A newly issued bond pays its coupons once a year. Its coupon rate is 4.1%, its m
ID: 2797101 • Letter: A
Question
A newly issued bond pays its coupons once a year. Its coupon rate is 4.1%, its maturity is 15 years, and its yield to maturity is 7.1%.
a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.1% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Holding-period return %
b. If you sell the bond after one year when its yield is 6.1%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
After-tax holding-period return %
d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 6.1% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.1% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Realized compound yield before taxes %
e. Use the tax rates in part (b) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
After-tax two-year realized compound yield %
Tax on interest income $ Tax on capital gain $ Total taxes $Explanation / Answer
The initial price is: P0 = $728.48, for [n = 15; PMT = 41; FV = 1000; i = 7.1]
The next year’s price is: P1 = $815.25, for [n = 14; PMT = 41; FV = 1000; i = 6.1]
Thus, the holding period return (HPR) is given by:
HPR = [$41 + ($815.25 – $728.48)]/$728.48 => HPR = 0.175387059= 17.54%
Constant yield prices:
P0 = $728.48
P1 = $815.25 (implies implicit interest over first year = $25.10)
P2 = $823.98 (implies implicit interest over second year = $26.63) ·
Tax on explicit plus implicit interest in the first year = 0.40 x ($41 + $25.10)= $26.44·
Capital gain in the first year = actual price – constant yield price = $793.29 – 711.89 = $81.40
Tax on capital gain = 0.30 x $81.40 = $24.42 ·
Total taxes = $22.57 + $24.42 = $46.99
(c) The after-tax HPR = [$50 + ($793.29 - $705.46) - $46.99]/$705.46 = 0.129 = 12.9%
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