This Document Contains Chapters 5 to 7 CHAPTER 5 THE TIME VALUE OF MONEY CHAPTER IN PERSPECTIVE In this first chapter of Part Two entitled “Value,” the time dimension of value is developed. The scope of business decisions covers a considerable period of time. The values of cash flows related to those decisions occurring over this wide time period are affected by the time value of money. Most decisions focus on doing something today, such as making an investment, with returns flowing over future time periods. It is important for students to understand that cash flows in different time periods are not comparable and must be adjusted to a common time period, usually to the present, before comparison and analyses can be performed. This adjustment reflects the opportunity cost of alternative investments. This chapter initiates the analytical or arithmetical dimension of business finance and at least half of your class is terrified of arithmetic and has poor problem-solving skills. This is the chapter where we make it or break it for those students. If they limp away from this chapter, the next is worse for them. Their anxiety must be calmed here or they are lost. How is that accomplished you ask? You have made the first step when you adopted this text. It starts simply with compound interest and slowly builds. Arithmetic expressions, which half the class cannot visualize, are talked through, displayed visually via graphs, and simplified. Unknowns or “what am I solving for” has plagued half of your students since fourth grade. They have always guessed (what table should I use?), so work with these people. Visual time line analysis, discussed in a later teaching note, is a very valuable pedagogical tool that works. The student who cannot conceptualize the problem or unknown now can “see” it. Try it. It is also crucial that students read this chapter with a pencil and paper and solve the problems. Encourage them to try the Check Point questions as they go through the material. Stress to them that reading the solution to a problem before attempting to solve it cheats them of a key component of the learning process: the experience of analyzing the question and pondering the solution. We find that students often know how to solve the question but lack confidence about their answer. This is the time to build confidence. One other tip that we can offer: When we give out solutions to problems, we say something like this, “Give these solutions to someone you trust, like your mother, boyfriend or girlfriend. Tell this trusted person to refuse to return the answers until you have really tried to answer the problems. This means that you’ve read the problem and tried to answer it. If you aren’t really confident that you’ve go it right, read your notes and the textbook and try the question again. If you are still unsure, talk about with a classmate or 5-1 This Document Contains Chapters 5 to 7 the instructor. Only then, when you are sure you’ve done all that you can to answer the problem, ask your trusted person to let you see the answer. Remember, you won’t have the solutions when you write the midterm and final exams and certainly won’t have it when you are on the job!!!” This is the first “valuation” chapter and we carefully seed the chapter with valuation concepts, ideas, examples, etc., that will be presented formally in the next few chapters. Review the concepts to come in the next couple of chapters and treat this chapter as a building block to accomplish understanding of the valuation process. It may eliminate the boredom of teaching time value if we understand the students’ perspective and arithmetic anxiety and the connection to valuation concepts, the heart of finance, which all come in the next chapter. The time value of money concepts above assume no inflation or, another way, assumes a constant purchasing power in any future period. A present value dollar reflects the real opportunity costs (rates) equivalency of having cash now (at present). The growth or interest rate associated with accumulating future values are “real” rates—thus no inflation! In the second-last section of the chapter the impact of inflation on dollars received or paid across time periods is considered. Such is an extension of the time value concept. Now the cash flows received over a time line have different purchasing power of real goods. How are adjustments made? Previous time value rates (real) now must be adjusted for an assumed decline (constant rate) in purchasing power. Nominal rates (those observed in financial markets and used in chapter problems) reflect time value “real” rates plus expected inflation! Be careful to establish the time value (real) understanding before the inflation adjustments are added. This is the first text that has approached time value and inflation in the same chapter. Inflation implications are best introduced here, but the time value concept must be clear before the inflation impact concepts are added. CHAPTER OUTLINE 5.1 FUTURE VALUES AND COMPOUND INTEREST 5.2 PRESENT VALUES Finding the Interest Rate Finding the Investment Period 5.3 MULTIPLE CASH FLOWS Future Value of Multiple Cash Flows 5-2 Present Value of Multiple Cash Flows 5.4 LEVEL CASH FLOWS: PERPETUITIES AND ANNUITIES How to Value Perpetuities How to Value Annuities Annuities Due Future Value of an Annuity Cash Flows Growing at a Constant Rate – Variations on Perpetuities and Annuities 5.5 INFLATION AND THE TIME VALUE OF MONEY Real Versus Nominal Cash Flows Inflation and Interest Rates Valuing Real Cash Payments Real or Nominal? 5.6 EFFECTIVE ANNUAL INTEREST RATES 5.7 SUMMARY TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 5.1 FUTURE VALUES AND COMPOUND INTEREST A. Cash flows occurring in different time periods are not comparable unless adjusted for time value. B. The future value is the amount to which an investment will grow after earning interest. Future value = investment × (1+r)t. 5-3 C. The expression, (1+r)t, refers to compound interest or interest earned on interest at the rate, r, for t periods. An investment of $100 for five years at 6 percent interest, compounded annually would be $100 × (1.06)5 = $133.82, with the $33.82 representing the accumulated interest. D. If the $100 investment above earned 6 percent simple interest, or annual interest on the original investment, the sum of the original $100 plus accumulated simple interest of $100 × (.06) = $6.00 × five years = $30.00 would be $130. Note that with compound interest an additional $3.82 is earned in the five-year period. See Table 5.1 and Figure 5.1 for arithmetic and graphical analyses, respectively. Year Balance at Start of Year Interest Earned during Year Balance at End of Year 1 2 3 4 5 $100.00 $106.00 $112.36 $119.10 $126.25 .06 × $100.00 = $6.00 .06 × $106.00 = $6.36 .06 × $112.36 = $6.74 .06 × $119.10 = $7.15 .06 × $126.25 = $7.57 $106.00 $112.36 $119.10 $126.25 $133.82 E. In addition to the future value factors in Table 5.2, future values for a larger range of years and interest rates are found in Table A.1 at the Online Learning Centre, www.mcgrawhill.ca/college/brealey. 5.2 PRESENT VALUES A. The value today of a future cash flow is called the present value. The present value computation solves for the original investment at a certain rate when one knows the future value. The present value is the reciprocal of the future value calculation. Present value (1+r)t = future value, while the present value (PV) = 1/(1+r)t × future value. 5-4 B. The interest rate used to compute present values of future cash flows is called the discount rate. This will be an important variable when value determination is studied in the next chapter. C. Present values are directly related to the future cash flows and inversely related to the discount rate, r, and time, t. The higher the future cash flows, the higher the PV; the higher the discount rate and longer the term, the lower the PV. D. The expression, 1/(1+r)t, is called a discount factor, which is the PV of a $1 future payment. Discount factors for whole number discount rates and years are calculated and available for use in Table 5.3 and in Table A.2 at the Online Learning Centre, www.mcgrawhill.ca/college/brealey. E. Cash flows occurring at different time periods are not comparable for financial decision-making. The cash flows must be time adjusted at an appropriate discount rate, usually to the “present” for comparison, summation, or other analysis. A time line presentation helps students visualize the concept. See Figure 5.4. 