chap005 - Chapter 5 How to Value Bonds and Stocks 5.1 a b c...

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L j » * Chapter 5: How to Value Bonds and Stocks 5.1 a. $1,000 / 1.05 10 = $613.91 b. $1,000 / 1.10 10 = $385.54 c. $1,000 / 1.15 10 = $247.18 5.2 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 b the rate to be used is 5% and for part c is it 3%. a. $40 (19.7928) + $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 (17.1591) + $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 (23.1148) + $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. 5.3 Semi-annual discount factor = (1.12) 1/2 - 1 = 0.05830 = 5.83% a. Price = $40 40 0583 . 0 Α + $1,000 / 1.0583 40 = $614.98 + $103.67 = $718.65 b. Price = $50 30 0583 . 0 Α + $1,000 / 1.0583 30 = $700.94 + $182.70 = $883.64 5.4 Effective annual rate of 10%: Semi-annual discount factor = (1.1) 0.5 - 1 = 0.04881 = 4.881% Price = $40 40 04881 . 0 Α + $1,000 / 1.04881 40 = $846.33 5.5 $923.14 = C 30 05 . 0 Α + $1,000 / 1.05 30 = (15.37245) C + $231.38 C = $45 The annual coupon rate = $45 × 2 / $1,000 = 0.09 = 9% 5.6 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%.
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