bkmsol_ch14

# 46 29 4 b using oid tax rules the cost basis and

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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] Add: after-tax coupon interest received in second year: + 30.00 [\$50 × (1 – 0.40)] Less: Capital gains tax on (sales price – constant yield value): – 23.99 [0.30 × (798.82 – 718.84)] Add: CF from first year's coupon (reinvested): + 27.92 [from above] Total \$829.97 \$705.46 (1 + r) 2 = \$829.97 r = 0.0847 = 8.47% 14. The reported bond price is: 100 2/32 percent of par = \$1,000.625 However, 15 days have passed since the last semiannual coupon was paid, so: accrued interest = \$35 × (15/182) = \$2.885 The invoice price is the reported price plus accrued interest: \$1,003.51 15. If the yield to maturity is greater than the current yield, then the bond offers the prospect of price appreciation as it approaches its maturity date. Therefore, the bond must be selling below par value. 16. The coupon rate is less than 9%. If coupon divided by price equals 9%, and price is less than par, then price divided by par is less than 9%. 17. Time Inflation in year just ended Par value Coupon payment Principal repayment 0 \$1,000.00 1 2% \$1,020.00 \$40.80 \$ 0.00 2 3% \$1,050.60 \$42.02 \$ 0.00 3 1% \$1,061.11 \$42.44 \$1,061.11 14-6

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