5-5 Finding the Interest Rate A. In the expression, PV = FV×(1+r)t, when the PV, FV, and t are known, (1+r) may be solved arithmetically. The discount rate calculated is also called the annual interest rate, growth rate, and internal rate of return, depending on the situation. Finding the Investment Period A. The expression PV = FV×(1+r)t can also be solved for t, the investment period, when the other values are known. 5.3 MULTIPLE CASH FLOWS Future Value of Multiple Cash Flows A. Many finance situations involve more than one cash flow. Whether they are equal, consecutive payments or irregular, unequal cash flows over time, they are referred to as a stream of cash flows. B. To find the value at some certain date of a stream of cash flows, calculate what each cash flow will be worth at that future date, and sum up these future values. Present Value of Multiple Cash Flows A. Calculating the present value of an unequal series of future cash flows is determined by summing the present values of each discounted single future cash flow. 5.4 LEVEL CASH FLOWS: PERPETUITIES AND ANNUITIES A. A future stream of cash flows associated with an investment may be compared or summed if adjusted to a common time period, usually the present (PV). B. The multiple cash flows may be the same amount and be equally spaced over the term, called an annuity, may be an annuity with cash flows assumed to be received forever, called a perpetuity, or the future cash flow stream may be unequal and intermittent over some future period. C. The future value of a sum of equal, annual (or every period) cash flows is the future value of an annuity. Annuity refers to equal, consecutive payments. An ordinary annuity assumes cash flows occur at the end of each period; an annuity due assumes they are paid at the beginning of the period. 5-6 D. The present value of a sum of equal, annual (or every period) cash flows is the present value of an annuity. E. The key point is that when discounted to the present, all future cash flows are standardized for comparison, for summing, and other analysis, such as net present value studied later. How to Value Perpetuities A. The present value of a never-ending equal stream of cash flows is called a perpetuity. B. The PV of a perpetuity is equal to the periodic cash flow divided by the appropriate discount rate, or PV (perpetuity) = cash payments discount rate = C r . How to Value Annuities A. An annuity is an equally spaced, level stream of cash flows, such as $50 per year for ten years. If cash flows occur at the end of each period, it is called an ordinary annuity. If cash flows occur at the beginning of each period, it is called an annuity due. Figure 5.10 assumes an ordinary annuity. B. The present value of an annuity is the difference between an immediate perpetuity and a delayed perpetuity. The delayed perpetuity’s cash flows start the first period after the end of the relevant annuity period. Arithmetically, the PV of a t year annuity is C × 1r − r ×(11 + r)t , where C represents the annuity cash flows per period, and r is the appropriate discount rate. The bracketed quantity in the formula above is called a present value annuity factor. Tables 5.4 and A.3, found at the Online Learning Centre, www.mcgrawhill.ca/college/brealey, have present value annuity factors with varied whole numbers r and t. Annuities Due A. A financial calculator refers to annuity cash flows as payments. The annuity default mode in the financial calculator is the ordinary, end-of-period, annuity. To switch to annuity due, there is usually a “due” or “beg” key. When in “due” mode, it will indicate so in the display. Remind students to check the display before the next problem to make sure the correct mode has been selected. See time line, Figure 5.12, for a comparison of an ordinary annuity versus an annuity due annuity. B. The present value sum of a series of consecutive, equal payments, C, paid at the 5-7 beginning of each period, is called the present value of an annuity due Present value of a $C annuity due = C × [1 + 1r − r ×(11+ r)t-1 ] C. A loan amortization problem uses the formula for the present value of an annuity, solving for C, the loan payment per period. If loan payments are made at the end of the month, use the formula for the present value of a regular (deferred) annuity. If loan payments are made at the beginning of the month, use the formula for the present value of an annuity due. D. Often loans are paid monthly. The adjustment of annual to more frequent payments or compounding is to multiply the annual t by the number of payments per year and use the appropriate interest rate for the period. A ten-year loan with monthly payments would have t = 12 × 10 = 120 payments and the monthly interest rate would have to be determined. We return to issue of determining interest rates when payments are made more frequently that once per year in Section 5.5, toward the end of the chapter. Future Value of an Annuity A. The present value sum of a series of consecutive, equal payments, C, is called the present value of an annuity or: Present Value of an Annuity = C × 1r − r ×(11 + r)t B. The future value sum of a series of consecutive, equal payments, C, is called the future value of an annuity, calculated by multiplying the present value of annuity, above, by (l+r)t or: Future Value of an Annuity = C × 1r − r × (11 + r)t × (1+r)t = C × (1 + r)t - 1 r C. With an ordinary annuity the cash flows (PMT or payments in a financial calculator) are assumed to flow at the end of the year. Cash Flows Growing at a Constant Rate – Variations on Perpetuities and Annuities A. When cash flows are not level over time but are growing at a constant rate, variations of the annuity formulas can be used. 5-8 B. The present value of a perpetual stream of cash flows growing at constant rate g is: Present value of a growing perpetuity = first cash payment discount rate - growth rate = C1 r - g , where C1 is the first payment, r is the discount rate and g is the constant growth rate of the cash flows. C. The present value of a finite stream of payments growing at constant rate g for T periods is: Present value of a growing annuity = rC1 - g × [1 - ( 1 + g 1 + r ) T] 5.5 INFLATION AND THE TIME VALUE OF MONEY A. Inflation is an overall general rise in the price level for goods and services. B. In the time value of money analysis above, interest rates were assumed to be “real” rates, and the cash flows over the time line were assumed to have the same purchasing power. With inflation the purchasing power of cash flows over a time line declines at the rate of inflation. Real Versus Nominal Cash Flows A. One measure of inflation is the Consumer Price Index (CPI). The annualized percentage increases in the CPI are a measure of the rate of inflation. B. Consumers and investors are concerned about the real value of $1 or the purchasing power of the dollar or investment return in a period of time. Inflation and Interest Rates A. Actual dollar prices or interest rates are called nominal dollars or interest rates. Bonds, loans, and most financial contracts are quoted in nominal interest rates. B. Nominal rates, adjusted for inflation in a period, are real interest rates, or the rate at which the purchasing power of an investment increases. C. The real rate of interest is calculated as follows: 5-9 1 + real interest rate = 1 + nominal rate 1+ inflation rate D. The approximate real rate is the nominal rate minus the inflation rate for the period: real interest rate ≈ nominal interest rate – inflation rate The approximation is most accurate when both the nominal interest rate and the inflation rate are low. E. Investors and lenders include expected inflation rates in nominal rates to compensate for the loss of purchasing power. F. Nominal rates include expected real rates of return plus expected inflation rates. Valuing Real Cash Payments A. Since nominal rates include real rates plus expected inflation, discounting nominal future cash flows by nominal rates will give the same answer as discounting real, expected-inflation-adjusted cash flows by the real interest rate. B. Current dollar cash flows must be discounted by the nominal interest rate; real cash flows must be discounted by the real interest rate. C. Expected inflation is a significant variable in retirement planning, tuition savings plans, choice of vocation, or any long-term financial planning. Even a low rate of inflation can have a major negative effect on people who will receive relatively fixed nominal income or returns. D. The actual purchasing power rate of return (real rate) on an investment is the nominal expected rate of return, 1+r, divided by 1 + the expected inflation rate. With high inflation, the realized real rate may be negative. Real or Nominal? Most financial analyses in this text will assume nominal rates and will discount nominal cash flows. When one set of cash flows are presented in real terms and another in nominal terms, you cannot combine or compare them directly. You must first convert one of the cash flows to match the other in order to compare, contrast, and mix the cash flows. Same holds for interest rates: real and nominal rates cannot be directly compared. Adjust one of them for inflation. Do not mix nominal and real or you will have garbage! 