CHAPTER 4: ANSWERS TO CONCEPTS IN REVIEW 4.1 The return on investment is the expected profit that motivates people to invest. It includes both current income and/or capital gains (or losses). Without a positive expected return, there is no benefit to investing and individuals have no reason to save and invest. Since net demanders are willing to pay net savers a positive return for their funds, the opportunity to earn a positive return exists. Return on investment can come from either current income or capital gains, or both. Current income, most commonly, is periodic payments, such as interest received on bonds, dividends on stock, or rent received from real estate. To be considered income, these payments must be received in cash or be readily convertible to cash. Capital gain refers to the change in the market value of the investment. The amount by which the proceeds from the sale of an investment exceed the original purchase is called a capital gain. If it is sold for less than the original purchase price, a capital loss is realized. The use of percentage returns is generally preferred to dollar returns to allow investors to directly compare different sizes and types of investments. 4.2 Although future returns are not guaranteed by past performance, historical data often gives the investor a meaningful basis on which to form future expectations. Past return data, such as average returns or trends seen in certain time periods, can be used along with the investor s insights about future prospects of the investment. Together the historical data and future prospects help the investor to formulate an expected return on the investment. The level of expected returns depends on many internal characteristics of the investment and the external forces on the investment. Internal characteristics include the type of investment, the quality of management, the method by which the investment is financed, and the customer base of the issuer. External forces include war, shortages, price controls, Federal Reserve actions, and political events, among others. External forces, unlike internal characteristics, cannot be controlled by the issuer of the investment. Investment vehicles are affected differently by these forces -- the expected return of one investment may increase while the expected return of another may decrease in response to external forces. 4.3 History tells us that stock market returns have averaged well above the interest rates payable on savings accounts at banks. In recent years especially during the latter part of the 1990 s the returns were well above the stock market averages for the earlier part of the century. Unfortunately, the article does not provide a clear message for investors other than history can repeat itself. If the investor is looking for short-term gains over a year or two, the probabilities are mixed depending on what time periods are cited. The best advice, given these statistics, is to invest to hold for the long term in order to ride out the market s twists and turns. 4.4 Time value of money refers to the fact that, with the opportunity to earn interest on funds, the value of money depends on the point in time when the money is expected to be received. Thus, the sooner one receives money the better -- the more valuable is that money. Because money has time value, people willing to invest their money should be able to earn a positive return. For example, an investor expecting to receive a $100 interest payment for 2 Fundamentals of Investing, by Gitman and Joehnk 1
different securities doesn t necessarily value them equally. If the first investment pays the interest at the end of one year, but the second investment pays the interest at the end of two years, the first investment will be more valuable. The $100 can be reinvested to earn interest for an entire year. At the end of Year 2, the first investment has returned $100 + interest, the second has returned $100 to the investor. The $100 reinvestment has earned a positive return; the other $100 has not had a chance to accumulate interest. 4.5 a. Interest is the current income you receive from placing available funds in a savings account, CD, bond, or by making a loan. It is in effect the rent paid on your money by those who obtain use of it. b. Simple interest is interest paid (earned) only on the initial balance for the actual amount of time it is on deposit. With simple interest, the stated interest rate is always equal to the true rate of interest (or return). c. Compound interest is interest paid not only on the initial deposit but also on interest accumulated from one period to the next. This is the method savings institutions generally employ. When interest is compounded annually, the simple, compound, and true rate of interest are the same. d. The true rate of interest (or return) takes the concept of compounding into account. When interest is compounded annually, the stated and true interest rates are equal. For more frequent compounding, the "true" rate of interest would be higher than the stated rate. Hence an APR of 15% on a credit card which is compounded daily has a true interest rate of 16.18%. 4.6 The true rate of interest rises as interest is compounded more frequently than annually. The true and stated rates are the same when interest is compounded annually. Continuous compounding occurs when interest is compounded over the smallest possible time period. 4.7 The future value of a cash flow represents the amount to which a current deposit will grow over a given time period if it is placed in an account paying compound interest. Present value is concerned with finding the current value of a future sum, given that the investor earns a stated return the discount rate (or opportunity cost) on similar investments. The discount rate is the rate at which future sums are discounted to find their present values. The present value concept is the inverse of the future value concept. 