Question

Please copy and paste your Excel bond calculations under each relevant question. Do NOT submit an Excel spreadsheet, only your word document with your name on it.

A) A 30-year Treasury bond expiring on February 15, 2048 with a 3% coupon has a yield of 5%. Calculate its price. Assume the bond’s settlement date is June 30^th, 2018.

B) You want to buy a bond that pays an annual coupon of 4.2% on March 31^st of each year. On June 30^th, 2018, the bond is priced at 99-12 (in points and fractions). You decide to buy (and pay for) the bond on that date at that price. What is the final invoice price that you must pay to the bond seller?

C) Consider an original 5-year US Treasury note with a 3.5% coupon expiring on 06/15/2022. If this note sells at 101-07 in the bond market, what would be its yield to maturity? Assume the bond’s settlement date is 6/30/2018. Remember that US government bonds and notes pay the coupon on a semi-annual basis)

D) General Motors recently issued a 7-year note that pays a 4% coupon rate (paid annually) and expires on February 15, 2025. The current price of this note is 100-04 (in points and fractions). What is this note’s yield to maturity? And assume that the bond’s settlement date is 6/30/2018.

E) It is now one year later and market yields for bonds/notes with similar characteristics have risen to 4.5%. What should now be the (dollar) price of the Albertson’s note? How do you explain the change of price from one year to the other?

Answer 1

Soln : 1) Please refer the table :

Year	1	2.0000	3	4.0000	5	6.0000	7	8.0000	9	10.0000	11	12.0000	13	14.0000	15	16.0000	17	18.0000	19	20.0000	21	22.0000	23	24.0000	25	26.0000	27	28.0000	29	30.0000
Cash flow	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	30.00	1030.00
Discount at 5%	0.95	0.91	0.86	0.82	0.78	0.75	0.71	0.68	0.64	0.61	0.58	0.56	0.53	0.51	0.48	0.46	0.44	0.42	0.40	0.38	0.36	0.34	0.33	0.31	0.30	0.28	0.27	0.26	0.243	0.236
PV	28.57	27.21	25.92	24.68	23.51	22.39	21.32	20.31	19.34	18.42	17.54	16.71	15.91	15.15	14.43	13.74	13.09	12.47	11.87	11.31	10.77	10.26	9.77	9.30	8.86	8.44	8.04	7.65	7.29	242.66
Sum	696.89

Price of the bond = $ 696.89

B) Bond is priced at 99-12 i.e. 99*1000/100 +12/32*1000/100 = 993.75. As bond is to be bought on 30th June 2018

Coupon = 4.2% , Here the buyer will pay the accrued interest also on this bond

Accrued interest = 42 *270/360 = 31.5

Invoice value that seller will get = 993.75 + 31.5 = $1025.25

3) Let r be the yield to maturity, Price of the bond = 101*10 + 2.1875 = 1012.1875

Accrued interest = 17.5*168/360 = 8.16

Actual price = 1012.1875-8.16 = 1004

On solving by hit & trial we get r = 1.71*2 = 3.42%

d) Similarly here we will calculate the yield rate R , price = 1000 + 1.25 = 1001.25

We will get the yield rate as R = 4% (approx.)

Year	1	2.0000	3	4.0000	5	6.0000	7	8.0000	9	10.0000	11	12.0000	13	14.0000
Cash flow	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	1040.00
Discount factor	0.96	0.92	0.89	0.85	0.82	0.79	0.76	0.73	0.70	0.68	0.65	0.62	0.60	0.58
PV	38.46	36.98	35.56	34.19	32.88	31.61	30.40	29.23	28.10	27.02	25.98	24.98	24.02	601.52
Sum	1000.94