Chapter 05 - R 1 R 2 R 3 R 4 R 5 R 6 CHAPTER 5 REVIEW...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. CHAPTER 5 REVIEW QUESTIONS An annuity is a series of equal cash flows through time. A perpetuity is a series of equal cash flows though time that continue forever. Therefore, a perpetuity is a special type of annuity. Pure discount securities are securities that pay a single cash flow. The return on the pure discount security is comprised of the difference between the purchase price and the security’s value at maturity or when sold. Treasury bills are discount securities issued by the US. Treasury because they offer no interim cash flow payments but instead are issued at a price below its par or maturity value. Bond prices are inversely related to changes in market interest rates, that is, rising interest rates reduce the value of outstanding bonds, and falling interest rates increase the value of outstanding bonds. When market interest rates rise, investors comparing already issued bonds with new bonds will place a higher value on the newly issued bonds. In this scenario, the price of the already issued bonds must fall to keep competitive with new bonds. In a similar way, the price of already issued bonds will rise when market interest rates fall because these bonds become more attractive when compared with newly issued bonds. Bonds paying interest on a semiannual basis will place dollars in the hands of the bond investor sooner than if interest were paid on an annual basis. Given the time value of money, paying semiannual interest makes a bond more valuable than it would be with annual coupon payments. A bond’s yield to maturity is the interest rate that discounts the promised future cash flows to a present value equal to the bond’s current price. The yield to maturity can be thought of as the average rate of return that would be earned on a bond each year if purchased at the current price and held to maturity. Determining the value of a bond means finding its price given the set of cash flows and the bond’s discount rate or required rate of return. Bonds, known also as fixed payment securities, offer a fixed stream of cash flows that are known to any bond investor. In contrast, the set of cash flows to be received by common stock investors are not fixed but rather are represented by the cash flow left over after the claims of all other people who contract through the corporation are satisfied. These residual cash flow amounts, when compared with a bond’s fixed payments, are more difficult to estimate. 22 R. 7. R. 8. R. 9. Related to question 6 above, the value of common stock requires estimates of residual cash flows. One simple model of common stock valuation is the no growth in dividends model. This particular model assumes that the current dividend represents the residual cash flow and this amount never changes. In this case, the value of the stock is the present value of the current dividend received at the end of each year forever, or the present value of a perpetuity. This formula would be useful for a firm that never expected to grow. In common stock valuation, the interest rate (small r in the formula) is an estimate of the rate of return investors expect to receive when investing in a share of stock. The dividend cash flow model can be used to show that the interest rate is composed of a dividend yield and a capital gain yield. The equity value model requires estimates of the cash flow stream (see question 7 above) and the required rate of return (see question 8 above). The biggest shortcoming of the equity value model is the difficulty of estimating both residual cash flows and the required rate of return. 23 CHAPTER 5 PROBLEMS 1. Using lump sum present value method: $103.67 2. $797.19. The price of the two year bond is higher since they offer the same amount of cash, the two year bond’s cash flow is received sooner and there is a positive time value of money. 3. Bond A: $712.99 Bond B: $926.39 Bond C: $620.17 4. $1,000. A bond sells for par when its yield equals its coupon. 5. $961.10. It is irrelevant when the bond was issued. Simply enter five as the number of periods, $80 as the payment, $1,000 as the future value and 9% as the discount rate and solve using the calculator or formula methods. 6. Price of 5% Coupon Bond = >$947.51 Price of 7% Coupon Bond = >$949.37 Difference in Prices = >$ 1.86 7. a. Price of bond with three years remaining = $925.39 b. Because the current required rate of return exceeds the bond’s coupon. 8. The interest rate must be divided by two and the number of years must be multiplied by two in order to reflect semi—annual compounding. Therefore, using two as the number of periods and 5% as the interest rate, price=$981.41. 9. Using $950 as the present value and the other variables as given ($1,000 is future value, n= 3 years, payment=$100), the yield is 12.08%. 