4.8 An annuity is a stream of equal cash flows that occur in equal intervals over time. These cash flows can be paid out or received. An ordinary annuity has cash flows occur at the end of each year. To simplify the calculation of the future value of an annuity, one can use the future value interest factor of the annuity table included in Appendix A, Table A.2. The present value of an annuity can be found similarly in the present-value interest factor of the annuity table in Appendix A, Table A.4. 4.9 A mixed stream of returns is a series of returns that exhibits no pattern. To find the present value of a mixed stream, calculate the present value of each component of the mixed stream. The summation of the present value of individual components gives us the present value of the entire mixed stream. 4.10 Ignoring risk, a satisfactory investment is one for which the present value of benefits (discounted) equals or exceeds the present value of costs. If the present value of benefits exceeds the cost, the investor would earn more than the discount rate i.e. the return on the investment is greater than the discount rate. Fundamentals of Investing, by Gitman and Joehnk 2
4.11 a. The real rate of return is the return earned in a certain, risk-free world. It would equal the nominal rate of return on a risk-free security less inflation. For risky securities, it would equal the nominal rate less inflation (plus risk premium). b. The expected inflation premium represents the expected average future rate of inflation. It is the compensation that investors demand for future expected inflation. c. The risk premium varies for different security issues and represents the additional return required to compensate an investor for the risk characteristics of the issue and the issuer. It is the return on a risk security (e.g. stocks, bonds) minus the risk-free rate of return, which is the rate on a 90-day T-Bill. The risk-free rate of return equals the real rate of return plus the expected inflation premium: R F = r* + IP. It is the return on a riskless security as measured by the 90-day T-Bill. The required rate of return equals the real rate of return plus the expected inflation premium (together, the risk-free rate) and the risk premium: r i = R F + IP. OR it equals the risk-free rate of return plus the risk premium. 4.12 The holding period is simply the period of time over which the investor wishes to measure the return on an investment. In comparing alternative investment vehicles, it is essential to use equal-length holding periods so that the two vehicles being compared are judged under identical conditions. This adds objectivity to the comparison. Most interest rates are quoted on an annual basis, so it is generally convenient to use a one-year holding period. The holding period return (HPR) is the total return earned from holding an investment for a specified period of time. To calculate HPR, all that is needed is the beginning- and end-ofperiod investment values along with the value of current income received by the investor. Because HPR doesn t account for the time value of money, the holding period is usually one year or less. 4.13 The yield, or IRR, is the annual rate of return earned by a long-term investment. It is also defined as the discount rate that produces a present value of benefits received equal to the present value of costs/investments. Unlike the HPR, it takes into account the time value of money and can be used to calculate the return on investments held for over one year. The HPR is inappropriate for investments held for more than one year. 4.14 The critical assumption underlying the use of yield as a return measure is an ability to earn a return equal to the calculated yield on all income received from the investment during the holding period. If you earn 10 percent on all income received from an investment during the holding period, your yield on the investment will be 10 percent. On the other hand, if you earn 0 percent on the income received, your rate of return on the investment would actually be less than 10 percent. If the interest-on-interest earned from the investment is less than its calculated yield, the investment s return will fall below the yield. Clearly when using yield as a measure of investment return, the validity of this assumption must be recognized and evaluated. If the interest-on-interest assumption does not hold, use of the calculated yield could lead to poor investment decisions. (Note: The instructor may want to use the discussion of interest-on-interest and Figure 4.1 to demonstrate this somewhat complex, but extremely important, yield concept.) 4.15 If the present value of returns from an investment is greater than the initial cost of the investment, it is a satisfactory investment and should be acceptable. If the yield from an Fundamentals of Investing, by Gitman and Joehnk 3
