Question

Data on a bond:

Face amount of bond : $1000

Terms of redemption: $1000 is redeemable after 10 years

Coupon rate: 5% per year, payable semi-annually

X = Premium if the effective annual yield to maturity is 4%

Y = Discount if the effective annual yield to maturity is 6%

Compute the difference X minus Y

Answer 1

Coupoun rate per 6 month= 5% of 1000*6/12= 25

Prinicpal repayment after 10 years = 1000

Value of bond if YTM is 4% is given as

Time	Coupon Interest	Principal	Total cash flow	Discounting rate at 4%	Discounted Cashflow
	5% of 1000*6/12
N in 6 Months	A	B	C=A+B	D=1/(1+4%)^N	E= C*D
0.5	25.00	-	25.00	0.980580676	24.51
1	25.00	-	25.00	0.961538462	24.04
1.5	25.00	-	25.00	0.942866034	23.57
2	25.00	-	25.00	0.924556213	23.11
2.5	25.00	-	25.00	0.906601956	22.67
3	25.00	-	25.00	0.888996359	22.22
3.5	25.00	-	25.00	0.87173265	21.79
4	25.00	-	25.00	0.854804191	21.37
4.5	25.00	-	25.00	0.838204471	20.96
5	25.00	-	25.00	0.821927107	20.55
5.5	25.00	-	25.00	0.805965838	20.15
6	25.00	-	25.00	0.790314526	19.76
6.5	25.00	-	25.00	0.774967152	19.37
7	25.00	-	25.00	0.759917813	19.00
7.5	25.00	-	25.00	0.745160723	18.63
8	25.00	-	25.00	0.730690205	18.27
8.5	25.00	-	25.00	0.716500695	17.91
9	25.00	-	25.00	0.702586736	17.56
9.5	25.00	-	25.00	0.688942976	17.22
10	25.00	1,000.00	1,025.00	0.675564169	692.45
				Total	1085.12

Hence X= Price of bond - Face value = 1085.12-1000=85.12

Value of bond if YTM is 6% is given as

Time	Coupon Interest	Principal	Total cash flow	Discounting rate at 6%	Discounted Cashflow
	5% of 1000*6/12
N in 6 Months	A	B	C=A+B	D=1/(1+6%)^N	E= C*D
0.5	25.00	-	25.00	0.971285862	24.28
1	25.00	-	25.00	0.943396226	23.58
1.5	25.00	-	25.00	0.916307417	22.91
2	25.00	-	25.00	0.88999644	22.25
2.5	25.00	-	25.00	0.86444096	21.61
3	25.00	-	25.00	0.839619283	20.99
3.5	25.00	-	25.00	0.815510339	20.39
4	25.00	-	25.00	0.792093663	19.80
4.5	25.00	-	25.00	0.769349377	19.23
5	25.00	-	25.00	0.747258173	18.68
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