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

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Unformatted text preview: Chapter 5: How to Value Bonds and Stocks 5.1 a. b. c. $1,000 / 1.0510 = $613.91 $1,000 / 1.1010 = $385.54 $1,000 / 1.1510 = $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 / 1.0440 = $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 / 1.0540 = $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 / 1.0340 = $1,231.15 Notice that whenever the coupon rate is above the market rate, the bond is priced above par. Semi-annual discount factor = (1.12)1/2 - 1 = 0.05830 = 5.83% 40 a. Price = $40 0.0583 + $1,000 / 1.058340 = $614.98 + $103.67 = $718.65 30 b. Price = $50 0.0583 + $1,000 / 1.058330 = $700.94 + $182.70 = $883.64 Effective annual rate of 10%: Semi-annual discount factor = (1.1)0.5 - 1 = 0.04881 = 4.881% 40 Price = $40 0.04881 + $1,000 / 1.0488140 = $846.33 $923.14 = C 0.05 + $1,000 / 1.0530 = (15.37245) C + $231.38 C = $45 The annual coupon rate = $45 2 / $1,000 = 0.09 = 9% 30 5.3 5.4 5.5 5.6 a. b. c. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 = 0.1236 = 12.36%. 12 Price = $30 0.06 + $1,000 / 1.0612 = $748.48 12 Price = $30 0.04 + $1,000 / 1.0412 = $906.15 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. Answers to End-of-Chapter Problems B-59 5.7 a. b. c. 20 PA = $100 0.10 + $1,000 / 1.1020 = $1,000 10 PB = $100 0.10 + $1,000 / 1.1010 = $1,000 20 PA = $100 0.12 + $1,000 / 1.1220 = $850.61 10 PB = $100 0.12 + $1,000 / 1.1210 = $887.00 20 PA = $100 0.08 + $1,000 / 1.0820 = $1,196.36 10 PB = $100 0.08 + $1,000 / 1.0810 = $1,134.20 5.8 falls. a. b. rate; i.e., The price of long-term bonds should fall. The price is the PV of the cash flows associated with the bond. As the interest rate rises, the PV of those flows This can be easily seen by looking at a one-year, pure discount bond. Price = $1,000 / (1 + i) As i. increases, the denominator rises. This increase causes the price to fall. The effect upon stocks is not as certain as that upon the bonds. The nominal interest rate is a function of both the real interest rate and the inflation (1 + i) = (1 + r) (1 + inflation) From this relationship it is easy to conclude that as inflation rises, the nominal interest rate rises. 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. When inflation occurs, it may increase or decrease firm earnings. Thus, the effect of a rise in the level of general prices upon the level of stock prices is uncertain. 5.9 a. b. $1,200 = $80 20 + $1,000 / (1 + r)20 r r = 0.0622 = 6.22% $950 = $80 10 + $1,000 / (1 + r)10 r r = 0.0877 = 8.77% 16 12 5.10 PA = ($2,000 0.06 ) / (1.06)12 + ($2,500 0.06 ) / (1.06)28 + $40,000 / (1.06)40 = $18,033.86 PB = $ 40,000 / (1.06)40 = $3,888.89 a. b. c. d. e. a. b. c. d. True True False False True True False True False 5.11 5.12 5.13 Price = $2 (1.08) / 1.12 + $2 (1.082) / 1.122 + $2 (1.083) / 1.123 + {$2 (1.083) (1.04) / (0.12 - 0.04)} / 1.123 = $28.89 B-60 Answers to End-of-Chapter Problems 5.14 a. b. c. d. e. False True False False True 5.15 98.125 = 1.30 ( 1.07) / r - 0.07 r = 8.4175 % 5.16 Price = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153 = $36.31 The number of shares you own = $100,000 / $36.31 = 2,754 shares a. b. P = $2 / (0.12 - 