Question

On the 1st October 2016, K.J Limited issued bonds with a maturity date of 1st October 2028. One K.J bond has a face value of $100,000 and the coupon rate is 4.50% p.a. with interest payable half-yearly. Assuming the market yield is 6% p.a. calculate the value of one bond:

(a) on the 1st October 2020.

(b) five years before maturity.

(c) one year before maturity.

Please do NOT use excel. Please calculate using formulas. Please show detailed calculations & please show formulas.

Answer 1

Face value of bond = redemprion value of bond = $100,000

Coupon rate 4.5% p.a. payable half yearly i.e 2.25% for 6 months = $100,000 x 2.25% = $2,250

Yield to maturity 6% p.a. or 3% for 6 months

Current price of bond = Present Value ( PV) of periodic coupons + PV of redemption value

(a) Price of bond on 1st October 2020 :

Time to maturity = 8 years or 16, 6 month periods

Periods	Periodic payments	PV at 3%
1	$2,250	2184.47
2	$2,250	2120.84
3	$2,250	2059.07
4	$2,250	1999.10
5	$2,250	1940.87
6	$2,250	1884.34
7	$2,250	1829,45
8	$2,250	1776.17
9	$2,250	1724.44
10	$2,250	1674.21
11	$2,250	1625.44
12	$2,250	1578.10
13	$2,250	1532.14
14	$2,250	1487.51
15	$2,250	1444.19
16	$2,250 + $100,000	1402.12 + 62,316.69
	Total	90,579.15

Hence, value of bond on 1st October 2020 is $90,579.15

(b) Price of bond five years before maturity :

Time to maturity = 5 years or 10, 6 month periods

Periods	Periodic payments	PV at 3%
1	$2,250	2184.47
2	$2,250	2120.84
3	$2,250	2059.07
4	$2,250	1999.10
5	$2,250	1940.87
6	$2,250	1884.34
7	$2,250	1829,45
8	$2,250	1776.17
9	$2,250	1724.44
10	$2,250 + $100,000	1674.21 + 74,407.39
	Total	$93,602.34

Hence, value of bond 5 years before maturity is $93,602.34

(c) Price of bond one year before maturity :

Time to maturity = 1 year or 2, 6 month periods

Periods	Periodic payments	PV at 3%
1	$2,250	2184.47
2	$2,250 + $100,000	2120.84 + 94259.96
	Total	$98,564.89

Hence, value of bond 1 year before maturity is $98,564.89