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Considering 30-year maturity bond (Original-issue discount bond) that is issued

ID: 1175837 • Letter: C

Question

Considering 30-year maturity bond (Original-issue discount bond) that is issued with a coupon rate of 4% and aYTM of 9%. Assuming that the bond pays coupons once annually. Case 1: If you do not sell the bond at year end. If your tax rate on interest income is 38% and the combined tax rate on capital gain is 20% at year end. How much will you will owe taxes on this investment? What is your after-tax holding period return? Case 2: Suppose the yield to maturity drops to 7% by the end of the first year and you sell it after the first year. How much will you will owe taxes on this investment ? What is your holding period return?

Explanation / Answer

Case 1:

Interest income = coupon payment = 4% * 1000 = 40

Tax on interest income = 38% * 40 = 15.2

Current bond price = 486.3. Calculation is below.

PV = cash flow / ((1 + ytm)^ period)

Bond price = sum of all PVs

Bond price at the end of year 1 = 490.1

Capital gains = 490.1 - 486.3 = 3.8

since the bond is not sold in case 1, there will be no capital gains taxes.

Hence, total taxes owed= 15.2

Holding period return = (40 - 15.2)+ (490.1-486.3) / 486.3 = 5.9%

Case 2:

Interst income in second year = 40

Tax on interest income = 38% * 40 = 15.2

Interest income = 24.8

Bond price at year end 1 = 631.7

capital gains = 631.7 -486.3 = 145.4

tax on capital gains = 20% * 145.4 = 29.1

Total taxes owed = 15.2+29.1 = 44.3

Holding period return = (24.8 + (145.4-29.1) / 486.3) = 141.1 / 486.3 = 29.0%

Period Cashflow PV 1 40 36.7 2 40 33.7 3 40 30.9 4 40 28.3 5 40 26.0 6 40 23.9 7 40 21.9 8 40 20.1 9 40 18.4 10 40 16.9 11 40 15.5 12 40 14.2 13 40 13.0 14 40 12.0 15 40 11.0 16 40 10.1 17 40 9.2 18 40 8.5 19 40 7.8 20 40 7.1 21 40 6.5 22 40 6.0 23 40 5.5 24 40 5.1 25 40 4.6 26 40 4.3 27 40 3.9 28 40 3.6 29 40 3.3 30 1040 78.4
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