averse?
Are investors more risk averse for small bets or for large bets? Should“small” be defined relative to investor wealth?
Reconsider the stock investment from Question 6.4.What is its risk, that is, the standard deviation of its outcome P+1?
A stock that has the following probability distribution (outcome P+1)costs $50. Is an investment in this stock a fair bet?Prob P+1 Prob P+1 Prob P+1 Prob P+1 5% $41 20% $45 20% $58 5% $75 10% $42 30%
An ordinary die throw came up with a yesterday. What was its expected outcome before the throw?What was its realization?
Could it be that the expected value of a bet is a random variable?
Is the expected outcome (value) of a die throw a random variable?
If the continuously compounded interest rate is 10% per annum in the first year and 20% the following year, what is your total continuously compounded interest rate over the 2 years?How much will you
A 25-year bond costs $25,000 today and will pay $1,000 at year-end for the following 25 years. In the final year (T = 25), it also repays$25,000 in principal. (Use 4 decimal places of accuracy when
A 10-year zero-bond has a YTM of 10%.What is its plain duration? What is its Macaulay duration?

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