5-10 5.6 EFFECTIVE ANNUAL INTEREST RATES A. The effective annual interest rate (EAR) is the period interest rate annualized using compound interest. If the three-month period interest rate is 5 percent, the effective annual rate is 5 percent to the fourth power, for there are four three- month periods in a year or, (1.05)4 -1 = 21.55 percent. The exponent used is the number of periods, in this case three months, equal to one year. B. The effective annual interest rate is the annual interest rate equivalent to the period interest rate. In other words, investing at the period rate will give the exact same future value as investing at its effective annual equivalent rate. Use the EAR to ensure that the same interest rate is being used to value cash flows with different frequency of payment. C. The annual percentage rate (APR) is the period rate times the number of periods to complete a year or the interest rate that is annualized using simple interest. In the case above the three-month period rate of 5 percent times the number of three- month periods in a year, four, equals 20 percent, an annual percentage rate (APR). Another way, for any investment, 5 percent per three-month period using simple interest will equal the amount, say $100, times 5 percent times four to calculate the annualized amount of simple interest of $20.00. That works out to a $20/$100 = 20 percent APR. D. To convert an annual percentage rate (APR) to an effective annual rate, divide the APR, using our 20 percent rate above, by the number of annual interest periods (4), and annualize that period rate or 1.054 -1 = 21.55 percent. See Table 5.7 which calculates the effective rates for several compounding periods using a 6 percent APR. Compounding Period Periods Per Year Per-Period Interest Rate Growth Factor of Invested Funds Effective Annual Rate 1 year Semianually Quarterly Monthly Weekly Daily 1 2 4 12 52 365 6% 3 1.5 .5 .11538 .01644 1.06 1.032 = 1.0609 1.0154 = 1.061364 1.00512 = 1.061678 1.001153852 = 1.061800 1.0001644365 = 1.061831 6.0000% 6.0900 6.1364 6.1678 6.1800 6.1831 E. To summarize: If you have an APR and the number of payments per year is m, the effective annual equivalent is: EAR = 1 + APR m m - 1 Likewise, if the per period rate is i and there are m payment (or compounding) periods per year, the effective annual equivalent formula is also: 5-11 EAR = [1 + i] m- 1 If you have an EAR and want to determine the equivalent period rate, i, where interest is paid m times per year, the formula is: Period rate equivalent to an annual rate = i = (1 + EAR)1/m - 1 5.7 SUMMARY PEDAGOGICAL IDEAS General Teaching Note - As noted in the introduction to the chapter, the time line is an effective tool for visually analyzing a time value problem and identifying the unknown value in a problem. It is a good classroom tool and essential for tutoring sessions with students with conceptualization problems. Combined with a financial calculator, the student can identify the given parts of the problem, on the time line and calculator PV line, and if necessary determine the unknown through a process of elimination. Student Career Planning - Every business college course that a student takes gives them the opportunity to study entry-level position areas and career paths related to the field. They should approach every course as a career alternative, review it, and for many, eliminate the area. Eliminating career alternatives is a better strategy than looking for that “right one.” It keeps them flexible for opportunities. Encourage students to use your business finance course as a means for studying careers in finance even though it may not be their major. Many marketing majors find that financial services offer many opportunities, and later, opt for electives in your department. Almost every financial firm with a WWW home page has a section listing their entry-level positions. Give your students a new WWW address every day. A good starting point is the web site of the Financial Management Association (http://www.fma.org), which has an excellent “student” section with many “hot links” to careers and finance related items of interest to students. Another great “career” site is WetFeet.com (http://www.wetfeet.com). WetFeet.com discusses a wide range of finance and business careers, features a variety of companies each week, and provides video clips and chats with professionals in a variety of jobs. Print out the home page to circulate in class with the URL address highlighted. Assign a one-page review of the site or a career discussed on WetFeet. Internet Exercises - The theme of this chapter is the time value of money. There are many business and personal decisions that “should” utilize this concept. A search of the Internet using “financial calculators” links to many financial planning and personal sites with financial models with easy “plug and crank” operation. From home mortgage analysis to tuition savings plans, these available sites offer students a chance to see many 5-12 applications that use the time value concept. Ask your students to search for a few, or check out the ones in the text. Ask them what time value concept, for example, present value of annuity, is utilized in the models. 5-13 CHAPTER 6 VALUING BONDS CHAPTER IN PERSPECTIVE This chapter continues the cash flow and timing concepts in formal valuation of bonds. The valuation of bonds involves calculation of the present value of an expected annuity cash flow payments (interest) followed by the principal (face value, future value) at maturity. Bond yields, both promised (yield to maturity) and realized (holding period return) are discussed, as is the inverse relationship between bond prices and interest rates. The discounted cash-flow model, studied in the previous chapter, is extended to cover fixed rate bonds. Emphasize that the same concepts are applied in valuing financial assets: cash flows, timing of the cash flows, the riskiness or variability of cash flows and the discount rate needed to compensate for the risk. The market rates of return on bonds of different maturity are examined by first looking at the term structure of interest rates. A number of factors affecting the yield curve level and shape are introduced, including the expected inflation (from Chapter 5), expectations of future interest rates, interest rate risk, and the liquidity premium. In Appendix 6.B, found at the Online Learning Centre, www.mcgrawhill.ca/college/brealey, duration is examined. In Appendix 6.A, located in the textbook, theories of term structure are examined in more detail. The bond market quotations, both Treasury and corporate, from Globe and Mail are presented, providing plenty of examples for in-class work. CHAPTER OUTLINE 6.1 BONDS AND THE BOND MARKET Bond Market Data 6.2 INTEREST RATES AND BOND PRICES How Bond Prices Vary with Interest Rates 6.3 CURRENT YIELD AND YIELD TO MATURITY 6.4 BOND RATES OF RETURN Taxes and Rates of Return Multiperiod Rates of Return 6-1 6.5 THE YIELD CURVE Nominal and Real Rates of Interest The Determinants of the Yield Curve Expectations Theory Interest Rate Risk and the Liquidity Premium 6.6 CORPORATE BONDS AND THE RISK OF DEFAULT Variations in Corporate Bonds 6.7 SUMMARY APPENDIX 6.A: A MORE DETAILED LOOK AT THE YIELD CURVE APPENDIX 6.B: DURATION: MEASURING THE LIFE OF A BOND (Available in Connect) TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 6.1 BONDS AND THE BOND MARKET A. A bond is a debt security that obligates the borrower or issuer to make specified payments (periodic interest payments and return of principal) to the lender or investor. B. The bond promises to pay periodic interest or coupons to the bondholder at the contract rate of interest, called the coupon rate, plus return the face value or principal amount borrowed at maturity. C. For a fixed coupon rate bond, the coupon rate is constant throughout the life of the bond. The convention is to set the coupon rate to equal the bond’s market rate, or discount