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# Using a financial calculator enter n 20 fv 1000 pv

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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 46 . 705 \$ ) 46 . 705 \$ 29 . 793 (\$ 50 \$ = = + = 14-4

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b. Using OID tax rules, the cost basis and imputed interest under the constant yield method are obtained by discounting bond payments at the original 8% yield, and simply reducing maturity by one year at a time: Constant yield prices (compare these to actual prices to compute capital gains): P 0 = \$705.46 P 1 = \$711.89 implicit interest over first year = \$6.43 P 2 = \$718.84 implicit interest over second year = \$6.95 Tax on explicit interest plus implicit interest in first year = 0.40 × (\$50 + \$6.43) = \$22.57 Capital gain in first year = Actual price at 7% YTM – constant yield price = \$793.29 – \$711.89 = \$81.40 Tax on capital gain = 0.30 × \$81.40 = \$24.42 Total taxes = \$22.57 + \$24.42 = \$46.99 c. After tax HPR = % 88 . 12 1288 . 0 46 . 705 \$ 99 . 46 \$ ) 46 . 705 \$ 29 . 793 (\$ 50 \$ = = + d. Value of bond after two years = \$798.82 [using n = 18; i = 7%] Reinvested income from the two coupon interest payments = \$50 × 1.03 + \$50 = \$101.50 Total funds after two years = \$798.82 + \$101.50 = \$900.32 Therefore, the investment of \$705.46 grows to \$900.32 in two years: \$705.46 (1 + r) 2 = \$900.32 r = 0.1297 = 12.97% e. Coupon interest received in first year: \$50.00 Less: tax on coupon interest @ 40%: – 20.00 Less: tax on imputed interest (0.40 × \$6.43): – 2.57 Net cash flow in first year: \$27.43 The year-1 cash flow can be invested at an after-tax rate of: 3% × (1 – 0.40) = 1.8% By year 2, this investment will grow to: \$27.43 × 1.018 = \$27.92 14-5
In two years, sell the bond for: \$798.82 [n = 18; i = 7%] Less: tax on imputed interest in second year: – 2.78 [0.40 × \$6.95]

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Using a financial calculator enter n 20 FV 1000 PV price...

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