Question

The City of Aurora issued bonds on Dec 1, 2014 with a 4% coupon from year1through year7, 5% coupon from year 8 through 10, 6% from year 11 through year 13,and a 7% coupon from year 14 through year 15. that will mature on Dec 1, 2029 (15 years

You buy the bond on Dec 1, 2020 (six years after it was issued The YTM for bonds such as the City of Aurora was 6% on Dec 1, 2020 and the stock returns was 10%. You plan to hold the bond until maturity (9 years from now]. Calculate the value (price) of a $1000City of Aurora bond as of Dec

you had to sell this bond 6 years after you purchased the bond when the bond yield similar to your bond was 4% and the stock return was 6% what would be the price you sold your bond at? Remember bond s interest is received semi-annually.

please show me the work or the steps

Thank you.

Answer 1

As it's variable coupons, we need to calculate the PV of cash flows on the bond separately--- at the semi-annual YTM of 6%/2= 3% 0r 0.03 per s/a period

so, PV /Price of the bond as of Dec 1, 2020=

(20/1.03^1)+(20/1.03^2)+(25/1.03^3)+(25/1.03^4)+(25/1.03^5)+(25/1.03^6)+(25/1.03^7)+(25/1.03^8)+(30/1.03^9)+(30/1.03^10)+(30/1.03^11)+(30/1.03^12)+(30/1.03^13)+(30/1.03^14)+(35/1.03^15)+(35/1.03^16)+(35/1.03^17)+(35/1.03^18)+(1000/1.03^18)=

967.62

which can be tabulated as follows:

Semi-annual coupon period no.	Semi-annual coupon amt.	$ coupon amt.(% *$1000)	Semi-annual period no.for YTM	PV of semi-annual coupon($ amt./1.03^ (YTMn)
13	2%	20	1	19.42
14	2%	20	2	18.85
15	2.50%	25	3	22.88
16	2.50%	25	4	22.21
17	2.50%	25	5	21.57
18	2.50%	25	6	20.94
19	2.50%	25	7	20.33
20	2.50%	25	8	19.74
21	3%	30	9	22.99
22	3%	30	10	22.32
23	3%	30	11	21.67
24	3%	30	12	21.04
25	3%	30	13	20.43
26	3%	30	14	19.83
27	3.50%	35	15	22.47
28	3.50%	35	16	21.81
29	3.50%	35	17	21.18
30	3.50%	1035	18	607.95
			Price =	967.62

Price of the bond after 6 years , at 4% p.a. or 2% , 0.02 market interest rate per semi-annual period ----is the PV of the remaining coupons PLUS face value to be received at maturity, ie.

(30/1.02^1)+(30/1.02^2)+(35/1.02^3)+(35/1.02^4)+(35/1.02^5)+(35/1.02^6)+(1000/1.02^6)=

1074.31

With same columns as above, price to be sold is

25	3%	30	1	29.41
26	3%	30	2	28.84
27	3.50%	35	3	32.98
28	3.50%	35	4	32.33
29	3.50%	35	5	31.70
30	3.50%	1035	6	919.05
			Price =	1074.31