CHAPTER 4: ANSWERS TO CONCEPTS IN REVIEW
CHAPTER 4: ANSWERS TO CONCEPTS IN REVIEW
CHAPTER 4: ANSWERS TO CONCEPTS IN REVIEW
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<strong>CHAPTER</strong> 4: <strong>ANSWERS</strong> <strong>TO</strong> <strong>CONCEPTS</strong> <strong>IN</strong> <strong>REVIEW</strong><br />
4.1 The return on investment is the expected profit that motivates people to invest. It includes both<br />
current income and/or capital gains (or losses). Without a positive expected return, there is no<br />
benefit to investing and individuals have no reason to save and invest. Since net demanders are<br />
willing to pay net savers a positive return for their funds, the opportunity to earn a positive return<br />
exists.<br />
Return on investment can come from either current income or capital gains, or both. Current<br />
income, most commonly, is periodic payments, such as interest received on bonds, dividends on<br />
stock, or rent received from real estate. To be considered income, these payments must be<br />
received in cash or be readily convertible to cash. Capital gain refers to the change in the market<br />
value of the investment. The amount by which the proceeds from the sale of an investment<br />
exceed the original purchase is called a capital gain. If it is sold for less than the original<br />
purchase price, a capital loss is realized.<br />
The use of percentage returns is generally preferred to dollar returns to allow investors to directly<br />
compare different sizes and types of investments.<br />
4.2 Although future returns are not guaranteed by past performance, historical data often gives the<br />
investor a meaningful basis on which to form future expectations. Past return data, such as<br />
average returns or trends seen in certain time periods, can be used along with the investor’s<br />
insights about future prospects of the investment. Together the historical data and future<br />
prospects help the investor to formulate an expected return on the investment.<br />
The level of expected returns depends on many internal characteristics of the investment and the<br />
external forces on the investment. Internal characteristics include the type of investment, the<br />
quality of management, the method by which the investment is financed, and the customer base<br />
of the issuer. External forces include war, shortages, price controls, Federal Reserve actions,<br />
and political events, among others. External forces, unlike internal characteristics, cannot be<br />
controlled by the issuer of the investment. Investment vehicles are affected differently by these<br />
forces -- the expected return of one investment may increase while the expected return of<br />
another may decrease in response to external forces.<br />
4.3 History tells us that stock market returns have averaged well above the interest rates payable on<br />
savings accounts at banks. In recent years especially during the latter part of the 1990’s the<br />
returns were well above the stock market averages for the earlier part of the century.<br />
Unfortunately, the article does not provide a clear message for investors other than “history can<br />
repeat itself.” If the investor is looking for short-term gains over a year or two, the probabilities<br />
are mixed depending on what time periods are cited. The best advice, given these statistics, is to<br />
invest to hold for the long term in order to ride out the market’s twists and turns.<br />
4.4 Time value of money refers to the fact that, with the opportunity to earn interest on funds, the<br />
value of money depends on the point in time when the money is expected to be received. Thus,<br />
the sooner one receives money the better -- the more valuable is that money.<br />
Because money has time value, people willing to invest their money should be able to earn a<br />
positive return. For example, an investor expecting to receive a $100 interest payment for 2<br />
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different securities doesn’t necessarily value them equally. If the first investment pays the<br />
interest at the end of one year, but the second investment pays the interest at the end of two<br />
years, the first investment will be more valuable. The $100 can be reinvested to earn interest for<br />
an entire year. At the end of Year 2, the first investment has returned $100 + interest, the second<br />
has returned $100 to the investor. The $100 reinvestment has earned a positive return; the other<br />
$100 has not had a chance to accumulate interest.<br />
4.5 a. Interest is the current income you receive from placing available funds in a savings account,<br />
CD, bond, or by making a loan. It is in effect the “rent” paid on your money by those who<br />
obtain use of it.<br />
b. Simple interest is interest paid (earned) only on the initial balance for the actual amount of<br />
time it is on deposit. With simple interest, the stated interest rate is always equal to the true<br />
rate of interest (or return).<br />
c. Compound interest is interest paid not only on the initial deposit but also on interest<br />
accumulated from one period to the next. This is the method savings institutions generally<br />
employ. When interest is compounded annually, the simple, compound, and true rate of<br />
interest are the same.<br />
d. The true rate of interest (or return) takes the concept of compounding into account. When<br />
interest is compounded annually, the stated and true interest rates are equal. For more<br />
frequent compounding, the "true" rate of interest would be higher than the stated rate. Hence<br />
an APR of 15% on a credit card which is compounded daily has a true interest rate of<br />
16.18%.<br />
4.6 The true rate of interest rises as interest is compounded more frequently than annually. The true<br />
and stated rates are the same when interest is compounded annually. Continuous compounding<br />
occurs when interest is compounded over the smallest possible time period.<br />
4.7 The future value of a cash flow represents the amount to which a current deposit will grow over a<br />
