Question

Consider a 10 year bond which pays 6% coupon annually and has a yield-to-maturity of 7%. How much would the price of bond change if investors required return increases to 8% per year?

		decrease by approximately $64
		decrease by approximately $52
		increase by approximately $64
		increase by approximately $54

Answer 1

First we need to find the price at 7% yield:

Year	CF	Discount Factor		Discounted CF
1	$       60.00	1/(1+0.07)^1=	0.934579439	0.934579439252336*60=	$   56.07
2	$       60.00	1/(1+0.07)^2=	0.873438728	0.873438728273212*60=	$   52.41
3	$       60.00	1/(1+0.07)^3=	0.816297877	0.816297876890852*60=	$   48.98
4	$       60.00	1/(1+0.07)^4=	0.762895212	0.762895212047525*60=	$   45.77
5	$       60.00	1/(1+0.07)^5=	0.712986179	0.712986179483668*60=	$   42.78
6	$       60.00	1/(1+0.07)^6=	0.666342224	0.666342223816512*60=	$   39.98
7	$       60.00	1/(1+0.07)^7=	0.622749742	0.622749741884591*60=	$   37.36
8	$       60.00	1/(1+0.07)^8=	0.582009105	0.582009104565038*60=	$   34.92
9	$       60.00	1/(1+0.07)^9=	0.543933743	0.543933742584148*60=	$   32.64
10	$ 1,060.00	1/(1+0.07)^10=	0.508349292	0.508349292134718*1060=	$ 538.85
				Price= Sum of all Discounted CF	$ 929.76

Now we find the price at 8% yield:

Year	CF	Discount Factor		Discounted CF
1	$       60.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*60=	$   55.56
2	$       60.00	1/(1+0.08)^2=	0.85733882	0.857338820301783*60=	$   51.44
3	$       60.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*60=	$   47.63
4	$       60.00	1/(1+0.08)^4=	0.735029853	0.735029852796453*60=	$   44.10
5	$       60.00	1/(1+0.08)^5=	0.680583197	0.680583197033753*60=	$   40.83
6	$       60.00	1/(1+0.08)^6=	0.630169627	0.630169626883105*60=	$   37.81
7	$       60.00	1/(1+0.08)^7=	0.583490395	0.583490395262134*60=	$   35.01
8	$       60.00	1/(1+0.08)^8=	0.540268885	0.540268884501976*60=	$   32.42
9	$       60.00	1/(1+0.08)^9=	0.500248967	0.500248967131459*60=	$   30.01
10	$ 1,060.00	1/(1+0.08)^10=	0.463193488	0.463193488084684*1060=	$ 490.99
				Price= Sum of all Discounted CF	$ 865.80

So the difference in the price is 929.76-865.80= $63.96

So the price has decreased by approx. $64