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Ii yield to maturity assumes the bond is held until

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reinvestment income on coupon payments. (ii) Yield to maturity assumes the bond is held until maturity and that all coupon income can be reinvested at a rate equal to the yield to maturity. (iii) Realized compound yield is affected by the forecast of reinvestment rates, holding period, and yield of the bond at the end of the investor's holding period. 14-2
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8. a. Zero coupon 8% coupon 10% coupon Current prices $463.19 $1,000.00 $1,134.20 b. Price 1 year from now $500.25 $1,000.00 $1,124.94 Price increase $ 37.06 $ 0.00 $ 9.26 Coupon income $ 0.00 $ 80.00 $100.00 Pre-tax income $ 37.06 $ 80.00 $ 90.74 Pre-tax rate of return 8.00% 8.00% 8.00% Taxes* $ 11.12 $ 24.00 $ 28.15 After-tax income $ 25.94 $ 56.00 $ 62.59 After-tax rate of return 5.60% 5.60% 5.52% c. Price 1 year from now $543.93 $1,065.15 $1,195.46 Price increase $ 80.74 $ 65.15 $ 61.26 Coupon income $ 0.00 $ 80.00 $100.00 Pre-tax income $ 80.74 $145.15 $161.26 Pre-tax rate of return 17.43% 14.52% 14.22% Taxes** $ 19.86 $ 37.03 $ 42.25 After-tax income $ 60.88 $108.12 $119.01 After-tax rate of return 13.14% 10.81% 10.49% * In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year end is treated as a capital loss and therefore is not treated as an offset to ordinary income. ** In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary income (see part (b)) and the remainder of the price increase is taxed as a capital gain. 9. a. On a financial calculator, enter the following: n = 40; FV = 1000; PV = –950; PMT = 40 You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity equal to: 4.26% × 2 = 8.52% Effective annual yield to maturity = (1.0426) 2 – 1 = 0.0870 = 8.70% b. Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon rate, i.e., 4%. The bond equivalent yield to maturity is 8%. Effective annual yield to maturity = (1.04) 2 – 1 = 0.0816 = 8.16% c. Keeping other inputs unchanged but setting PV = –1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis. Effective annual yield to maturity = (1.0376) 2 – 1 = 0.0766 = 7.66% 14-3
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10. Since the bond payments are now made annually instead of semi-annually, the bond equivalent yield to maturity is the same as the effective annual yield to maturity. Using a financial calculator, enter: n = 20; FV = 1000; PV = –price, PMT = 80. The resulting yields for the three bonds are: Bond Price Bond equivalent yield = Effective annual yield $950 8.53% $1,000 8.00% $1,050 7.51% The yields computed in this case are lower than the yields calculated with semi- annual payments. All else equal, bonds with annual payments are less attractive to investors because more time elapses before payments are received. If the bond price is the same with annual payments, then the bond's yield to maturity is lower. 11. Price Maturity (years) Bond equivalent YTM $400.00 20.00 4.688% $500.00 20.00 3.526% $500.00 10.00 7.177% $385.54 10.00 10.000% $463.19 10.00 8.000% $400.00 11.91 8.000% 12. a. The bond pays $50 every 6 months. The current price is: [$50 × Annuity factor (4%, 6)] + [$1,000 × PV factor (4%, 6)] = $1,052.42 Assuming the market interest rate remains 4% per half year, price six months from now is: [$50 × Annuity factor (4%, 5)] + [$1,000 × PV factor (4%, 5)] = $1,044.52 b. Rate of return 42 . 052 , 1 $ 90 . 7 $ 50 $ 42 . 052 , 1 $ ) 42 . 052 , 1 $ 52 . 044 , 1 ($ 50 $ = + = = 0.04 = 4.0% per six months 13. a. Initial price P 0 = $705.46 [n = 20; PMT = 50; FV = 1000; i = 8] Next year's price P 1 = $793.29 [n = 19; PMT = 50; FV = 1000; i = 7] HPR % 54 . 19 1954 . 0
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