investment is greater than the appropriate discount rate for that investment, the present value and yield provide the same conclusion regarding acceptability. In the example given, Investment A is clearly acceptable since its yield (8 percent) is greater than the appropriate discount rate (7 percent). Investment B, on the other hand, is not acceptable since its present value of returns ($150) is $10 less than its cost ($160). Investment C is not acceptable since its yield (8 percent) is lower than the appropriate discount rate (9 percent). 4.16 Risk is the chance that the actual return from an investment may differ from what is expected. The standard deviation is the statistic used to measure risk. The risk-return tradeoff is the relationship between the expected returns from an investment and the risk associated with them. The required returns from an investment increase as risk increases to provide an incentive for him or her to take higher risks i.e. in order to accept higher risks, the investors have to be compensated with higher returns. 4.17 a. Business risk is concerned with the degree of uncertainty associated with an investment s earnings and the investment s ability to pay investors interest, dividends, and other returns owed them. Business risk is usually related to the firm s line of business. b. Financial risk is the risk associated with the mix of debt and equity (capital structure) used to finance the firm. The greater the firm s debts and interest obligations, the greater its financial risk. c. Purchasing power risk arises because of uncertain inflation rates and price-level changes in the future. When prices rise, each dollar invested has less value it can buy less, and vice versa. d. Interest rate risk is risk associated with changes in the prices of fixed-income securities resulting from changing market interest rates. As the market interest rates change, the prices of these securities change in the opposite direction, thereby changing the level of return that an investor can expect to obtain from them. Another important aspect of interest rate risk involves the ability to reinvest income received at the initial rate of return in order to earn the fully compounded rate of return. e. Liquidity risk is the risk of not being able to liquidate an investment conveniently and at a reasonable price. In general, investment vehicles traded in markets with small demand and supply characteristics tend to be less liquid than those traded in broad markets. f. Tax risk is the risk that tax laws enacted by Congress will adversely affect certain types of investments and decrease their after-tax returns. g. Market risk is the risk of changes in investment returns caused by factors independent of the given investment vehicle. It results from factors such as political, economic, and social events, or changes in investor tastes and preferences. h. Event risk is the risk that comes from a largely or totally unexpected event which has a significant and usually immediate effect on the underlying value of an investment. The effect of this risk seems to be isolated in most cases, affecting only certain companies and properties. 4.18 Standard deviation is the most common measure of an asset s risk. It measures the dispersion of returns around an asset s average or expected return. Standard deviation is an absolute measure of risk, and thus can be used to compare the riskiness of competing investments with the same expected return. The coefficient of variation (CV) measures the relative dispersion of an asset s average or expected returns. Like standard deviation, the higher the CV, the higher the risk. CV Fundamentals of Investing, by Gitman and Joehnk 4
differs from standard deviation because it is a relative measure of risk and can be used to compare the riskiness of competing investments with different expected returns. 4.19 Investors attitudes toward risk or their risk-return tradeoffs may be classified as one of the following: Risk-indifferent investors do not require a greater return in exchange for each unit of additional risk. Risk-averse investors require greater return in exchange for each unit of additional risk. The trade-off here is positive; return must increase as risk increases. Risk-taking investors accept a lower return in exchange for greater risk. This tradeoff is negative; such investors enjoy risk and are therefore willing to accept lower returns for increasing levels of risk. In general, most investors are risk-averse. They require increased returns from an investment as its risk increases. The risk preference of an investor is an important determinant of his/her investment decisions. Risk-averse investors may not make speculative investments, while risk-taking investors may. Thus, an investment that is considered unsatisfactory by a risk-averse investor may be deemed satisfactory by a risk-taking investor. 4.20 The answer to the first part depends on the risk tolerance of the student. a. If the investor is conservative, the appropriate investment vehicles would be U.S. Government securities, savings accounts, Certificate of Deposits and high-quality bonds. b. If the investor is a moderate risk taker, the appropriate investment vehicles include bonds, preferred stocks, convertible securities, mutual funds and blue-chip common stocks. c. An aggressive investor can put his/her money in investment vehicles such as volatile stocks, real estate, and speculative securities such as options and futures. 4.21 The investment process can be summarized in four steps: (1) Estimate the expected return over a given holding period using historical data or projected return data, or both. The time value of these returns must be considered for long-term investments. (2) Assess the risk of the investment returns through the subjective (judgmental) evaluation of historical returns and by using beta (for securities). (3) Evaluate the risk-return behavior of each alternative investment. The expected return must be reasonable given the level of risk possessed by the investment. Only investments offering the highest expected return for a given level of risk are considered reasonable. (4) Select the vehicles with the highest return for the level of risk the investor is willing to take. These fit the definition of a good investment. Fundamentals of Investing, by Gitman and Joehnk 5