Questions and Answers of Theory Of Corporate Finance

A junk bond with a beta of 0.4 will default with 20% probability. If it does, investors receive only 60% of what is due to them. The risk-free rate is 3% per annum and the risk premium is 5% per
Draw the SML if the true expected rate of return on the market is 6% per annum and the risk-free rate is 2% per annum. How would the figure look if you were not sure about the expected rate of return
The risk-free rate is 6%. The expected rate of return on the stock market is 10%.What is the appropriate cost of capital for a project that has a beta of −2? Does this make economic sense?
The risk-free rate is 6%. The expected rate of return on the stock market is 8%. What is the appropriate cost of capital for a project that has a beta of 2?
Write down the CAPM formula. Which are economy-wide inputs, and which are projectspecific inputs?
In a perfect world and in the absence of externalities, should you take only the projects with the highest NPV?
If the CAPM holds, then what should you do as the manager if you cannot find projects that meet the hurdle rate suggested by the CAPM?
What are the assumptions underlying the CAPM? Are the perfect market assumptions among them? Are there more?
For short-term investments, the expected cash flows are most critical to estimate well (see Section 4.1A on page 70). In this case, the trouble spot (d) is really all that matters. For long-term
The CAPM should work very well if beta is about 0. The reason is that you do not even need to guess the equity premium if this is so.
Even though the CAPM is empirically rejected, it remains the benchmark model that everyone uses in the real world. Moreover, even if you do not trust the CAPM itself, at the very least it suggests
No, the empirical evidence suggests that the CAPM does not hold. The most important violation seems to be that value firms had market betas that were low, yet average returns that were high. The
Your combined happy-marriage beta would be βCombined= (3/4) . 2.4 + (1/4) . 0.4 = 1.9.
This is an asset beta versus equity beta question. Because the debt is almost risk free, we can use βDebt≈ 0.(a) First compute an unlevered asset beta for your comparable with its debt-to-asset
Yes, a zero-beta asset can still have its own idiosyncratic risk. And, yes, it is perfectly kosher for a zerobeta asset to offer the same expected rate of return as the risk-free asset. The reason is
The duration of this cash flow is around, or a little under, 5 years. Thus, a 5-year zero Treasury would be a reasonably good guess. You should not be using a 30-day, a 30-year, or even a 10-year
Use the 1-year Treasury rate for the 1-year project, especially if the 1-year project produces most of its cash flows at the end of the year. If it produces constant cash flows throughout the year, a
An estimate between 1% and 8% per year is reasonable. Anything below 0% and above 10% would seem unreasonable to me. For reasoning, please see the different methods in the chapter.
The cost needs to be discounted with the current interest rate. Since payment is up front, this cost is $30,000 now! The appropriate expected rate of return for cash flows (of your earnings) is 3% +
It does not matter what you choose as the per-unit payoff of the bond. If you choose $100, you expect it to return $99.(a) Thus, the price of the bond is PV = $99/(1 + [3% + 5% . 0.2]) ≈ $95.19.(b)
The equity premium, E(˜rM) − rF, is the premium that the stock market expects to offer on the risky market above and beyond what it offers on Treasuries.
A firm reported the following cash flows: Exp. rate of return (in %) 15 10- S Risk-free Treasury F Market M -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 True market beta
Write down the CAPM formula and solve E(˜ri) = rF+ [E(˜rM) − rF] . βi= 4% + (7% − 4%) . βi= 5%.Therefore, βi= 1/3. Note that we are ignoring the promised rate of return.
No—the real-world SML is based on historical data and not true expectations. It would be a scatterplot of historical risk and reward points. If the CAPM holds, a straight, upward-sloping line would
With rF= 4% and E(˜rM) = 12%, the cost of capital for a project with a beta of −3 is E(˜r) = rF+ [E(˜rM) −rF] . βi= 4% + (12% − 4%) . (−3) = −20%. Yes, it does make sense that a project
With rF= 4% and E(˜rM) = 12%, the cost of capital for a project with a beta of 3 is E(˜r) = rF+ [E(˜rM) −rF] . βi= 4% + (12% − 4%) . 3 = 28%.
With rF= 4% and E(˜rM) = 7%, the cost of capital for a project with a beta of 3 is E(˜r) = rF+ [E(˜rM) −rF] . βi= 4% + (7% − 4%) . 3 = 13%.
Yes, the perfect market is an assumption underlying the CAPM. In addition,(a) Investors are rational utility maximizers.(b) Investors care only about overall portfolio mean rate of return and risk at
To value an ordinarily risky project, that is, a project with a beta in the vicinity of about 1, what is the relative contribution of your personal uncertainty (lack of knowledge) in (a) the
Is the CAPM likely to be more accurate for a project where the beta is very high, one where it is very low, or one where it is zero?
If the CAPM is wrong, why do you need to learn it?
Does the empirical evidence suggest that the CAPM is correct?