rate, at the time the bond is issued. Thereafter, the market rate may vary; the coupon rate, which determines the periodic interest payment, stays the same. D. Figure 6.1 shows the cash flows of a three-year bond with an annual 3.5 percent coupon rate. The coupon payments are .035 × 1000 = $35 per year and the 6-2 principal or face value of $1000 will be repaid at the end of the three years. Using a time line to present the cash flows allows the student to see the need for discounting. Bond Market Data A. Bond price quotes are available from The National Post and The Globe and Mail’s Report on Business websites. The Web sites for bond prices are www.financialpost.com/markets/data/bonds-canadian.html and www.globe investor.com/servlet/Page/document/v5/data/bonds . B. Government of Canada and corporate bond prices are quoted as percentage of face value. A quote of 103.86 translates to $1,038.60 for a $1,000 par value bond. C. Bonds are sold on a bid (dealer offer to buy) and ask (dealer offer to sell) basis. The investor can sell at the bid price and buy at the ask price. In order that the dealer makes money, the bid price is lower than the ask price. The dealer buys low and sells high, making money on the difference. This is called the bid-ask spread. D. Reported on the Globe website is the issuer, coupon rate, maturity date, closing bid price, yield to maturity and the price change from the previous day. Ask students to prove the yield to maturity as quoted. To get both bid and ask prices (as shown in Table 6.1), we had to use GlobeInvestor Gold (found at www.globeinvestorgold.com), also run by the Globe and Mail but is available only by subscription. E. Write a bond quote on the board and ask the students to list the variables for calculating the yield to maturity. The use of real, current bond quotes along with discussion of recent bond market activity stimulates students’ interest in the topic. F. The fact that coupon payments are paid in lumps, typically every 6 months, creates the need to adjust the bond price to include a partial coupon payment when the bond is bought between coupon payment dates. So, if a bond is purchased between coupon payment dates, the price paid is actually higher than the quoted price. The buyer pays the seller his/her share of the coupon, based on the fraction 6-3 of the time that has passed since the last coupon payment. As shown in Equation 6.1, the adjustment is equal to the total coupon multiplied by the number of days from the last coupon to the purchase date divided by the total number of days between the payment of coupons. This payment is called accrued interest. Bond price quoted without the accrued interest is called the clean bond price. If the accrued interest is included in the bond price, the price is called the dirty bond price. 6.2 INTEREST RATES AND BOND PRICES A. The price of a bond is the sum of the present values of the interest payment annuity plus the present value of the single cash flow or face value, usually $1000, at maturity. Using a financial calculator, solve for the present value with the coupon annuity expressed as a payment (PMT), the face value at maturity expressed as a single future value (FV), the discount rate () and the number of years to maturity (N). B. Bond coupons are usually paid semi-annually. To calculate the price of the bond on a semi-annual basis, halve the coupon annuity payment and double the maturity of the bond. Determining the correct discount rate is a source of confusion. The key is to know how the discount rate was originally calculated: as an APR or as an effective annual rate. Use the formulas from Chapter 5 to get the correct per-period discount rate. Figure 6.2 shows the cash flows of the 3.5%, 3- year bond with semi-annual compounding. How Bond Prices Vary with Interest Rates A. When the coupon rate equals the discount rate, the PV price equals the original face value. When market rates of interest are greater (less) than the coupon rate, the PV of the bond is less (greater) than the face value. Figure 6.4 shows how bond prices (PV) vary inversely with changes in market interest rates. 6-4 B. The intuition about bond price and coupon rate will help students remember the relationship between bond prices and interest rates: The bond sells at face value when its coupon rate equals to the market interest rate. Also, when the bond sells at its face value, its coupon rate is the rate of return earned by the investor. If market interest rate rises and the bond price does not change, now the bond’s rate of return (and its coupon rate) is less than the market rate. No one will want to buy the bond and its price must fall. When the bond price is lower, the bond's rate of return will be higher, compensating for its low coupon rate. Likewise, if the market interest rate falls and the bond price does not change, the bond’s rate of return (and its coupon rate) is greater than the market rate. Everyone will want to buy the bond and its price is pushed up, resulting in a rate of return of an investor who buys the higher-priced bond. 6.3 CURRENT YIELD AND YIELD TO MATURITY A. The current yield, calculated by dividing the annual coupon interest by the price of the bond, is a rough approximation of the expected return on the bond. The current yield assumes that one will hold the bond forever or that the bond is a perpetuity. B. A better estimate of the expected return on the bond is the yield to maturity or YTM. The YTM is the interest rate for which the PV of the bond cash flows (coupons and face value) equals the current bond price. The YTM is the approximate market rate of return and assumes that one will hold the bond until maturity. 6-5 C. The complicated nature of the cash flows of the bond (the annuity plus the principal) makes it necessary to estimate the YTM rather than calculate it. It can be estimated using trial-and-error (pick a discount rate and see if it makes the bond’s cash flows equal to its price or present value). Using a financial calculator is the most common and easiest way to estimate the YTM. Enter the current price (PV), coupon payment (PMT), principal (FV) and the number of years to maturity (n) and compute the yield to maturity (i or r). D. Bond coupon rates, for fixed rate bonds, determine the amount of annual coupon and remain the same over the life of the bond. Market interest rates, discount rates, and current borrowing rates change every day. Bond prices vary to give the new bond buyer the market rate of return. 6.4 BOND RATES OF RETURN A. If the bond is sold before maturity, the seller will receive the market price, which, depending on the direction of market rates since the bond was issued, will be higher or lower than face value. This is one dimension of interest rate risk or the variability of return from the expected YTM caused by selling the bond before maturity. B. The rate of return on a bond equals the coupon income plus the price change divided by the initial investment in the bond. The actual rate of return earned on the bond investment or the realized holding period return on the bond may be higher or lower than the YTM. Rate of return = coupon income + price change Investment C. The rate of return is different from the yield to maturity, which is the discount rate that equates the bond’s future cash flows to its current price. You can introduce the term "holding period rate of return", to distinguish the rate of return earned on a bond investment from its yield to maturity. D. If the yield to maturity stays constant during an investment period, then the bond’s rate of return will equal that yield. For the yield to maturity to not change, the market interest rate must also be constant. E. If YTM increases (market interest rates increases), the bond’s rate of return during that period will be less than the YTM. If the YTM decreases, the rate of return will be greater than the yield. F. Prices of both premium and discount bonds approach face value as their maturity 6-6 date approaches (Figure 6.5). Taxes and Rates of Return A. Taxes reduce the rate of return on a bond investment. B. Coupon payments are taxed as interest income and the difference between the purchase price and the selling price (or face value if the bond is held to maturity) is either a capital gain or a capital loss. C. In Chapter 3 we discussed the tax rates on different types of income. Interest income is taxed at the full personal or corporate tax rate. Capital gains are taxed at one-half the full tax rate and capital losses can only be used to offset capital gains. D. To calculate the after-tax rate