Question

Footsteps Co. has a bond outstanding with a coupon rate of 5.5 percent and annual payments. The bond currently sells for $1,000.41, matures in 19 years, and has a par value of $1,000. What is the YTM of the bond? Multiple Choice 4.95% 4.52% 5.50% 4.25% 6.00%

Answer 1

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Answer:

5.50%

As the PV almost equal to FV = $1000.41, the coupon rate has to be equal to YTM

Coupon Rate	5.50%
Coupon Amt	$55	1000*5.50%
Bond Price	$1,000.41
Par Value	$1,000
Value of Bond = Coupon payment*PV factor + Maturity amount*Discount factor
We would use trial and error to calculate, the yield to maturity
Assuming YTM is 6%
Years	Cash flow	Discount Factor @ 6%	Present Value
1	55	0.943396226	51.89
2	55	0.88999644	48.95
3	55	0.839619283	46.18
4	55	0.792093663	43.57
5	55	0.747258173	41.10
6	55	0.70496054	38.77
7	55	0.665057114	36.58
8	55	0.627412371	34.51
9	55	0.591898464	32.55
10	55	0.558394777	30.71
11	55	0.526787525	28.97
12	55	0.496969364	27.33
13	55	0.468839022	25.79
14	55	0.442300964	24.33
15	55	0.417265061	22.95
16	55	0.393646284	21.65
17	55	0.371364419	20.43
18	55	0.350343791	19.27
19	1055	0.33051301	348.69
			944.21
Assuming YTM is 4.5%
Years	Cash flow	Discount Factor @ 4.5%	Present Value
1	55	0.956937799	52.63
2	55	0.915729951	50.37
3	55	0.876296604	48.20
4	55	0.838561344	46.12
5	55	0.802451047	44.13
6	55	0.767895738	42.23
7	55	0.734828458	40.42
8	55	0.703185127	38.68
9	55	0.672904428	37.01
10	55	0.643927682	35.42
11	55	0.616198739	33.89
12	55	0.589663865	32.43
13	55	0.564271641	31.03
14	55	0.539972862	29.70
15	55	0.516720442	28.42
16	55	0.494469323	27.20
17	55	0.473176385	26.02
18	55	0.452800369	24.90
19	1055	0.433301788	457.13
			1125.93
Assuming YTM is 4.95%
Years	Cash flow	Discount Factor @ 4.95%	Present Value
1	55	0.952834683	52.41
2	55	0.907893933	49.93
3	55	0.865072828	47.58
4	55	0.824271394	45.33
5	55	0.785394373	43.20
6	55	0.748350999	41.16
7	55	0.713054787	39.22
8	55	0.679423332	37.37
9	55	0.647378115	35.61
10	55	0.616844321	33.93
11	55	0.587750663	32.33
12	55	0.560029217	30.80
13	55	0.533615262	29.35
14	55	0.508447129	27.96
15	55	0.484466059	26.65
16	55	0.461616064	25.39
17	55	0.439843796	24.19
18	55	0.419098424	23.05
19	1055	0.399331514	421.29
			1066.74
Assuming YTM is 5.4965%
Years	Cash flow	Discount Factor @ 5.4965%	Present Value
1	55	0.947898745	52.13
2	55	0.898512032	49.42
3	55	0.851698428	46.84
4	55	0.807323871	44.40
5	55	0.765261284	42.09
6	55	0.725390212	39.90
7	55	0.687596471	37.82
8	55	0.651771833	35.85
9	55	0.617813703	33.98
10	55	0.585624834	32.21
11	55	0.555113045	30.53
12	55	0.526190959	28.94
13	55	0.49877575	27.43
14	55	0.472788908	26.00
15	55	0.448156012	24.65
16	55	0.424806522	23.36
17	55	0.402673569	22.15
18	55	0.381693771	20.99
19	1055	0.361807047	381.71
			1000.41
At YTM of 5.4965% that is approx 5.50% the future value of payments is equal to current value of bond