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?

Answer 1

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.

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

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

Bond price = sum of all PVs

Bond price at the end of year 1 = 490.1

Period	Cashflow	PV	Bond price
1	40	36.7	490.1
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	1040	85.4

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

Period	Cashflow	PV	Bond price
1	40	37.4	631.7
2	40	34.9
3	40	32.7
4	40	30.5
5	40	28.5
6	40	26.7
7	40	24.9
8	40	23.3
9	40	21.8
10	40	20.3
11	40	19.0
12	40	17.8
13	40	16.6
14	40	15.5
15	40	14.5
16	40	13.5
17	40	12.7
18	40	11.8
19	40	11.1
20	40	10.3
21	40	9.7
22	40	9.0
23	40	8.4
24	40	7.9
25	40	7.4
26	40	6.9
27	40	6.4
28	40	6.0
29	1040	146.2

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%