given time period if it is placed in an account paying compound interest. Present value is<br />
concerned with finding the current value of a future sum, given that the investor earns a stated<br />
return – the discount rate (or opportunity cost) – on similar investments. The discount rate is the<br />
rate at which future sums are discounted to find their present values. The present value concept<br />
is the inverse of the future value concept.<br />
4.8 An annuity is a stream of equal cash flows that occur in equal intervals over time. These cash<br />
flows can be paid out or received. An ordinary annuity has cash flows occur at the end of each<br />
year. To simplify the calculation of the future value of an annuity, one can use the future value<br />
interest factor of the annuity table included in Appendix A, Table A.2. The present value of an<br />
annuity can be found similarly in the present-value interest factor of the annuity table in<br />
Appendix A, Table A.4.<br />
4.9 A mixed stream of returns is a series of returns that exhibits no pattern. To find the present value<br />
of a mixed stream, calculate the present value of each component of the mixed stream. The<br />
summation of the present value of individual components gives us the present value of the entire<br />
mixed stream.<br />
4.10 Ignoring risk, a satisfactory investment is one for which the present value of benefits<br />
(discounted) equals or exceeds the present value of costs. If the present value of benefits<br />
exceeds the cost, the investor would earn more than the discount rate i.e. the return on the<br />
investment is greater than the discount rate.<br />
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4.11 a. The real rate of return is the return earned in a certain, risk-free world. It would equal the<br />
nominal rate of return on a risk-free security less inflation. For risky securities, it would<br />
equal the nominal rate less inflation (plus risk premium).<br />
b. The expected inflation premium represents the expected average future rate of inflation. It is<br />
the compensation that investors demand for future expected inflation.<br />
c. The risk premium varies for different security issues and represents the additional return<br />
required to compensate an investor for the risk characteristics of the issue and the issuer. It is<br />
the return on a risk security (e.g. stocks, bonds) minus the risk-free rate of return, which is<br />
the rate on a 90-day T-Bill.<br />
The risk-free rate of return equals the real rate of return plus the expected inflation premium:<br />
RF = r* + IP. It is the return on a riskless security as measured by the 90-day T-Bill.<br />
The required rate of return equals the real rate of return plus the expected inflation premium<br />
(together, the risk-free rate) and the risk premium: ri = RF + IP. OR it equals the risk-free rate<br />
of return plus the risk premium.<br />
4.12 The holding period is simply the period of time over which the investor wishes to measure the<br />
return on an investment. In comparing alternative investment vehicles, it is essential to use<br />
equal-length holding periods so that the two vehicles being compared are judged under identical<br />
conditions. This adds objectivity to the comparison. Most interest rates are quoted on an annual<br />
basis, so it is generally convenient to use a one-year holding period.<br />
The holding period return (HPR) is the total return earned from holding an investment for a<br />
specified period of time. To calculate HPR, all that is needed is the beginning- and end-ofperiod<br />
investment values along with the value of current income received by the investor.<br />
Because HPR doesn’t account for the time value of money, the holding period is usually one<br />
year or less.<br />
4.13 The yield, or IRR, is the annual rate of return earned by a long-term investment. It is also<br />
defined as the discount rate that produces a present value of benefits received equal to the<br />
present value of costs/investments. Unlike the HPR, it takes into account the time value of<br />
money and can be used to calculate the return on investments held for over one year. The HPR<br />
is inappropriate for investments held for more than one year.<br />
4.14 The critical assumption underlying the use of yield as a return measure is an ability to earn a<br />
return equal to the calculated yield on all income received from the investment during the<br />
holding period. If you earn 10 percent on all income received from an investment during the<br />
holding period, your yield on the investment will be 10 percent. On the other hand, if you earn 0<br />
percent on the income received, your rate of return on the investment would actually be less than<br />
10 percent. If the interest-on-interest earned from the investment is less than its calculated yield,<br />
the investment’s return will fall below the yield. Clearly when using yield as a measure of<br />
investment return, the validity of this assumption must be recognized and evaluated. If the<br />
interest-on-interest assumption does not hold, use of the calculated yield could lead to poor<br />
investment decisions. (Note: The instructor may want to use the discussion of<br />
interest-on-interest and Figure 4.1 to demonstrate this somewhat complex, but extremely<br />
important, yield concept.)<br />
4.15 If the present value of returns from an investment is greater than the initial cost of the<br />
investment, it is a satisfactory investment and should be acceptable. If the yield from an<br />
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investment is greater than the appropriate discount rate for that investment, the present value<br />
and yield provide the same conclusion regarding acceptability.<br />
In the example given, Investment A is clearly acceptable since its yield (8 percent) is greater than<br />
the appropriate discount rate (7 percent). Investment B, on the other hand, is not acceptable<br />
since its present value of returns ($150) is $10 less than its cost ($160). Investment C is not<br />
acceptable since its yield (8 percent) is lower than the appropriate discount rate (9 percent).<br />
