Question

Today, a bond has a coupon rate of 10.16 percent, par value of 1,000 dollars, YTM of 10.5 percent, and semi-annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was 1,042.84 dollars and the bond had 19 years until maturity. What is the current yield of the bond today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Step 1: Calculation of a market price of a bond as on today:

Today YTM of a Bond = 10.5%

YTM for six months = 10.5% /2 = 5.25%

Coupon Amount = $ 1000*10.16%/2 = $ 50.8

Remaining maturity of a bond = 19 years

We know that at YTM , the Present value of the future cash inflows is equal to the Market price of a Bond.

No.of Coupon Repayments = 19*2= 38 Coupon Repayments

S.No	Cash flow	Disc @ 5.25%	Discounted Cash flow
1	$50.80	0.950118765	$48.27
2	$50.80	0.902725667	$45.86
3	$50.80	0.857696596	$43.57
4	$50.80	0.81491363	$41.40
5	$50.80	0.774264732	$39.33
6	$50.80	0.735643451	$37.37
7	$50.80	0.698948647	$35.51
8	$50.80	0.664084225	$33.74
9	$50.80	0.630958884	$32.05
10	$50.80	0.599485875	$30.45
11	$50.80	0.569582779	$28.93
12	$50.80	0.541171287	$27.49
13	$50.80	0.514176995	$26.12
14	$50.80	0.488529211	$24.82
15	$50.80	0.464160771	$23.58
16	$50.80	0.441007858	$22.40
17	$50.80	0.419009841	$21.29
18	$50.80	0.398109113	$20.22
19	$50.80	0.378250939	$19.22
20	$50.80	0.359383315	$18.26
21	$50.80	0.341456831	$17.35
22	$50.80	0.324424542	$16.48
23	$50.80	0.308241846	$15.66
24	$50.80	0.292866362	$14.88
25	$50.80	0.278257826	$14.14
26	$50.80	0.264377982	$13.43
27	$50.80	0.251190481	$12.76
28	$50.80	0.23866079	$12.12
29	$50.80	0.226756095	$11.52
30	$50.80	0.215445221	$10.94
31	$50.80	0.204698547	$10.40
32	$50.80	0.194487931	$9.88
33	$50.80	0.184786633	$9.39
34	$50.80	0.175569247	$8.92
35	$50.80	0.166811636	$8.47
36	$50.80	0.158490866	$8.05
37	$50.80	0.150585146	$7.65
38	$1,050.80	0.143073773	$150.34
		Total	$972.25

Hence the Current Market Price of a Bond is $ 972.25

Step 2: Calculation of Current yield

Annual interest = $ 1000*10.5$ = $ 105

We know that Current yield = (Annual interest / Current Market price )*100

= ($ 105/$ 972.25)*100

= 10.7996%

Hence the Current yield of a bond is 0.1079