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Fundamentals of Coporate Finance Ch9~11 Ross

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Fundamentals of Coporate Finance Ch9~11 Ross

CHAPTER 9

    RISK AND RETURN: LESSONS FROM

    MARKET HISTORY

Answers to Concepts Review and Critical Thinking Questions

    1. They all wish they had! Since they didn’t, it must have been the case that the stellar performance was

    not foreseeable, at least not by most.

    2. As in the previous question, it’s easy to see after the fact that the investment was terrible, but it

    probably wasn’t so easy ahead of time.

    3. No, stocks are riskier. Some investors are highly risk averse, and the extra possible return doesn’t

    attract them relative to the extra risk.

    4. Unlike gambling, the stock market is a positive sum game; everybody can win. Also, speculators

    provide liquidity to markets and thus help to promote efficiency.

    5. T-bill rates were highest in the early eighties. This was during a period of high inflation and is

    consistent with the Fisher effect.

    6. Before the fact, for most assets, the risk premium will be positive; investors demand compensation

    over and above the risk-free return to invest their money in the risky asset. After the fact, the

    observed risk premium can be negative if the asset’s nominal return is unexpectedly low, the

    risk-free return is unexpectedly high, or if some combination of these two events occurs.

7. Yes, the stock prices are currently the same. Below is a diagram that depicts the stocks’ price

    movements. Two years ago, each stock had the same price, P. Over the first year, General 0

    Materials’ stock price increased by 10 percent, or (1.1) ( P. Standard Fixtures’ stock price declined 0

    by 10 percent, or (0.9) ( P. Over the second year, General Materials’ stock price decreased by 10 0

    percent, or (0.9)(1.1) ( P, while Standard Fixtures’ stock price increased by 10 percent, or (1.1)(0.9) 0

    ( P. Today, each of the stocks is worth 99 percent of its original value. 0

     2 years ago 1 year ago Today

    General Materials P(1.1)P (1.1)(0.9)P = (0.99)P0 000

    Standard Fixtures P(0.9)P (0.9)(1.1)P= (0.99)P0 00 0

    8. The stock prices are not the same. The return quoted for each stock is the arithmetic return, not the

    geometric return. The geometric return tells you the wealth increase from the beginning of the period

    to the end of the period, assuming the asset had the same return each year. As such, it is a better

    measure of ending wealth. To see this, assuming each stock had a beginning price of $100 per share,

    the ending price for each stock would be:

     Lake Minerals ending price = $100(1.10)(1.10) = $121.00

     Small Town Furniture ending price = $100(1.25)(.95) = $118.75

     CHAPTER 9 B- 2

     Whenever there is any variance in returns, the asset with the larger variance will always have the

    greater difference between the arithmetic and geometric return.

    9. To calculate an arithmetic return, you simply sum the returns and divide by the number of returns.

    As such, arithmetic returns do not account for the effects of compounding. Geometric returns do

    account for the effects of compounding. As an investor, the more important return of an asset is the

    geometric return.

    10. Risk premiums are about the same whether or not we account for inflation. The reason is that risk

    premiums are the difference between two returns, so inflation essentially nets out. Returns, risk

    premiums, and volatility would all be lower than we estimated because aftertax returns are smaller

    than pretax returns.

Solutions to Questions and Problems

    NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.

     Basic

    1. The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the

    initial price. The return of this stock is:

     R = [($94 83) + 1.40] / $83

     R = .1494 or 14.94%

    2. The dividend yield is the dividend divided by price at the beginning of the period, so:

     Dividend yield = $1.40 / $83

     Dividend yield = .0169 or 1.69%

     And the capital gains yield is the increase in price divided by the initial price, so:

     Capital gains yield = ($94 83) / $83

     Capital gains yield = .1325 or 13.25%

3. Using the equation for total return, we find:

     R = [($76 83) + 1.40] / $83

     R = .0675 or 6.75%

     And the dividend yield and capital gains yield are:

     Dividend yield = $1.40 / $83

     Dividend yield = .0169 or 1.69%

     CHAPTER 9 B- 3

     Capital gains yield = ($76 83) / $83

     Capital gains yield = .0843 or 8.43%

     Here’s a question for you: Can the dividend yield ever be negative? No, that would mean you were

    paying the company for the privilege of owning the stock. It has happened on bonds. Remember the

    Buffett bond’s we discussed in the bond chapter.

    4. The total pound return is the change in price plus the coupon payment, so:

     Total pound return = ?1,074 1,120 + 90

     Total pound return = ?44

     The total percentage return of the bond is:

     R = [(?1,074 1,120) + 90] / ?1,120

     R = .0393 or 3.93%

    Notice here that we could have simply used the total pound return of ?44 in the numerator of this

    equation.

     Using the Fisher equation, the real return was:

     (1 + R) = (1 + r)(1 + h)

     r = (1.0393 / 1.030) 1

     r = .0090 or 0.90%

5. The nominal return is the stated return, which is 12.40 percent. Using the Fisher equation, the real

    return was:

     (1 + R) = (1 + r)(1 + h)

     r = (1.1240)/(1.031) 1

     r = .0902 or 9.02%

    6. Using the Fisher equation, the real returns for government and corporate bonds were:

     (1 + R) = (1 + r)(1 + h)

     r = 1.058/1.031 1 G

     r = .0262 or 2.62% G

     r= 1.062/1.031 1 C

     r = .0301 or 3.01% C

     CHAPTER 9 B- 4 7. The average return is the sum of the returns, divided by the number of returns. The average return for each

    stock was:

    N??.11.06.08.28.13!,XxN .1000 or 10.00% ??i51??i

    N??.36.07.21.12.43!, YyN .1620 or 16.20%?