Question

Bonds valuation You own a bond that pays 70$ in annual interest, with a 1 000$ par value. It matures in 15 years. Your required rate of return is 7%. Ba: Calculate the value of the bond. Bb: How does the value change if your required rate of return (i) increases to 9% or (ii) decreases to 5% ? Bc: Explain the implications of your answers in part Bb as they relate to interest rate risk, premium bonds, and discount bonds. Bd: Assume that the bond matures in 5 years instead of 15 years. Recompute your answers in part Bb. B1: Calculate the value of a bond that will mature in 16 years and has a 1 000$ face value. The yearly coupon interest rate is 4,5%, and the investor’s required rate of return is 6%. B2: Trico bonds have an annual coupon rate of 8% and a par value of 1 000$ and will mature in 20 years. B2a: If you require a return of 7%, what price would you be willing to pay for the bond ? B2b: What happens if you pay more for the bond? B2c: What happens if you pay less for the bond?

Answer 1

Value of bond

withannual int 70, par valur 1000,rate of return (r)7%,maturity (n) 15 yrs

, present val= pv factor * annual interest

		pv factor @7%	annual interest	present value
1		0.934579439	70	65.42056
2		0.873438728	70	61.14071
3		0.816297877	70	57.14085
4		0.762895212	70	53.40266
5		0.712986179	70	49.90903
6		0.666342224	70	46.64396
7		0.622749742	70	43.59248
8		0.582009105	70	40.74064
9		0.543933743	70	38.07536
10		0.508349292	70	35.58445
11		0.475092796	70	33.2565
12		0.444011959	70	31.08084
13		0.414964448	70	29.04751
14		0.387817241	70	27.14721
15		0.36244602	70	25.37122
		present value ofinterest flows	637.554
		15 yrs maturity value of 1000	363.63
			value of bond	1001.184

value of bond @9%

		pv factor @9%	annual interest	present value
1		0.917431193	70	64.22018
2		0.841679993	70	58.9176
3		0.77218348	70	54.05284
4		0.708425211	70	49.58976
5		0.649931386	70	45.4952
6		0.596267327	70	41.73871
7		0.547034245	70	38.2924
8		0.50186628	70	35.13064
9		0.46042778	70	32.22994
10		0.422410807	70	29.56876
11		0.38753285	70	27.1273
12		0.355534725	70	24.88743
13		0.326178647	70	22.83251
14		0.299246465	70	20.94725
15		0.274538041	70	19.21766
		present value ofinterest flows	564.2482
		15 yrs maturity value of 1000	274.538
			value of bond	838.7862

value of bond @5%

		pv factor @5%	annual interest	present value
1		0.952380952	70	66.66667
2		0.907029478	70	63.49206
3		0.863837599	70	60.46863
4		0.822702475	70	57.58917
5		0.783526166	70	54.84683
6		0.746215397	70	52.23508
7		0.71068133	70	49.74769
8		0.676839362	70	47.37876
9		0.644608916	70	45.12262
10		0.613913254	70	42.97393
11		0.584679289	70	40.92755
12		0.556837418	70	38.97862
13		0.530321351	70	37.12249
14		0.505067953	70	35.35476
15		0.481017098	70	33.6712
		present value ofinterest flows	726.5761
		15 yrs maturity value of 1000	481.0171
			value of bond	1207.593

Premium bond: A bond which sells at a value greater than face value .discount bond: A bond which sells at a value less than face value.usually if a bond have less interest rate sell at discount and if a bond have high interest rate sell at premium.from above examples when interest rate changes to a higher rate the value of bond will decrease and vice versa.

@5% with maturity 5 rs

		pv factor @5%	annual interest	present value
1		0.952380952	70	66.66667
2		0.841679993	70	58.9176
3		0.77218348	70	54.05284
4		0.708425211	70	49.58976
5		0.649931386	70	45.4952
		present value ofinterest flows	274.7221
		15 yrs maturity value of 1000	649.9314
			value of bond	924.6535

@ 9% with maturity 5 years

		pv factor @9%	annual interest	present value
1		0.917431193	70	64.22018
2		0.841679993	70	58.9176
3		0.77218348	70	54.05284
4		0.708425211	70	49.58976
5		0.649931386	70	45.4952
		present value ofinterest flows	272.2756
		15 yrs maturity value of 1000	649.9314
			value of bond	922.207

with face value 1000, coupon rate 4.5%, rate of return 6%, maturity perion 16 yrs

		pv factor @6%	annual interest	present value
1		0.943396226	45	42.45283
2		0.88999644	45	40.04984
3		0.839619283	45	37.78287
4		0.792093663	45	35.64421
5		0.747258173	45	33.62662
6		0.70496054	45	31.72322
7		0.665057114	45	29.92757
8		0.627412371	45	28.23356
9		0.591898464	45	26.63543
10		0.558394777	45	25.12776
11		0.526787525	45	23.70544
12		0.496969364	45	22.36362
13		0.468839022	45	21.09776
14		0.442300964	45	19.90354
15		0.417265061	45	18.77693
16		0.393646284	45	17.71408
		present value ofinterest flows	454.7653
		15 yrs maturity value of 1000	393.6463
			value of bond	848.4116

with 20 yrs maturity coupon rate 8% face value 1000 he bond price as below

		pv factor @7%	annual interest	present value
1		0.934579439	80	74.76636
2		0.873438728	80	69.8751
3		0.816297877	80	65.30383
4		0.762895212	80	61.03162
5		0.712986179	80	57.03889
6		0.666342224	80	53.30738
7		0.622749742	80	49.81998
8		0.582009105	80	46.56073
9		0.543933743	80	43.5147
10		0.508349292	80	40.66794
11		0.475092796	80	38.00742
12		0.444011959	80	35.52096
13		0.414964448	80	33.19716
14		0.387817241	80	31.02538
15		0.36244602	80	28.99568
16		0.338734598	80	27.09877
17		0.31657439	80	25.32595
18		0.295863916	80	23.66911
19		0.276508333	80	22.12067
20		0.258419003	80	20.67352
		present value ofinterest flows	847.5211
		15 yrs maturity value of 1000	258.419
			value of bond	1105.94

when required rate of return is greater than coupon rate , value of bond is greater than its face value or par value and vice versa.