bkmsol_ch14

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\$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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nominal rate of return and real rate of return on the bond in each year are computed as follows: Nominal rate of return = interest + price appreciation initial price Real rate of return = 1 + nominal return 1 + inflation 1 Second year Third year Nominal return 071196 . 0 020 , 1 \$ 60 . 30 \$ 02 . 42 \$ = + 050400 . 0 60 . 050 , 1 \$ 51 . 10 \$ 44 . 42 \$ = + Real return % 0 . 4 040 . 0 1 03 . 1 071196 . 1 = = % 0 . 4 040 . 0 1 01 . 1 050400 . 1 = = The real rate of return in each year is precisely the 4% real yield on the bond. 18. The price schedule is as follows: Year Remaining Maturity (T) Constant yield value \$1,000/(1.08) T Imputed interest (Increase in constant yield value) 0 (now) 20 years \$214.55 1 19 \$231.71 \$17.16 2 18 \$250.25 \$18.54 19 1 \$925.93 20 0 \$1,000.00 \$74.07 19. The bond is issued at a price of \$800. Therefore, its yield to maturity is: 6.8245% Therefore, using the constant yield method, we find that the price in one year (when maturity falls to 9 years) will be (at an unchanged yield) \$814.60, representing an increase of \$14.60. Total taxable income is: \$40.00 + \$14.60 = \$54.60 20. a. The bond sells for \$1,124.72 based on the 3.5% yield to maturity . [n = 60; i = 3.5; FV = 1000; PMT = 40] Therefore, yield to call is 3.368% semiannually, 6.736% semi-annually. [n = 10 semiannual periods; PV = –1124.72; FV = 1100; PMT = 40] b. If the call price were \$1,050, we would set FV = 1,050 and redo part (a) to find that yield to call is 2.976% semiannually, 5.952% annually. With a lower call price, the yield to call is lower. c.
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