of return, convert each cash flow into its after-tax amount and then divide by the investment or initial price paid: After-tax Rate of return = after-tax coupon income + after-tax capital gain Investment Multiperiod Rates of Return A. When looking at the before- or after-tax rate of return over a multi-year investment period, it is necessary to make an assumption about the reinvestment of intermediate coupon payments in order that their future value at the end of the investment period be calculated. Several approaches are possible: (1) assume the coupon payments are spent and not reinvested. In this case, their future value is simply their sum. (2) If you know the rates at which they were reinvested, use them to calculate the future value of the coupons. (3) Use the “yield-to-maturity” method to calculate the rate of return: find the discount rate that equates the bond’s cash flows (either before or after-tax) to the price paid to buy the bond. 6-7 This method assumes that all intermediate cash flows are reinvested at the same rate. 6.5 THE YIELD CURVE A. The yield curve or the term structure of interest rates is a plot of an issuer’s, such as the Canadian Government, bond yields (YTM) by time to maturity. B. Expectations of future interest rates have a significant impact upon the level and shape of the yield curve. Expectations of higher future interest rates will produce an upward sloping yield curve. In addition, we expect the yield-to-maturity on longer-term bonds to be higher because of their greater interest rate risk. Nominal and Real Rates of Interest A. In Chapter 5 the difference between real and nominal rates of interest was presented. B. Cash flows of bonds are nominal and hence the yield-to-maturity and the bond’s rate of return are also nominal. C. According to Fisher, the real rate of interest is determined by the supply of savings and demand for new investment. The real side of the economy drives the real rate of interest. According Fisher's theory, the rate of inflation does not affect the real rate of interest. D. Following Fisher's theory, the nominal rate of interest is determined by the real rate of interest and expected rate of inflation. This is known as the Fisher effect: 1 + nominal interest rate = (1 + real interest rate) × (1 + expected inflation rate) E. Using the Fisher effect, the real yield to maturity of the bond can be calculated using the following formula: real YTM = 1+ 1 + YTM inflation rate - 1 Likewise, the real rate of return is one plus the nominal rate of return divided by one plus the inflation rate, all minus one. F. Real return or indexed bonds, with coupon and principal linked to the rate of inflation, guarantee investors a real rate of return. The coupon is determined each 6-8 period by the Consumer Price Index (CPI). G. Real return bonds have been issued by the Canadian federal government, the U.S. government, the United Kingdom and by some corporate issuers. H. The nominal and real yield on real return bonds shown in Figure 6.7 shows the dramatic impact of inflation on nominal yields. As inflation fell during the 1990s, so did the nominal yield on the long-term bonds. However, the figure also suggests that inflation may affect the real rate of interest. Although the real yield was less variable than the nominal yield, it too fell over the 1990s. If firms real investment decisions are affected by expected inflation, then Fisher's theory that real rates are unaffected by inflation may be wrong. The Determinants of the Yield Curve A. The general level of interest rates, and hence the level of the yield curve, is largely determined by the real rate of interest and expected rate of inflation. The shape of the yield curve, the difference between yields on longer-term and shorter-term bonds, is driven by expected inflation and interest-rate risk. Expectations Theory A. According to the expectations theory, the difference between the yield on a long- term bond and a short-term bond is driven by expected future interest rates. If the market expects future short-term interest rates to be higher than today, then the current yield to maturity on the longer bond will have to be higher than the current yield on the shorter bond. B. Since expected inflation is a key driver of interest rates, a major factor determining expected future interest rates is the expected inflation rate. C. According to the expectations hypothesis, the shape of the yield curve reveals the market's current expectation of future interest rates and inflation. D. To see an example, look at Appendix 6.A, A More Detailed Look at the Yield Curve, found at the end of the chapter. Interest Rate Risk and the Liquidity Premium A. The expectations theory is not a complete explanation of the yield curve as it does not consider risk. B. Bond prices (PV) vary inversely with changes in market interest rates. Bondholders hope that market interest rate will fall so that price of their bonds 6-9 will rise. Likewise, they hope that market interest rates won't rise and cause bond prices to fall. C. The variation in bond prices due to changes in interest rates is called interest rate risk. D. The longer (shorter) the maturity of the bond, the greater (less) the change in the bond price for every change in bond discount rates. Thus longer-term bonds have more interest rate risk than shorter-term bonds. E. The higher the coupon rate, the greater the change in the bond price for every change in bond discount rates. In Appendix 6.B, Duration: Measuring the Life of a Bond, found at the Online Learning Centre, www.mcgrawhill.ca/college/brealey, details on why bond prices vary with coupon rates and introduces the concept of duration. The higher the coupon rate, the greater the interest rate risk. F. Investors who do not like price fluctuations can invest their funds in short term bonds and reduce their interest rate risk. Thus longer-term bonds and higher coupon rate bonds must have a higher yield to compensate investors for the greater interest rate risk. This extra return is called the liquidity premium. G. According to the liquidity preference theory, the yield curve is upward sloping because investors require compensation for interest rate risk. H. With expected inflation and the liquidity premium, the yield curve will tend to be upward sloping. However, if future interest rates are expected to fall, due to lower expected inflation (or even deflation), the yield curve can be downward sloping. However, with the liquidity premium, impact of lower expected future interest rates will be at least partially offset. 6.6 CORPORATE BONDS AND THE RISK OF DEFAULT A. The market yield to maturity on bonds, other than Government of Canada bonds, includes a default or credit risk premium, or added yield to cover the market’s expected default loss on risk bonds. B. The credit risk premium is the difference between the yield on a risky bond and a Canada bond of similar maturity. C. The higher the expected loss in yield from the risky bond, the higher the credit risk premium. D. Bond rating firms, like the Dominion Bond Rating Service (DBRS), Moody’s and Standard and Poor’s, rate the default risk of risky bonds. 6-10 E. High investment grades are in the range from AAA (or Aaa) to BBB (or Baa); speculative or junk bonds are rated below BBB (Baa). F. See Figure 6.9 for a graph of the default risk premia on various risk bonds over time. The vertical distance between yields on securities of varying default risk is the default risk premium at a point in time. Variations in Corporate Bonds A. Not all bonds are the plain vanilla type, with fixed coupon rates and fixed maturity dates. B. Variations in the coupon rates include zero coupon bonds and floating-rate bonds. C. Variations in the maturity date include convertible bonds and callable bonds. D. When a company has an option to pay of the bonds early, they are said to hold a call option or the bonds are callable. E. Callable bonds will likely be called when interest rates decline, unless they have a Canada (or Doomsday) call. With a Canada call, the bond's call price is determined by prevailing interest rates, making it less attractive for the issuer to call the bond. F. Investors demand a higher yield on callable bond, for the investor is faces reinvestment risk (reinvested at a lower rate) on high coupon callable bonds. G. The yield to nearest call date is a practical estimated yield on a callable bond. 6.7 SUMMARY PEDAGOGICAL IDEAS General Teaching Note - When discussing and calculating yields and the real interest rate concept, students often confuse expected, or ex ante, with realized, or ex post. The yield to maturity (YTM) is an expected yield that assumes away the reinvestment risk component of interest rate risk. The YTM will be realized if interim cash flows, coupon payments, are reinvested at the YTM. The realized holding period yield or the bond rate of return is calculated ex post, after the fact. In the case of the real rate concept, we usually note that nominal rates include expected real rates plus expected inflation. Realized real rates, ex post, represent the holding period, nominal rate of return adjusted for the actual inflation in the period. In both cases the use of the time line helps students see the different time perspective of the expected and realized concepts. 