4.16 Risk is the chance that the actual return from an investment may differ from what is expected.<br />
The standard deviation is the statistic used to measure risk. The risk-return tradeoff is the<br />
relationship between the expected returns from an investment and the risk associated with them.<br />
The required returns from an investment increase as risk increases to provide an incentive for<br />
him or her to take higher risks i.e. in order to accept higher risks, the investors have to be<br />
compensated with higher returns.<br />
4.17 a. Business risk is concerned with the degree of uncertainty associated with an investment’s<br />
earnings and the investment’s ability to pay investors interest, dividends, and other returns<br />
owed them. Business risk is usually related to the firm’s line of business.<br />
b. Financial risk is the risk associated with the mix of debt and equity (capital structure) used to<br />
finance the firm. The greater the firm’s debts and interest obligations, the greater its<br />
financial risk.<br />
c. Purchasing power risk arises because of uncertain inflation rates and price-level changes in<br />
the future. When prices rise, each dollar invested has less value – it can buy less, and vice<br />
versa.<br />
d. Interest rate risk is risk associated with changes in the prices of fixed-income securities<br />
resulting from changing market interest rates. As the market interest rates change, the prices<br />
of these securities change in the opposite direction, thereby changing the level of return that<br />
an investor can expect to obtain from them. Another important aspect of interest rate risk<br />
involves the ability to reinvest income received at the initial rate of return in order to earn the<br />
fully compounded rate of return.<br />
e. Liquidity risk is the risk of not being able to liquidate an investment conveniently and at a<br />
reasonable price. In general, investment vehicles traded in markets with small demand and<br />
supply characteristics tend to be less liquid than those traded in broad markets.<br />
f. Tax risk is the risk that tax laws enacted by Congress will adversely affect certain types of<br />
investments and decrease their after-tax returns.<br />
g. Market risk is the risk of changes in investment returns caused by factors independent of the<br />
given investment vehicle. It results from factors such as political, economic, and social<br />
events, or changes in investor tastes and preferences.<br />
h. Event risk is the risk that comes from a largely or totally unexpected event which has a<br />
significant and usually immediate effect on the underlying value of an investment. The<br />
effect of this risk seems to be isolated in most cases, affecting only certain companies and<br />
properties.<br />
4.18 Standard deviation is the most common measure of an asset’s risk. It measures the dispersion of<br />
returns around an asset’s average or expected return. Standard deviation is an absolute measure<br />
of risk, and thus can be used to compare the riskiness of competing investments with the same<br />
expected return. The coefficient of variation (CV) measures the relative dispersion of an asset’s<br />
average or expected returns. Like standard deviation, the higher the CV, the higher the risk. CV<br />
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differs from standard deviation because it is a relative measure of risk and can be used to<br />
compare the riskiness of competing investments with different expected returns.<br />
4.19 Investors’ attitudes toward risk or their risk-return tradeoffs may be classified as one of the<br />
following:<br />
Risk-indifferent investors do not require a greater return in exchange for each unit of<br />
additional risk.<br />
Risk-averse investors require greater return in exchange for each unit of additional risk. The<br />
trade-off here is positive; return must increase as risk increases.<br />
Risk-taking investors accept a lower return in exchange for greater risk. This tradeoff is<br />
negative; such investors enjoy risk and are therefore willing to accept lower returns for<br />
increasing levels of risk.<br />
In general, most investors are risk-averse. They require increased returns from an investment as<br />
its risk increases. The risk preference of an investor is an important determinant of his/her<br />
investment decisions. Risk-averse investors may not make speculative investments, while<br />
risk-taking investors may. Thus, an investment that is considered unsatisfactory by a risk-averse<br />
investor may be deemed satisfactory by a risk-taking investor.<br />
4.20 The answer to the first part depends on the risk tolerance of the student.<br />
a. If the investor is conservative, the appropriate investment vehicles would be U.S.<br />
Government securities, savings accounts, Certificate of Deposits and high-quality bonds.<br />
b. If the investor is a moderate risk taker, the appropriate investment vehicles include bonds,<br />
preferred stocks, convertible securities, mutual funds and blue-chip common stocks.<br />
c. An aggressive investor can put his/her money in investment vehicles such as volatile stocks,<br />
real estate, and speculative securities such as options and futures.<br />
4.21 The investment process can be summarized in four steps:<br />
(1) Estimate the expected return over a given holding period using historical data or projected<br />
return data, or both. The time value of these returns must be considered for long-term<br />
investments.<br />
(2) Assess the risk of the investment returns through the subjective (judgmental) evaluation of<br />
historical returns and by using beta (for securities).<br />
(3) Evaluate the risk-return behavior of each alternative investment. The expected return must<br />
be “reasonable” given the level of risk possessed by the investment. Only investments<br />
offering the highest expected return for a given level of risk are considered reasonable.<br />
(4) Select the vehicles with the highest return for the level of risk the investor is willing to take.<br />
These fit the definition of a good investment.<br />
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