Question

(1 point) A 11-year bond pays semi-annual coupons at C2 = 9.5%, has a yield rate of y2 = 7.3%, and is redeemable for $ W. If the book value immediately after the 7th coupon payment is $1049.42, and the book value immediately after the 11th coupon payment is $1010.57, what is the bond's face value? Answer: $

Answer 1

Period	Discounting Factor [1/(1.0365^period)]	Discounting Factor Annuity (Sum of discounting factor & all previous discounting factors)
1	0.964785335
2	0.930810743
3	0.898032555
4	0.86640864
5	0.83589835
6	0.80646247
7	0.778063164
8	0.750663931
9	0.724229552
10	0.698726051
11	0.674120648	8.928201438	After 11th
12	0.650381715
13	0.627478741
14	0.605382287
15	0.584063953	11.39550813	After 7th
16	0.563496337
17	0.543653002
18	0.524508444
19	0.506038055
20	0.488218095
21	0.471025658
22	0.454438647

Let Coupons be $C

Value of Bond after 11th coupon payment

= PV of all the future coupons at the end of 11th coupon payment + PV of redemption value at the end of 11th coupon payment

= C*PV Annuity Factor + W*PV discounting factor

= C*8.9282 + W*0.6741

Therefore, 1010.57 = 8.9892C + 0.6741W........................(1)

Value of Bond after 7th coupon payment

= PV of all the future coupons at the end of 7th coupon payment + PV of redemption value at the end of 7th coupon payment

= C*PV Annuity Factor + W*PV discounting factor

= C*11.3955 + W*0.5841

Therefore, 1049.42 = 11.3955C + 0.5841W......................(2)

Solving (1) and (2) simultaneously,

Multiplying (2) by 0.6741/0.5841 = 1.1541, we get

1.1541[1049.42 = 11.3955C + 0.5841W]

1211.14 = 13.1515C + 0.6741W....................................(3)

Now, Subtracting (1) from (3), we get

200.57 = 4.1632C

Therefore, Coupon(semi annual) = C = 200.57/4.1632 = 48.1769

Coupon(semi annual) = Face Value * Coupon Rate(semi annual)

48.1769 = Face Value * 0.0475

Therefore, Face Value = 48.1769/0.0475 = $1014.25 approx

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