6-11 Student Career Planning - Writing and oral communication skills are developed and honed over a college or university career and should peak, about graduation time. Most required courses in the area were taken in the first or second year, and given the practice of the student, may not be what the marketplace demands today. Business writing courses are provided for students in many colleges and universities. Oral communication skills develop with classroom involvement and presentations, leadership in student organizations, part-time sales jobs, and telling a good joke! Writing skills are kept at their best with daily class writing assignments, writing a letter home, penning a thank you, or a love letter. Remind students that their communications skills development is part of your course, but the responsibility for their development lies with the student. Remind them of ten powerful two-letter words, “If it is to be, it is up to me.” Encourage your students to allocate time for career planning. Most of our personal planning has been done very informally, occasionally, or when we were in a crunch and had to! Many students have not assigned planning as a high priority in their “To Do” list. But time is running out. All of their focus for the last eight years has been toward their college or university degree. Aside from clearing up some details, like this course, graduation and the opportunity to realize their life-long dream is here. College is structured; the afterward is not! Students will say, “I cannot plan. Anything can happen.” The response is, “Anything will happen if you do not plan.” Planning, if not structured, will be assigned a low priority. To structure means a regular time, place, and possibly a small notebook to jot down brainstorming ideas and eventually the student’s “plan.” Suggest placing their notebook by their bed, desk, or “wherever” so that it is staring at them. Eventually, hopefully sooner than later, they will begin to 1) think about the future, 2) think about their goals, and 3) begin to formulate written, time-based plans! Note that no one has forty hours to do the job. It must be completed in many five- or ten-minute parcels of time. Suggest they start now! A good beginning question is, “Can you visualize your typical day five years from now?” Internet Exercises - While there are many “stock-focused” sites on the Internet, there are few good “bond” sites. Here are two excellent sites that provide good, basic information about bonds, glossaries of terms, yield curves, bond calculators, and much more. Each site is excellent for a “show and tell” classroom presentation or for a class assignment. Warning: these are US websites. For Canadian data, see the websites listed below. SmartMoney.com http://www.smartmoney.com SmartMoney.com is the Internet equivalent of the popular magazine. For our interest in this chapter, SmartMoney.com has an excellent “bond” link providing current bond market updates, a primer on bonds for beginning students, investor information and strategy, a “living yield curve” that works very well for classroom instruction, and a bond 6-12 calculator that is a fantastic “demo” for the classroom. Change the price and watch the change in bond yields! A great site overall, SmartMoney.com, a Dow Jones entity, has one of the best “bond” sites on the Internet. BondsOnLine.com http://www.bondsonline.com BondsOnLine.com is another bond site. It offers information on trading bonds in its "Educated Investor Center". Unfortunately, as is the case for many sites, it charges a fee bond prices and yields. Canadian Bond data http://www.pfin.ca/canadianfixedincome/Default.aspx Provides yields on selected bonds at no charge. Bond data is available to subscribers to GlobeInvestor Gold, www.globeinvestorgold.com, an online investor resource. The subscription also gives access to current and historical stock prices for Canadian listed stocks. 6-13 CHAPTER 7 VALUING STOCKS CHAPTER IN PERSPECTIVE The previous chapter focused on the valuation of bonds where the cash flows are contractual and determinable. This chapter continues the valuation study to non- contractual and varied future cash flows of common stock. The authors start the chapter with RIM which story is told in Chapter 1.Covering an increasingly complex variety of cash-flow patterns from constant dollar (no-growth), constant growth (Gordon Model), and growth over a specific time period, we provide valuation techniques for a variety of common stock and business cash-flow patterns. The chapters that follow apply these concepts to specific value-creating, cash-flow generating projects. As in the previous chapter, the required/expected rate of return concept is reinforced. These rate-of-return discussions provide an important building block for the later study of capital budgeting and risk analysis. Another important concept covered in this chapter is market efficiency. Methods used by investors for identifying opportunities to "beat the market" are discussed and evidence on their success is provided. Varying degrees of efficiency are covered, as are classic issues such as timing, insider trading and other issues related to less than efficient markets. The students may have encountered the efficient markets concept in their microeconomics course. Comparing the pure competitive model of economics with the efficient markets discussion with multiple period decision periods and variability of results of decisions (risk) helps students make the transition from prior knowledge to this chapter. CHAPTER OUTLINE 7.1 STOCKS AND THE STOCK MARKET Reading Stock Market Listings 7.2 MARKET VALUES, BOOK VALUES, AND LIQUIDATION VALUES 7.3 VALUING COMMON STOCKS Valuation by Comparables Price and Intrinsic Value 7-1 The Dividend Discount Model 7.4 SIMPLIFYING THE DIVIDEND DISCOUNT MODEL The Dividend Discount Model with No Growth The Constant-Growth Dividend Discount Model Estimating Expected Rates of Return Non-Constant Growth 7.5 GROWTH STOCKS AND INCOME STOCKS 7.6 THERE ARE NO FREE LUNCHES ON BAY STREET Method 1: Technical Analysis Method 2: Fundamental Analysis A Theory to Fit the Facts 7.7 MARKET ANOMALIES AND BEHAVIOURAL FINANCE Market Anomalies Behavioural Finance 7.8 SUMMARY TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 7.1 STOCKS AND THE STOCK MARKET A. Financial markets provide a source of financing for businesses and governments. They also provide financial investment opportunities for individual and institutional investors. B. The initial, funds-raising sale of securities, usually with an investment banker, is in the primary market; subsequent trading between investors for liquidity, financial investing, and portfolio rebalancing is in the secondary market. 7-2 C. There are two types of primary market issues: an initial public offering or IPO and a seasoned offering. An IPO is the first sale of newly issued stock to “public” investors. The company receives the funds and investors receive the shares. We say the company “goes public” when it undertakes an IPO. A seasoned offering is the sale of additional shares by a company that has already gone public. In a seasoned offering, the company raises additional equity financing from investors who receive new shares in return. Reading Stock Market Listings A. Figure 7.1 lists the trading data for RIM, January 12, 2011. Note prices and price changes in dollars and cents. Since RIM pays no dividend the dividend and yield are reported as N/A (not available). If a company paid dividend what would be reported is an “annualized” quarterly (last) dividend, and the dividend yield as the annualized dividend divided by the closing price. B. Table 7.2 lists a number of stock quotations. Annualized dividends are in this table. If the company normally pays quarterly dividends, the reported dividend is four times its last quarterly dividend. The dividend yield is the annualized dividend divided by the closing price. B. Why do the dividend yields vary? Expected price appreciation and risk. C. The price-earnings (P/E) multiple is the closing price divided by the earnings per share. Commonly used in valuation assessment, the ratio indicates the number of years of current earnings the market is willing to pay to own the stock. For example, if the current price is $100 and the earnings per share are $10, the P/E multiple is 10. Given the current earnings per share, it would take 10 years for the stock to generate earnings equal to the current price, ignoring the time value of money! 