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Ross4eChap06sm - Chapter 6 How to Value Bonds and Stocks...

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Chapter 6: How to Value Bonds and Stocks 6.1 a. $1,000 / 1.05 10 = $613.91 b. $1,000 / 1.10 10 = $385.54 c. $1,000 / 1.15 10 = $247.18 6.2 The amount of the semi-annual interest payment is $40 (=$1,000 × 0.08 / 2). There are a total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity. The annuity factor tables can be used to price these bonds. The appropriate discount rate to use is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part a the rate to be used is 4.0%, for part b the rate to be used is 5% and for part c it is 3%. a. $40 40 04 . 0 Α + $1,000 / 1.04 40 = $1,000 Notice that whenever the coupon rate and the market rate are the same, the bond is priced at par. b. $40 40 0.05 Α + $1,000 / 1.05 40 = $828.41 Notice that whenever the coupon rate is below the market rate, the bond is priced below par. c.$40 40 0.03 Α + $1,000 / 1.03 40 = $1,231.15 Notice that whenever the coupon rate is above the market rate, the bond is priced above par. 6.3 Semi-annual discount factor = (1.12) 1/2 - 1 = 0.058300 = 5.83% a. Price = $40 40 0.0583 Α + $1,000 / 1.0583 40 = $614.98 + $103.67 = $718.65 b. Price = $50 30 0.0583 Α + $1,000 / 1.0583 30 = $700.94 + $182.70 = $883.64 6.4 Effective annual rate of 10%: Semi-annual discount factor = (1.10) 0.5 - 1 = 0.048809 = 4.8809% Price = $40 40 0.048809 Α + $1,000 / 1.048809 40 = $697.71 + $148.64 =$846.35 6.5 $923.14 = C 30 0.05 Α + $1,000 / 1.05 30 = (15.3725) C + $231.38 C = $45.00 The annual coupon rate = $45.00 × 2 / $1,000 = 0.09 = 9% 6.6 a. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.06 2 - 1 = 0.1236 = 12.36%. b. Price = $30 12 0.06 Α + $1,000 / 1.06 12 = $251.52 + $496.97 = $748.49 c. Price = $30 12 0.04 Α + $1,000 / 1.04 12 = $281.55+ $624.60= $906.15 Answers to End-of-Chapter Problems B-41
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Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for year 6 as well. 6.7 a. P A = $100 20 0.10 Α + $1,000 / 1.1 20 = $1,000.00 P B = $100 10 0.1 Α + $1,000 / 1.10 10 = $1,000.00 b. P A = $100 20 0.12 Α + $1,000 / 1.12 20 = $850.61 P B = $100 10 0.12 Α + $1,000 / 1.12 10 = $ 887.00 c. P A = $100 20 0.08 Α + $1,000 / 1.08 20 = $1,196.36 P B = $100 10 0.08 Α + $1,000 / 1.08 10 = $1,134.20 6.8 a. The prices of long-term bonds should fall. The price of any bond is the PV of the cash flows associated with the bond. As the interest rate increases, the PV of those cash flows falls. This can be easily seen by looking at a one-year, pure discount bond. P = $1,000 / (1+i) As i increases, the denominator, (1 + i ), rises, thus reducing the value of the numerator ($1,000). The price of the bond decreases. b. The effect on stocks is not as clear-cut as the effect on bonds. The nominal interest rate is a function of both the real interest rate, r , and the inflation rate, i.e., (1+i) = (1+r) (1+Inflation) From this relationship it is easy to conclude that, as inflation rises, the nominal interest rate, i , rises. However, stock prices are a function of dividends and future prices as well as the interest rate. Those dividends and future prices are determined by the earning power of the firm. Inflation may increase or decrease firm earnings. Thus, a rise in interest rates has an uncertain effect on the general level of stock prices. 6.9 a. $1,200 = $80 20 r Α + $1,000 / (1 + r) 20 r = 0.0622 = 6.22% The yield to maturity is 6.22%. b. $950 = $80 10 r Α + $1,000 / (1 + r) 10 r = 0.0877 = 8.77% The yield to maturity is 8.77% 6.10 The appropriate discount rate is the semiannual interest rate because the bond makes semiannual payments. Thus, calculate the appropriate semiannual interest rate for both bonds A and B .
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