Question

Which of the following bonds would be cheapest to deliver given a T-note futures price of 78.6075? (Assume that all bonds have semiannual coupon payments based on a par value of $100.)

Please show steps and formulas

Answers:	a. 6.5-year bond with 3% coupons and a yield of 1.5%
	b. 8.5-year bond with 8.5% coupons and a yield of 10%
	c. 10-year bond with 5.5% coupons and a yield of 6%

Answer 1

ANSWER = B)

8.5-year bond with 8.5% coupons and a yield of 10%

EXPLN:

Par value = $ 100

Semi -annual Coupon = Coupon rate/2

Semi-annual Yield rate = Yield rate / 2

a) 6.5-year bond with 3% coupons and a yield of 1.5%

Coupon	Yield	Semi-annual year
1.5	0.75	13
Semi- annual Year	PVF (0.75%)	Cash flow	PVCF
1	0.99256	1.5	1.488834
2	0.98517	1.5	1.477751
3	0.97783	1.5	1.46675
4	0.97055	1.5	1.455831
5	0.96333	1.5	1.444994
6	0.95616	1.5	1.434237
7	0.94904	1.5	1.42356
8	0.94198	1.5	1.412963
9	0.93496	1.5	1.402445
10	0.92800	1.5	1.392005
11	0.92109	1.5	1.381642
12	0.91424	1.5	1.371357
13	0.90743	1.5	1.361149
13	0.90743	100	90.74324
Current bond value			109.2568

b) 8.5-year bond with 8.5% coupons and a yield of 10%

Coupon	Yield	Semi-annual year
4.25	5	17
Semi- annual Year	PVF (5%)	Cash flow	PVCF
1	0.952381	4.25	4.047619
2	0.907029	4.25	3.854875
3	0.863838	4.25	3.67131
4	0.822702	4.25	3.496486
5	0.783526	4.25	3.329986
6	0.746215	4.25	3.171415
7	0.710681	4.25	3.020396
8	0.676839	4.25	2.876567
9	0.644609	4.25	2.739588
10	0.613913	4.25	2.609131
11	0.584679	4.25	2.484887
12	0.556837	4.25	2.366559
13	0.530321	4.25	2.253866
14	0.505068	4.25	2.146539
15	0.481017	4.25	2.044323
16	0.458112	4.25	1.946974
17	0.436297	4.25	1.854261
17	0.436297	100	43.62967
Current bond value			91.54445

c)

Coupon	Yield	Semi-annual year
2.75	3	20
Semi- annual Year	PVF (3%)	Cash flow	PVCF
1	0.970874	2.75	2.669903
2	0.942596	2.75	2.592139
3	0.915142	2.75	2.51664
4	0.888487	2.75	2.443339
5	0.862609	2.75	2.372174
6	0.837484	2.75	2.303082
7	0.813092	2.75	2.236002
8	0.789409	2.75	2.170875
9	0.766417	2.75	2.107646
10	0.744094	2.75	2.046258
11	0.722421	2.75	1.986659
12	0.70138	2.75	1.928795
13	0.680951	2.75	1.872616
14	0.661118	2.75	1.818074
15	0.641862	2.75	1.76512
16	0.623167	2.75	1.713709
17	0.605016	2.75	1.663795
18	0.587395	2.75	1.615335
19	0.570286	2.75	1.568287
20	0.553676	2.75	1.522608
20	0.553676	100	55.36758
Current bond value			96.28063