Question

Smith purchases a 20 year, 8%, $1000 face value bond with a yield rate of 10%. After the 10th coupon he sells the bond. If the new buyer keeps the bond until maturity (at which time she will receive the face value redemption and her last coupon) and her actual semiannual yield rate is also 10% then find her purchase price.

Answer 1

In the given quetion buyer's actual return is 10% which is semiannual

But she is receiving the coupone annually so we have to convert her semiannual yield to annual yield

Annual Yield = (1.05)*(1.05) - 1 ; = 0.1025 or 10.25%

Coupone rate is 8% therefore coupone received per year will be $80

Calculation of purchase price of the bond

Year	Cash flows	Discounting factor @ 10.25%		Present Value
1	$               80.00	0.9070	1/(1.1025)^1	$               72.56
2	$               80.00	0.8227	1/(1.1025)^2	$               65.82
3	$               80.00	0.7462	1/(1.1025)^3	$               59.70
4	$               80.00	0.6768	1/(1.1025)^4	$               54.15
5	$               80.00	0.6139	1/(1.1025)^5	$               49.11
6	$               80.00	0.5568	1/(1.1025)^6	$               44.55
7	$               80.00	0.5051	1/(1.1025)^6	$               40.41
8	$               80.00	0.4581	1/(1.1025)^6	$               36.65
9	$               80.00	0.4155	1/(1.1025)^6	$               33.24
10	$         1,080.00	0.3769	1/(1.1025)^6	$             407.04
			Net present value	$             863.22

hence purchase price of the bond should be $863.22