7.2 MARKET VALUES, BOOK VALUES, AND LIQUIDATION VALUES A. Book value of common shares equals the accounting value of assets minus the accounting value of liabilities. B. Book value is biased toward historical or original costs. This reflects the accounting rules which govern how a company records its financial and operating transactions. C. Liquidation value of common shares represents the proceeds from the quick sale of individual assets minus liabilities owed. D. Going concern value represents the difference between a minimum liquidation 7-3 value and actual or “true” value (market), the worth of an on-going business by investors considering, (1) future earning power of existing tangible and intangible assets and (2) the value of future investment opportunities of the firm. E. Market value represents the value assigned a firm by investors in a reasonable market driven by the expected level and variability of cash flows. When the market/book ratio exceeds one, the economic value of the assets exceeds the accounting value or the expected rate of return to shareholders exceeds their minimally acceptable rate of return. A MARKET-VALUE BALANCE SHEET Assets Liabilities and Shareholders’ Equity Assets in place Investment Opportunities Market value of debt and other obligations Market value of shareholders’ equity 7.3 VALUING COMMON STOCKS Valuation by Comparables A. Investors and analysts compare price-to-earnings and price-to-book ratios for judging the value of a common stock and other multiples. B. All these ratios vary from stock to stock even for firms that are in the same line of business. It is important to understand what make the ratios different and what determines a stock’s value. Price and Intrinsic Value A. The expected and actual, realized rate of return to common stockholders comes from 1)cash dividends, DIV1, and 2) capital gains or losses, P1-P0. B. The intrinsic value of a stock is the present value of the stock’s expected future cash flows discounted at the expected rate of return. C. Investors compare expected returns, based on expected dividends and price changes, with minimum required returns, comparable returns on similar securities (opportunity costs). D. If expected returns exceed comparable returns elsewhere, investors will want to purchase the stock, bidding the price up and the expected return down to the minimum acceptable return. 7-4 E. At any market price, expected returns equal that required by investors. F. All securities of the same risk are priced to offer the same expected rate of return. G. If you know what the future dividend and selling price in one year will be, you can calculate the actual rate of return. With expected dividends and expected future price, you can calculate the expected rate of return. The rate of return is calculated as: Rate of return = DIV1 + Capital Gain P0 = DIV1 + P1 - P0 P0 = DIV1 P0 + Capital Gain P0 H. Taxes reduce the expected and actual rate of return earned on a stock investment. To calculate the after-tax rate of return, convert both dividends and capital gain to their after-tax amounts by subtracting the appropriate taxes: After-tax Rate of return = DIV1 - dividend tax P0 + Capital Gain - capital gains tax P0 The Dividend Discount Model A. The dividend discount model, or discounted cash flow model, states that share value equals the present value of all expected future dividends. B. With a specific investment time period or horizon, H, the intrinsic share value (value determined by the evidence) is shown in Equation 6.3: P0 = DIV1 + DIV22 +.... DIVHH + PH H 1+ r (1+ r) (1+ r) (1+ r) C. The stock price at the horizon date, PH, is the present value of cash dividends 7-5 received beyond the horizon date. D. As the horizon date changes, the present value of the stock will remain the same as dividends are expected to grow at the rate of “g” (see Example 7.3, Table 7.4, and Figure 7.2). E. At extreme horizon dates the present value of PH becomes insignificant; thus the dividend discount model share value equals the present value of future, expected dividends. 7.4 SIMPLIFYING THE DIVIDEND DISCOUNT MODEL The Dividend Discount Model with No Growth A. When all earnings are paid as cash dividends, no growth is possible (reinvestment = depreciation to maintain the current stock of capital). B. The stock value of a no-growth firm is the expected dividend capitalized (perpetuity) at the required rate of return or: P0 = DIV1 r C. Assuming all earnings are paid as dividends, P0 = r EPS1 where EPS1 represents next year’s earnings per share. The Constant-Growth Dividend Discount Model A. The Constant-Growth Discount Model is an arithmetic expression calculating the present value of a perpetual stream of cash flows, DIV, growing at a constant rate of growth, g, and discounted at a required rate of return, r: P0 = DIV1 r - g B. With a sustained positive growth rate in the economy and business activity, the Gordon Model and its assumptions are reasonable. 7-6 C. DIV1 represents the dividend received at the end of period one. D. The constant-growth formula is valid only when “g” is less than “r.” E. P0 is directly related to DIV1 and g; inversely related to r. Estimating Expected Rates of Return A. In constant-growth business situations, if g is capitalized in the market in higher stock prices, r may be a proxy for the market expected rate of return on similar risk situations. B. The expected rate of return is a combination of the dividend yield, DIV1/P0, and capital appreciation rate, g, or: 1 0 r = DIV + g P C. The required rate of return, r, is a market-determined rate related to the risk-free rate adjusted upward for risk, given expectations of DIV1 and g. The stock price, P0, adjusts to equate the market-expected rate with the required rate of return. Non-constant Growth A. The no-growth and constant-growth dividend discount models above assume two patterns of cash flows while reality presents the analyst with many variations. The dividend discount model is easily adapted. B. Changing future dividend patterns from non-growth to constant-growth to variable-growth rates over a given horizon requires that the analyst estimate the stock price by forecasting the cash-flow patterns and discounting the cash flows at the market-required rate of return. C. The terminal value, PH, represents the present value of the cash flows beyond the horizon. 7.5 GROWTH STOCKS AND INCOME STOCKS A. Income stock returns are derived from the dividend yield, DIV/price, and are associated with businesses with a high payout ratio, the fraction of earnings paid out as dividends. B. Growth stock returns are derived from a combination of no or relatively small 7-7 dividend yields (low payout ratio) and a high plowback ratio or earnings retention ratio (the proportion of current period earnings or free cash flow retained in firm), and earning high asset returns, in excess of that required by the market, on reinvested earnings. C. The sustainable growth rate, g, discussed in the constant-growth rate discussion above, relates to the expected asset returns on reinvested capital adjusted for the proportion of earnings plowed back into the firm. Dividends (payout ratio) limit the level of reinvested capital and the growth potential of future earnings and dividends. g = return on equity x plowback ratio, where the return on equity is the expected return on equity capital plowed back into earning assets. D. Similar stock prices ($41.67) will result from a 100 percent payout ratio and any less payout where the plowed back earnings earn just the required rate of return. E. When rates of return on reinvested capital exceed the required rate of return, added value, often called “value added” or the present value of growth opportunities or (PVGO), is capitalized in the market price of the stock. F. Higher price-earnings ratios are associated with higher expected growth opportunities and lower earnings-price ratios (earnings yield), reflecting that some portion of the required rate of return is expected to be derived from growth opportunities. G. Expected future earnings are expected cash flows less any reinvestment associated with the economic depreciation of earning assets or earnings (cash flow) above that needed to maintain the earning power of the firm. 7.6 THERE ARE NO FREE LUNCHES ON BAY STREET Some students may expect to learn from this finance course how to make big money on the stock market. It is time to tell them that it is very difficult to beat the market. A. Does knowing how to value a stock allow an investor to make an instant fortune on the stock market? No, because the market is an excellent processor of information. B. Investors, seeking to find stocks that will earn superior returns, use various ways to analyze stocks. 