You own a stock market portfolio that has a market beta of 2.4, but you are getting married to someone who has a portfolio with a market beta of0.4. You are three times as wealthy as your future
A comparable firm(with comparable size and in a comparable business)has a Yahoo! Finance–listed equity beta of 2.5 and a debt/asset ratio of 2/3. Assume the debt is risk free.(a) Estimate the beta
According to the CAPM formula, a zero-beta asset should have the same expected rate of return as the risk-free rate. Can a zero-beta asset still have a positive standard deviation? Does it make sense
If you can use only one Treasury, which risk-free rate should you use for a project that will yield $5 million each year for 10 years?.
What is today’s risk-free rate for a 1-year project? For a 10-year project?
What are appropriate equity premium estimates? What are not? What kind of reasoning are you relying on?
Going to your school has total additional and opportunity costs of$30,000 this year and up front. With 90% probability, you are likely to graduate fromyour school. If you do not graduate, you have
A corporate bond with a beta of 0.2 will pay off next year with 99%probability. The risk-free rate is 3% per annum, and the equity premium is 5% per annum.(a) What is the price of this bond?(b)What
What is the equity premium, both mathematically and intuitively?
Draw the security market line if the risk-free rate is 5% and the equity premium is 10%.
The risk-free rate is 4%. The expected rate of return on the stock market is 7%. A corporation intends to issue publicly traded bonds that promise a rate of return of 6% and offer an expected rate of
Is the real-world security market line a line?
The risk-free rate is 4%. The expected rate of return on the stock market is 12%. What is the appropriate cost of capital for a project that has a beta of −3? Does this make economic sense?
The risk-free rate is 4%. The expected rate of return on the stock market is 12%. What is the appropriate cost of capital for a project that has a beta of 3?
The risk-free rate is 4%. The expected rate of return on the stock market is 7%.What is the appropriate cost of capital for a project that has a beta of 3?
What are the assumptions underlying the CAPM? Are the perfect market assumptions among them? Are there more?
Return to the example with a risk-free asset in Formula 8.14 on page 240. What are the risk and reward of a portfolio that invests wH= 150%? (This means that if you have$100, you would borrow $50 at
The Vanguard European stock fund, Pacific stock fund, and Exxon Mobil reported the following historical dividend-adjusted prices:Year 1991 1992 1993 1994 1995 1996 VEURX 6.53 7.15 6.91 9.34 9.03
In the absence of a risk-free asset, would anyone buy the portfolio wH= 110%, wI=−10%?
Mathematically and based on Figure 8.6 on page 238, the risk and reward of the portfolio wH= −0.2, wI= −1.2.
An asset has an annual mean of 12% and standard deviation of 30% per year. What would you expect its monthly mean and standard deviation to be?
Recompute the portfolio variance if you invest in a portfolio O with wH= 90% and wI=10% in Table 8.4.(a) Compute the rates of return on the portfolio in each scenario, and then treat the resulting
If the risk-free rate were lower, then the tangency line would become steeper. The tangency portfolio would shift from around K to around L. Therefore, it would involve more H.
This question asks you to show howmuch better off you are with this particular risk-free asset for a particular risk choice.(a) In Formula 8.12 on page 237, we showed that this no-risk-free
Because the net-of-mean F is always 0, so is its coproduct with anything else. This means that the covariance of the risk-free asset with any risky asset is zero, too.
Portfolios to the right of H on the line have a negative weight in F and a weight above 1 in H. (The portfolio weights must add to 100%!) This means that they would borrow money at a 4% annual
The covariance between H and Z is 85.5%%, which is much higher than the 45%% covariance between H and I from Formula 8.9 on page 233. This means that the correlation between H and Z shoots up to
If the correlation was higher, diversification would help less, so the risk would be higher. Therefore, the efficient frontier would not bend as far toward the west (a risk of 0). An easy way to
Two risky portfolios with a correlation of −1 can be combined into an asset that has no risk. Thus, its expected rate of return has to be the same as that on the risk-free asset—or you could get
The mean rate of return for portfolio (wH= 0.1, wI= 0.9) is 0.1 . 6% + 0.9 . 9% = 8.7%. You can also compute this from the rates of return in the 4 states −11.4%, 17.4%, 21.6%, and 7.2%. Demeaned,
This is an important question. In fact, you should memorize Formula 8.15 that describes how risk grows over time. The assumption that there is no compounding (that you can ignore the cross-product)
The covariance between H and I is 45%% (Formula 8.9). The variance of H is 90%%, the variance of I is 189%% (Table 8.4). Therefore, the shortcut Formula 8.10 gives Var(˜rM) = (3/4)2 . 90%% + (1/4)2
For M, the covariance between H and I was computed as 45%% in Formula 8.9. The variance of H is 90%% (from Table 8.4 on page 232), the variance of I is 189%% (from the same figure). Therefore, using
The portfolio variance of portfolio N in Table 8.4 is Sdv(TH) = Var(TH) = = 22 (-7.5% -6.75%)2 + (13.5% 6.75%) 2 + (6% 6.75%) 2 + (15% 6.75%) 4 203.0625 %% + 45.5625% % +0.5625 %% + 68.0625%% 4
The rates of return of portfolioMin Table 8.4 are−8% (♣), +14% (♦), 8% (♥), and 14% (♠). The deviations from the mean are −15%, 7%, 1%, and 7%.When squared, they are 225%%, 49%%, 1%%, and
Would the tangency portfolio invest in more or less H if the risk-free rate were 3% instead of 4%? (Hint: Think visually.)