0.05) = $28.57 P10 = D11 / (r - g) = $2 (1.0510) / (0.12 - 0.05) = $46.54 5.17 5.18 5.19 Value = -$5,000,000 + $2,000,000 / {0.14 - (-0.02)} = $7,500,000 Price = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123 + {$1.152 (1.182) (1.06) / (0.12 - 0.06)} / 1.123 = $26.95 $30 = D / 1.12 + D / 1.122 + {D (1 + 0.04) / (0.12 - 0.04)} / 1.122 = 12.053571 D D = $2.49 Dividend one year from now = $5 (1 - 0.10) = $4.50 Price = $5 + $4.50 / {0.14 - (-0.10)} = $23.75 Since the current $5 dividend has not yet been paid, it is still included in the stock price. Price = $1 0.025 + {$1 (1 + 0.005) / (0.025 - 0.005)} / 1.02512 = $10.26 + $37.36 = $47.62 12 5.20 5.21 5.22 5.23 Growth rate g = 0.6 0.14 = 0.084 = 8.4% Next year earnings = $20 million 1.084 = $21.68 million g = retention ratio ROE = 0.75 0.12 = 0.09 = 9% Dividend per share = $10 million (1 - 0.75) / 1.25 million = $2 The required rate of return = $2 (1.09) / $30 + 0.09 5.24 Answers to End-of-Chapter Problems B-61 = 0.1627 = 16.27% 5.25 a. b. Price = ($3 - $1.5) 1.05 / (0.15 - 0.05) = $15.75 NPVGO = -$15,000,000 - $5,000,000 / 1.15 + ($6,000,000 / 0.15) / 1.15 = $15,434,783 The price increases by $15.43 per share. 5.26 a. b. c. 5.27 5.28 Price = EPS / r = {$100 million / 20 million} / 0.15 = $33.33 NPV = -$15 million - $5 million / 1.15 + ($10 million / 0.15) / 1.15 = $38,623,188 Price = $33.33 + $38,623,188 / 20,000,000 = $35.26 Price = 1.40 (1.05) / 0.10 - 0.05 Price = $29.40 Price = 2 / (1.16) 3 + 2 / (1.16)4 + 2.12 / 0.16 - 0.06 = 1.28 + 1.10 + 21.20 = $23.58 a. b. g = 0.4 0.15 = 0.06 = 6% Dividend per share = $1.5 million 0.6 / 300,000 = $3 Price = $3 (1.06) / (0.13 - 0.06) = $45.43 Assuming the additional earnings generated are all paid out as cash dividends. NPV = -$1.2 million + $0.3 million {1 / (0.13 - 0.10)} {1 - (1.10 / 1.13)10} = $1,159,136.93 Price = $45.43 + $1,159,136.93 / 300,000 = $49.29 = 2.61 + 3.40 + 47.52 = $53.53 5.29 c. d. 5.30 Price = 3 / 1.15 + 4.5 / ( 1.15)2 + 4.725 / 0.15- 0.05 5.31 a. P/E of Pacific Energy Company: EPS = ($800,000 / 500,000) = $1.6 NPVGO = {$100,000 / 500,000} / 0.15 = $1.33 P/E = 1 / 0.15 + 1.33 / 1.6 = 7.50 P/E of U. S. Bluechips, Inc.: NPVGO = {$200,000 / 500,000} / (0.15 - 0.10) = $8 P/E = 1 / 0.15 + 8 / 1.6 = 11.67 Price = $4 / 0.14 = $28.57 Price = 28.57 + (-1 + 0.40 / 0.14) / 0.04 b. 5.32 a. b. B-62 Answers to End-of-Chapter Problems (1.14) 3 c. d. = 28.57 + 31.33 = $59.90 The expected return of 14% less the dividend yield of 5% provides a capital gain yield of 9%. If there is no investment the yield is 14%. $3 / $59.90 = .05 and $4 / $28.57 = .14 without the investment. Appendix to Chapter 5 5A.1 a. P = $60 / 1.10 + $1,060 / (1.11)2 = $54.55 + $ 860.32 = $914.87 $914.87 = $60 / ( 1 + y ) + $1,060 / ( 1 + y )2 y = YTM = 10.97% P = $50 / 1.10 + $1,050 / (1.08)2 = $45.45 + $900.21 = $945.66 ( 1 + r1 )( 1 + 2 ) = ( 1 + r2 )2 ( 1.09 ) ( 1 + 2 ) = ( 1.10 )2 2 = .1101 ( 1 + r2 )2 = ( 1+ r1 ) ( 1 + 2 ) ( 1.07 )2 = ( 1.05 )( 1 + 2 ) 2 = .0904, one-year forward rate over the 2nd year is 9.04%. ( 1 + r3 )3 = ( 1 + r2 )2 ( 1 + 3 ) ( 1.10 )3 = ( 1.07 )2 ( 1 + 3 ) 3 = .1625, one-year forward rate over the 3rd year is 16.25%. b. 5A.2 5A.3 5A.4 Answers to End-of-Chapter Problems B-63 ...
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