10. $1,000 is future value: payment = coupon rate x face value = $75. Inputting variables as in previous problem, yield to maturity = 9.03%. 11. Noting that payment = coupon rate x face value = $80, this problem is solved as in previous two problems. Yield = 14.08%. 12. The same answer can be generated for any face value. We will use $100 as the face value. As above, payment = $9, present value = price = $105.04, etc. Yield = 8.24% 13. Yield = 8.00%. 14. $20 15. $100 16. $18.75 17. $150.00 18. $5.88 24 19. Since no perpetual growth rate is given, but rather the end of year price is given, we use a single period discount: ($50 + $2.11)/1.08 = $48.25. 20. Using the same approach as problem #19: a. Price with 7% required rate of return = $37.00 b. Price with 6% required rate of return = $37.35 Therefore the price would rise by $0.35. 21. $90.06 This problem requires a two period dividend/stock discount model and is analogous to a two period bond. The stock offers two periods of payments of $1.50 each and a future value in year two of $100. The present value can be found in one step as $90.06 or by summing the present value of the first dividend ($1.402) with the present value of the combined dividend and $100 price ($88654). 22. Each stock offers a total of three cashflows that must be present valued: dividends for two years and then a third dividend and $100 in the third year. Present values may be performed as follows: Cashflows in Dollars Present Values in Dollars Stock Year 1 Year 2 Year 3 Year 1 Year 2 Year 3 Price A $4.00 $4.00 $104.00 $3.76 $3.53 $86.10 $93.38 B $4.40 $4.84 $105.32 $4.13 $4.27 $87.19 $95.59 The dividends for Stock B are found by multiplying each year’s previous dividend by 1.1 to reflect 10% growth. All present values are found using lump sum present value discounting. The prices are the sum of the present values of the individual cashflows. Especially Stock A could have been solved using annuity shortcuts. 23. Each stock offers a total of two cashflows that must be present valued: a dividend for one year and then a second dividend and $100 in the second year. Present values may be performed as follows: Cashflows Present Values Stock Year 1 Year 2 Year 1 Year 2 Price C $2.00 $102.00 $1.85 $87.45 $89.30 D $1.00 $103.00 $0.93 $88.31 $89.23 Difference in Price: ' $0.07 Although both stocks offer the same total cashflows, Stock C offers $1 in dividends one year sooner and therefore is worth approximately $0.07 more today. 24. $40. This is found using the perpetuity model (dividing the dividend by the required rate of return. 25 25. $250 using the perpetuity model as above. 26. $33.00. The answer is found using the perpetual growth model. The difficulty is realizing that the numerator of the model requires the next dividend rather than the current dividend. Since dividends are growing at 5%, next year’s dividend of $1.155 can be found by multiplying the current dividend ($1.10) by 1.05. The price of the stock may be found by dividing the next dividend by the required rate of return (.085) minus the growth rate (0.05), in other words, 0.035. 27. 10%. The solution is found using the perpetual growth model. The three known variables are inserted and the equation is factored to determine the unknown variable: 10% = (Div/P) + g = ($1.50/$30.00) + 5%. 28. The solutions are found using the perpetual growth mode. The three known variables are inserted into the model for each stock and the equation is factored to determine the required rates of return. The difficulty is that current dividends are given rather than next period’s dividends. The next year’s dividends can be found by multiplying the current dividends by the expected growth rates (plus one). Since each stock has the same expected growth rates, the next dividends are the same: Next dividend = $1.00 x 1.05 = $1.05 Required rate of Return = (Div/P) + g Stock E: 15.500% = ($1.05/$10.00) + 5% Stock F: 14.375% = ($1.05/$11.20) + 5% 29. This problem is solved using the perpetual growth model. First, the current price is found by from knowing that the dividend is 2% of the stock price and that the dividend is $0.25: Dividend = 0.02x Price $0.25 = 0.02 X Price Price = $12.50 The next dividend is found by multiplying the current dividend by one plus the growth rate: Next Dividend Current Dividend x (1+g) = $0.25 x (1.05) = $02625 Next, the three known variables are inserted into the perpetual growth model and the equation is factored to find the required rate of return. Required Rate of Return = (Div/P) + g = ($0.2625/$12.50) + 5% = 7.1%. 