Formula 8.11 noted that the minimum-variance portfolio without a risk-free asset invests about 76.2% in H and about 24.8% in I. (Work with the rounded numbers to make your life easier.) With the
Compute the covariance of H and F.
What kind of portfolios are the points to the right of H on the line itself in Figure 8.7?
Draw the efficient frontier for the following two base assets, H and Z:Also, compute the covariance between H and Z. Is it higher or lower than what you computed in the text for H and I? How does the
If H and I were more correlated, what would the efficient frontier between them look like? If H and I were less (or more negatively) correlated, what would the efficient frontier between them look
If there are two risky portfolios that have a correlation of −1with positive investment weights, what would the expected rate of return on this portfolio be?
Compute the risk and reward of the portfolio wH= 0.1, wI= 0.9, as in Table 8.4 on page 232. Confirm that this portfolio is drawn correctly in Figure 8.5.
(This question is very important. Please do not pass over it.) Let’s consider a stock market index, such as the S&P 500. It had a historical average rate of return of about 12% per annum, and a
Show that the shortcut Formula 8.10 works for portfolio N, in which H is 3/4. That is, does it give the same 79.3%% noted in Table 8.4?
Show that the shortcut Formula 8.10 works for portfolio M, in which H is 2/3. That is, does it give the same 81.0%% noted in Table 8.4 on page 232?
Confirm the portfolio variance and standard deviation if you invest in portfolio N (wH= 3/4) in Table 8.4.
Confirm the portfolio variance and standard deviation if you invest in portfolio M (wH= 2/3) in Table 8.4.
Why do some statistical packages estimate covariances differently (and different from those we computed in this chapter)? Does the same problem also apply to expected rates of return (means) and
Are historical covariances or means more trustworthy as estimators of the future?
Download 5 years of historical monthly(dividend-adjusted) prices for Coca-Cola (KO)and the S&P 500 from Yahoo! Finance.(a) Compute the monthly rates of return.(b) Compute the average rate of return
Download the historical prices for the S&P 500 index (~spx or ~gspc) and for VPACX (the Vanguard Pacific Stock Index mutual fund)from Yahoo! Finance, beginning January 1, 2004, and ending December 31
The following represents the probability distribution for the rates of return for next month:Probability Pfio P Market M 1/6 −20% −5%2/6 −5% +5%2/6 +10% 0%1/6 +50% +10%Compute by hand (and show
Compute the expected rates of return and the portfolio betas for many possible portfolio combinations (i.e., different weights) of C and D from Table 8.1 on page 202. (Your weight in D is 1 minus
Consider the following assets:Scenario Bad Okay Good Market M −5% 5% 15%Asset X −2% −3% 25%Asset Y −4% −6% 30%(a) Compute the market betas for assets X and Y.(b) Compute the correlations of
Go to Yahoo! Finance. Obtain 2 years’worth of weekly rates of return for PepsiCo and for the S&P 500 index. Use a spreadsheet to compute PepsiCo’s market beta.
You estimate your project to return −20% if the stock market returns −10%, and +5% if the stock market returns +10%. What would you use as the market beta estimate for your project?
Look up the market betas of the companies in Table 8.2. Have they changed dramatically sinceMay 2008, or have they remained reasonably stable?
Is it wise to rely on historical statistical distributions as our guide to the future?
Why is it so common to use historical financial data to estimate future market betas?
Assume you have invested half of your wealth in a risk-free asset and half in a risky portfolio P. Is it theoretically possible to lower your portfolio risk if you move your risk-free asset holdings
Consider the following five assets, which have rates of return in six equally likely possible scenarios:Scenarios Awful Poor Med. Okay Good Great Asset P1 –2% 0% 2% 4% 6% 10%Asset P2 –1% 2% 2% 2%
What are the risk and reward of a combination portfolio that invests 40% in A and 60% in B?
Compute the value-weighted average of 1/3 of the standard deviation of C and 2/3 of the standard deviation of D. Is it the same as the standard deviation of a CDD portfolio of 1/3 C and 2/3 D, in
The following were the closing year-end prices of the Japanese stock market index, the Nikkei-225:1984 11,474 1992 16,925 2000 13,786 1985 13,011 1993 17,417 2001 10,335 1986 18,821 1994 19,723 2002
Multiply each rate of return for A by 2.0.This portfolio offers −2%, +4%, +8%, and+22%. Compute the expected rate of return and standard deviation of this new portfolio.How do they compare to those
For a firm whose debt is risk free, the overall firm beta is βFirm= 0.5 . βEquity+ 0.5 . βDebt. Thus, 0.5 . βEquity+ 0.5 . 0 = 2. Solve for βEquity= βFirm/0.5 = 4. For the (90%, 10%) case, the
The CCD portfolio has rates of return of 3.3333%, 4.00%, 4.6667%, and 4.00% in the four states. Demeaned, this is −0.6667%, 0%, 0.6667%, and 0%. Therefore, the variance of CCD is [(−0.6667%)2

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