Question

You purchase an ABC 10%, 30 Year bond with a $100 face value for 109.72

1) What is the yield to maturity of the bond?

2) What is the current yield on the bond?

3) What is the duration of the bond?

4) If you bought the bond today and sold it after 1 year at a ytm of 10% what is your cash flow yield ?

5) What is your realized compound yield if you held the bond for 11 years if the reinvestment rate (R) was 11%?

Answer 1

Solution:-

Price = $109.72

Coupun Rate = 10%

Time = 30 Years

Face Value = $100

To Calculate Yield to maturity (YTM) of Bond-

Interest Amount = $100 * 10%

Interest Amount = $10

YTM =

YTM =

YTM =

YTM = 9.23%

Yield to Maturity of the Bond is 9.23%.

To Calculate Current Yield of the Bond-

Current Yield =

Current Yield =

Current Yield = 9.11%

To Calculate Duration of Bond-

Duration of Bond
Year	Cash Flow	Discounting Factor @ 9.23%	Present Value	Weight	PV * Weight
1	10	0.915	9.155	1	9.155
2	10	0.838	8.381	2	16.763
3	10	0.767	7.673	3	23.019
4	10	0.702	7.025	4	28.099
5	10	0.643	6.431	5	32.156
6	10	0.589	5.888	6	35.326
7	10	0.539	5.390	7	37.732
8	10	0.493	4.935	8	39.478
9	10	0.452	4.518	9	40.660
10	10	0.414	4.136	10	41.360
11	10	0.379	3.787	11	41.652
12	10	0.347	3.467	12	41.599
13	10	0.317	3.174	13	41.257
14	10	0.291	2.905	14	40.676
15	10	0.266	2.660	15	39.899
16	10	0.244	2.435	16	38.963
17	10	0.223	2.229	17	37.900
18	10	0.204	2.041	18	36.738
19	10	0.187	1.869	19	35.502
20	10	0.171	1.711	20	34.213
21	10	0.157	1.566	21	32.888
22	10	0.143	1.434	22	31.543
23	10	0.131	1.313	23	30.190
24	10	0.120	1.202	24	28.841
25	10	0.110	1.100	25	27.504
26	10	0.101	1.007	26	26.187
27	10	0.092	0.922	27	24.896
28	10	0.084	0.844	28	23.637
29	10	0.077	0.773	29	22.412
30	110	0.071	7.783	30	233.483
		Present Value	107.752		1173.727

Duration Of Bond =

Duration Of Bond =

Duration Of Bond = 10.89 Years

If you have any query related to question then feel free to ask me in a comment. Thanks.