Question

7. A $20,000 par value bond matures on January 1, 2020. The bond pays coupons at the annual rate of 7%, payable semiannually (every January 1 and July 1 until maturity). The nominal annual yield to maturity is 10% compounded semiannually. Find the price of the bond on August 25, 2005. Solve this problem theoretically.

Answer 1

To calculate the bond price, one has to simply discount the known future cash flows. Further, there are some analogies, the price of a bond and its yield-to-maturity are negatively correlated to each other. When the yield-to-maturity is higher than the coupon rate, the price of a bond is less than the face value and vice-versa.

Coupon shall be 3.5 percent semiannually on $20,000 par value i.e. $20,000* 3.5% = $700

Time	Interest	Principle	Total cashflow	PV Factor at 5 percent	Present value of future cashflow
6/1/2005	700.00		700	0.9524	666.67
12/1/2005	700.00	-	700.00	0.9070	634.92
6/1/2006	700.00	-	700.00	0.8638	604.69
12/1/2006	700.00	-	700.00	0.8227	575.89
6/1/2007	700.00	-	700.00	0.7835	548.47
12/1/2007	700.00	-	700.00	0.7462	522.35
6/1/2008	700.00	-	700.00	0.7107	497.48
12/1/2008	700.00	-	700.00	0.6768	473.79
6/1/2009	700.00	-	700.00	0.6446	451.23
12/1/2009	700.00	-	700.00	0.6139	429.74
6/1/2010	700.00	-	700.00	0.5847	409.28
12/1/2010	700.00	-	700.00	0.5568	389.79
6/1/2011	700.00	-	700.00	0.5303	371.22
12/1/2011	700.00	-	700.00	0.5051	353.55
6/1/2012	700.00	-	700.00	0.4810	336.71
12/1/2012	700.00	-	700.00	0.4581	320.68
6/1/2013	700.00	-	700.00	0.4363	305.41
12/1/2013	700.00	-	700.00	0.4155	290.86
6/1/2014	700.00	-	700.00	0.3957	277.01
12/1/2014	700.00	-	700.00	0.3769	263.82
6/1/2015	700.00	-	700.00	0.3589	251.26
12/1/2015	700.00	-	700.00	0.3418	239.29
6/1/2016	700.00	-	700.00	0.3256	227.90
12/1/2016	700.00	-	700.00	0.3101	217.05
6/1/2017	700.00	-	700.00	0.2953	206.71
12/1/2017	700.00	-	700.00	0.2812	196.87
6/1/2018	700.00	-	700.00	0.2678	187.49
12/1/2018	700.00	-	700.00	0.2551	178.57
6/1/2019	700.00	-	700.00	0.2429	170.06
12/1/2019	700.00	20,000.00	20,700.00	0.2314	4,789.51
			Price of bond as on 30th June 2005	15,388