Question

A newly issued bond pays its coupons once annually. Its coupon rate is 9.2%, its maturity is 20 years, and its yield to maturity is 11%.

a. Find the realized compound yield before taxes for a 2-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 10% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. If you sell the bond after one year, 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 tax treatment. Compute the after-tax 2-year realized compound yield. Remember to take account of OID tax rules. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

ANSWER

a).

Purchase price (P0): FV (par value) = 1,000; PMT (annual coupon) = coupon rate*par value = 9.2%*1,000 = 92; N (number of coupons) = 20; rate = 11%, solve for PV.

P0 = 856.66

Selling price after 2 years (P2): FV = 1,000; PMT = 92; N = 20-2 = 18; rate = 10%, solve for PV.

P2 = 934.39

Reinvested value of Yr 1 coupon at the end of Yr 2 (RI2) = annual coupon*(1+reinvestment rate) = 92*(1+3%) = 94.76

Total cash flow at the end of Yr 2 = P2 + RI2 + Yr 2 coupon = 934.39+94.76+92 = 1,121.15

Pre-tax compound yield for 2 years = [(Total cash flow/P0)^(1/2)] -1 = [(1,121.15/856.66)^(0.5)]-1 = 14.40%

b).

Constant yield price after Yr 1 (CP1): FV = 1,000; PMT = 92; N = 19; rate = 11%, solve for PV. CP1 = 858.89

Constant yield price after Yr 2 (CP2): FV = 1,000; PMT = 92; N = 18; rate = 11%, solve for PV. CP2 = 861.37

Yr 1 cash flow (CF1) = after-tax Yr 1 coupon - tax on imputed Yr 1 imputed interest

Yr 1 annual coupon*(1-Interest income tax rate) - Interest income tax rate*(CP1-P0)

= 92*(1-40%) - 40%*(858.89-856.66) = 54.31

Reinvested value of CF1 (at the end of Yr 2) (RCF2) = CF1*reinvestment rate*(Interest income tax rate) = 54.31*3%*(1-40%) = 55.28

Yr 2 net cash flow (CF2) = selling price (P2) - tax on Yr 2 imputed interest - tax on capital gains + After-tax Yr 2 coupon + RCF2

P2 = 934.39

Tax on Yr 2 imputed interest = 40%*(CP2-CP1) = 40%*(861.37-858.89) = 0.99

Tax on capital gains = (P2-CP2)*capital gains tax rate = (934.39-861.37)*30% = 21.91

After-tax Yr 2 coupon = 92*(1-40%) = 55.20

CF2 = 934.39 - 0.99 - 21.91 + 55.20 + 55.28 = 1,021.98

After-tax 2-year compound yield = [(CF2/P0)^(1/2)]-1 = [(1,021/98/856.66)^0.5]-1 = 9.22%

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