26 CHAPTER 5 DISCUSSION QUESTIONS 1. The present value of a perpetuity is the sum of the present value of all of its future cashflows. Although a perpetuity offers an infinite number of future cashflows and therefore an infinite amount of money, the present values of the cashflows that are far off into the future are worth very little. For example, the present value of $1 to be received in 50 years at 10% interest is less than one cent. The present value of $1 to be received in 200 years at 10% interest is less than one millionth of one cent. Thus, the total present value of a perpetuity differs very little from the combined present values of its first 50 or so years of cashflows. 2. In general, when a bond is issued the amount of cash that it offers to investors is fixed. For example, a thirty year $1,000 bond with a coupon rate of 8% offers $80 per year in interest or coupon payments regardless of what happens to interest rates in the future. If interest rates rise above 8%, people will demand a higher rate of return on a $1,000 investment than simply $80 per year. Since the $80 payment if fixed, the price of the bond must drop in order to provide new investors in the bond the same rate that can be earned elsewhere. When interest rates fall, the opposite occurs. People will bid up the price of the bond since the fixed (e.g., $80) coupon is becoming more and more attractive relative to the coupons being issued on new bonds. 3. The price of a common stock is still the present value of the future dividends even if the stock has never paid a dividend and has no short term plan of paying a dividend. This is because the market is valuing the dividends that it anticipates in the medium to long term future. A reasonably good analogy is found in dairy farming. The price of dairy cows is primarily determined by the present value of the net proceeds from their future milk production. Baby cows (heifers) have never produced any milk and only can be hoped to produce milk when they mature. Nevertheless, these cows are worth money since farmers recognize the potential for milk. Similarly, immature companies have value and this value is derived from the cash that they will eventually be able to produce for their shareholders when they mature. 4. a. $0. There is no value to holding a stock or any other financial asset that has absolutely no probability of producing cash for its holder. We assume that voting rights to one share are worth zero and that any type of distribution is included in the arrangement. b. $0. Since the person who would end up with the stock would pay $0 since it would be worth nothing to them as well. c. $0. No rational person would buy this stock from its holder since they would know that they would be unable to find a rational person to buy it from them. 27 This problem is very difficult for some students to understand ("But you can sell the stock certificate at a profit as its price goes up!"). An excellent method of convincing them of its truth is to repeat the problem numerous times using different assets. The first time, solve the problem changing the financial asset from a share of stock to a normal bond. Thus, the orginal holder of the bond gets all of the bonds interest and principal payments while the new holder of the bond receives only the privilege of holding the bond certificate. It is relatively obvious that the person who gets all of the bond’s cash flows receives everything and that the person left holding the peice of paper gets nothing. This is especially clear because the bond’s cashflows are known and the bond has a fixed maturity date. The second time, repeat the problem assuming that the financial asset is a consol bond. In other words, the bond pays a perpetual interest payment and therefore has an infinite maturity. It is relatively easy to understand that this arrangement would produce no value to the person holding the piece of paper (the bond certificate) and all of its value to the person receiving the cash flows. Thus, it doesn’t matter that the financial asset has no maturity. The third time, repeat the problem assuming that the financial asset is a bond of fixed maturity but with a coupon that rises by a small amount each year. Thus the bond may pay 4% interest the first year, 4.5% interest the second year and so forth through the bond’s finite maturity. Similar results are obtained. Thus it doesn’t matter that the financial asset has growing cash flows (and even a growing price in certain circumstances). The final time, repeat the problem assuming that the financial asset has both of the features of the second and third financial assets. In other words, it is a bond of infinite maturity and with growing coupon payments. Similar results can be obtained and can be shown using the perpetual growth model. Finally, students should then be able to see that the infinite maturity and growing dividends of a common stock do not change the results even though dividend payments are more uncertain than coupon payments. 28 ...
View Full Document

{[ snackBarMessage ]}

Page1 / 7

Chapter 05 - R 1 R 2 R 3 R 4 R 5 R 6 CHAPTER 5 REVIEW...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online