Question

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 25 years to maturity, and a coupon rate of 7.1 percent paid annually.

If the yield to maturity is 8.2 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To solve for the current price we need to solve the following equation:

Following table shows the calculations:

Year	CF	Discount Factor		Discounted CF
1	€         71.00	1/(1+0.082)^1=	0.924214	0.924214417744917*71=	€               65.62
2	€         71.00	1/(1+0.082)^2=	0.854172	0.854172289967576*71=	€               60.65
3	€         71.00	1/(1+0.082)^3=	0.789438	0.789438345626225*71=	€               56.05
4	€         71.00	1/(1+0.082)^4=	0.72961	0.729610300948452*71=	€               51.80
5	€         71.00	1/(1+0.082)^5=	0.674316	0.674316359471767*71=	€               47.88
6	€         71.00	1/(1+0.082)^6=	0.623213	0.623212901545071*71=	€               44.25
7	€         71.00	1/(1+0.082)^7=	0.575982	0.575982348932598*71=	€               40.89
8	€         71.00	1/(1+0.082)^8=	0.532331	0.532331191250091*71=	€               37.80
9	€         71.00	1/(1+0.082)^9=	0.491988	0.49198816196866*71=	€               34.93
10	€         71.00	1/(1+0.082)^10=	0.454703	0.454702552651257*71=	€               32.28
11	€         71.00	1/(1+0.082)^11=	0.420243	0.420242654945709*71=	€               29.84
12	€         71.00	1/(1+0.082)^12=	0.388394	0.388394320652226*71=	€               27.58
13	€         71.00	1/(1+0.082)^13=	0.35896	0.35895963091703*71=	€               25.49
14	€         71.00	1/(1+0.082)^14=	0.331756	0.331755666281913*71=	€               23.55
15	€         71.00	1/(1+0.082)^15=	0.306613	0.306613369946315*71=	€               21.77
16	€         71.00	1/(1+0.082)^16=	0.283376	0.28337649717774*71=	€               20.12
17	€         71.00	1/(1+0.082)^17=	0.261901	0.261900644341719*71=	€               18.59
18	€         71.00	1/(1+0.082)^18=	0.242052	0.242052351517301*71=	€               17.19
19	€         71.00	1/(1+0.082)^19=	0.223708	0.22370827312135*71=	€               15.88
20	€         71.00	1/(1+0.082)^20=	0.206754	0.206754411387569*71=	€               14.68
21	€         71.00	1/(1+0.082)^21=	0.191085	0.191085407936755*71=	€               13.57
22	€         71.00	1/(1+0.082)^22=	0.176604	0.176603889035818*71=	€               12.54
23	€         71.00	1/(1+0.082)^23=	0.16322	0.163219860476727*71=	€               11.59
24	€         71.00	1/(1+0.082)^24=	0.15085	0.150850148314904*71=	€               10.71
25	€   1,071.00	1/(1+0.082)^25=	0.139418	0.139417881991594*1071=	€            149.32
				Sum of all Discounted CF	€            884.56