7-8 Method 1: Technical Analysis A. Technical analysts attempt to find patterns in security price movements and trade accordingly. Their trading tends to quickly offset any price trend and keep the markets efficient. B. Research has shown time and again that security market price changes are unrelated to prior price changes with no predictable trends or patterns. The prices tend to be a random walk over time. See Figure 7.4. Method 2: Fundamental Analysis A. Fundamental analysts attempt to find under- or over-valued securities by analyzing “fundamental” information, such as earnings, asset values, etc., to uncover yet undiscovered information about the future of a business. They attempt to forecast the impact of the information; technical analysts are studying past prices, looking for predictable patterns. B. Unfortunately, with so many investors following the news, it is very difficult to consistently make superior returns by buying or selling stock after the announcement of news. C. Trading on corporate information before the news is released to the market may be a successful strategy to beat the market. However, if the information is from an insider of the company, including managers, employees and others with a close relationship to the company, it is inside information and illegal to trade on. Penalties for insider trading can be very heavy, including large fines and jail time. A Theory to Fit the Facts A. The stock market is an efficient market, where security prices rapidly reflect all relevant information, currently available, about asset values. B. Investors react quickly to new information, trying to take advantage of it. In the process, stock prices quickly adjust to the new information and eliminate the profit opportunities. C. The efficient-market theory implies that portfolio managers work in a very competitive market with little or no added advantage over the next portfolio manager. They make few extraordinary returns, not because they are incompetent, but because the markets are so competitive and there are few easy profits. There are no free lunches on Wall Street or Bay Street. 7-9 D. The efficient market theory implies that security market prices represent fair value. Fair market value changes with new information about the future cash flows associated with a security. E. The three degrees of efficiency are defined relative to three types of information. F. The first form of market efficiency is weak-form efficiency, where market prices rapidly reflect all information contained in the history of past prices. Past price movements are random; the past cannot predict future price changes. Technical analysis is valueless in a weak-form efficient market. G. A second form of market efficiency, semi-strong form efficiency, is a market situation in which market prices reflect all publicly available information. See Figure 7.7. New information is quickly reflected in the price of the stock, and investors were not able to earn superior returns by buying or selling after the announcement date. H. A third form of market efficiency, strong-form efficiency, is a situation in which prices rapidly reflect all information that could be used to determine true value. In this market-pricing situation, all securities would always be fairly priced and no investor would be able to make superior, accurate forecasts of future price changes. Even professional portfolio managers do not consistently outperform the market, thus supporting the creation of “index” portfolios, assembled to match popular market indices. 7.7 MARKET ANOMALIES AND BEHAVIOURAL FINANCE Market Anomalies A. It is time to start to point out that there are still many puzzles that remain unsolved in finance. Those puzzles are interesting and challenging. Therefore, it is time also to encourage students to start thinking about them. B. It seems that investors underreacted to the earnings announcement and became aware of the full significance only as further information arrived. That stock prices did not reflect all available information following the earnings- announcement is called the earnings announcement puzzle. C. On average the investors who receive new-issues receive an immediate capital gain, but these early gains often turn into losses. This phenomenon is the new- issue puzzle. Behavioral Finance A. Behavioural finance, a relatively new field of finance, attempts to explain stock 7-10 market performance using behavioural psychology. B. This approach rejects the notion of rational market investors. Instead investors' attitudes towards risk and beliefs about probabilities lead them to "irrational exuberance" and an over-valued stock market. C. Whether behavioural finance will help to better understand the stock market is still to be seen. In the mean time, it is difficult for investment managers and corporate management to spot mispriced securities. 7.8 SUMMARY PEDAGOGICAL IDEAS General Teaching Note – Students often have difficulty with the common stock valuation problems in business finance. We present them with at least two, and maybe more, valuation models, and they try to memorize each and understand the cash flow pattern behind the valuation model. Using a time line, present the Blue Skies stock valuation example under three assumptions. For the first, assume no growth, with a $3 perpetuity discounted at 12% or a value of $25. Show the cash flow pattern as part of the presentation. In the next, use the constant growth model pattern of cash flows and the calculated $75 price as the PV of a constantly growing stream of cash flows. Finally, add above average growth to Blue Skies for three years, then returning to an 8% growth rate. Show the time line and the added current value from the higher expected growth rate. Instead of trying to memorize, students are usually able to see that each “model” depends on the future cash flow pattern. The results are amazing! Student Career Planning – A student’s career planning should not begin the semester before graduation, but as they enter the Business School. This is an area where “sooner the better” pays off in knowing what career route is best for the student and finding that “career beginning job.” Take a minute at the beginning of the next class and introduce your students to the services of your campus Career Centre. It could be a pamphlet or an Internet address (print home page), but hearing about “starting early” from their professor may spur some action. Career Centres are focusing more and more on the developing student and preparedness for graduation, in addition to placement at graduation. They offer “skills inventory tests” that point students to various careers, provide internship information and opportunities, provide free seminars, alumni mentoring programs, part- time jobs “related” to the students’ major, and much more. You have considerable influence in recommending that “career planning” should be a part of and should start early in their business school education. Give your Career Centre a plug in the next class. A career internet exercise: http://college.wsj.com 7-11 The College.wsj.com site, sponsored by Dow Jones, reflects their attempt to support their thousands of college-age readers. This “career planning” site provides a variety of time articles, job seeking capability, salary data, resume assistance, and also job posting. Click on “Finance Jobs” and then can select Canada in the box at the top of the page. Students can explore the job market, see the job descriptions. This may motivate them to take a variety of electives for a finance career! 7-12 Instructor Manual for Fundamentals of Corporate Finance Richard A. Brealey, Stewart C. Myers, Alan J. Marcus, Elizabeth Maynes, Devashis Mitra 9780071320573, 9781259272011
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