Question

A US treasury bond was issued today with a maturity of 30 years, face amount of $1000, redeemable at par, coupon rate of 2% convertible semiannually. The 30-year treasury yield today is at 1.2% convertible semiannually. Using the information above, answer the next four questions:

a. Without calculation, is the bond priced with a premium or a discount and why? Then, calculate the value of premium / discount.

b. Calculate the book value of the bond right after the 9th coupon payment.

c. Calculate the amount of amortization of premium / accumulation of discount in the 15th coupon payment.

d. Calculate the amount of interest in the 24th coupon payment.

Answer 1

a. Yield or YTM < coupon rate

so, Price > par

so, it's a bond priced with a premium

We will find the issue price of the bond

using the formula to find the present value,ie.current market Price of bonds,

Price=PV of its future cash flows=PV of all its future coupon cash flows+PV of face value to be received at maturity----both discounted at the Yield or YTM

Price of the bond=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where, price is to be found out------??

Pmt.= The semi-annual coupon in $ , ie. 1000*2%/2= $ 10

r= the semi-annual Yield or YTM --ie. 1.2%/2=0.6% or 0.006 per s/a period

n= no.of coupon period still to maturity, ie. 30 yrs.*2= 60

FV= face value, ie. $ 1000

So, plugging in these values in the formula,

Price=(10*(1-(1+0.006)^-60)/0.006)+(1000/(1+0.006)^60)=

1201.05

So, value of premium =1201.05-1000=

201.05

b.Book value of the bond right after the 9th pmt.

if bond premium is amortised on straight-line basis,

it can be answered with calculations

premium amortised with every semi-annual coupon pmt.=

201.05/60=

3.35

So,book value of the bond , right after the 9th pmt.=

Face value+Premium yet to be amotised

1000+(201.05-(3.35*9))=

1170.90

c. Amount of amortization of premium in the 15th coupon payment.

201.05/60=

3.35

d. Amount of interest in the 24th coupon payment.

Coupon amt.-Prem. Amortised

10-3.35= 6.65

if bond premium is amortised on effective interest rate method

Reading from the amortisation table,

b.Book value of the bond right after the 9th pmt.

1175.29

c. Amount of amortization of premium in the 15th coupon payment.

3.04

d. Amount of interest in the 24th coupon payment.

6.79

Effective interest rate amortisation of bond premium
No.of semi-annual period	Semi-annual coupon amt.	Interest expense	Premium amortised	Credit Bal. in Bond premium a/c	Face value	Book value
1	2=FV*1%	3=Prev. BV*0.6%	4=2-3	5=Prev.5+Current 4	6=FV	7=5+6
	Cr. Cash	Dr. Int. Exp.	Dr. Bond premium
0				201.05	1000	1201.05
1	10	7.21	-2.79	198.26	1000.00	1198.26
2	10	7.19	-2.81	195.45	1000.00	1195.45
3	10	7.17	-2.83	192.62	1000.00	1192.62
4	10	7.16	-2.84	189.77	1000.00	1189.77
5	10	7.14	-2.86	186.91	1000.00	1186.91
6	10	7.12	-2.88	184.03	1000.00	1184.03
7	10	7.10	-2.90	181.14	1000.00	1181.14
8	10	7.09	-2.91	178.23	1000.00	1178.23
9	10	7.07	-2.93	175.29	1000.00	1175.29
10	10	7.05	-2.95	172.35	1000.00	1172.35
11	10	7.03	-2.97	169.38	1000.00	1169.38
12	10	7.02	-2.98	166.40	1000.00	1166.40
13	10	7.00	-3.00	163.40	1000.00	1163.40
14	10	6.98	-3.02	160.38	1000.00	1160.38
15	10	6.96	-3.04	157.34	1000.00	1157.34
16	10	6.94	-3.06	154.28	1000.00	1154.28
17	10	6.93	-3.07	151.21	1000.00	1151.21
18	10	6.91	-3.09	148.11	1000.00	1148.11
19	10	6.89	-3.11	145.00	1000.00	1145.00
20	10	6.87	-3.13	141.87	1000.00	1141.87
21	10	6.85	-3.15	138.72	1000.00	1138.72
22	10	6.83	-3.17	135.56	1000.00	1135.56
23	10	6.81	-3.19	132.37	1000.00	1132.37
24	10	6.79	-3.21	129.16	1000.00	1129.16