Question

Eliza Mok spots two bonds in the market in which she is interested. The first bond is a 20-year bond issued by Orange Ltd two years ago with a coupon rate of 4.9%. The second bond is a 10-year bond issued by Pear Ltd one year ago at a coupon rate of 5.1%. Both bonds have a pa r value of $1,000 and make semiannual payments.

a. If the yield to maturity (YTM) on the Orange bond is 5.0%, what is the current bond price?

b. If the Pear bond currently sells for 102% of par value, what is the YTM?

c. Eliza wonders why some bonds are selling at premium over par value while other bonds sell at discount or at par. Explain.

Answer 1

ORANGE LTD BOND
Par/Face value	1000
Annual Coupon rate	0.049
Annual coupon	49
semi-annual coupon	24.5
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 5%.
m is the compounding period that is 2
mt is the time period.
price of the bond = sum of present values of future cash flows
r/2	0.025
mt	1	2	3	4	5	6	7	8
future cash flow	24.5	24.5	24.5	24.5	24.5	24.5	24.5	24.5
present value	23.90244	23.31945	22.75069	22.19579	21.65443	21.12627	20.611	20.10829
sum of present values	988.22
a) The current price of this bond is $988.22.
PEAR LTD BOND
Par/Face value	1000
Annual Coupon rate	0.051
Annual coupon	51
semi-annual coupon	25.5
price of the bond = sum of present values of future cash flows
102% of par value.	1020
price of the bond	1020
Use excel to find r
r/2	0.024	r	0.048
mt	1	2	3	4	5	6	7	8
future cash flow	25.5	25.5	25.5	25.5	25.5	25.5	25.5	25.5
present value	24.90234	24.3187	23.74873	23.19211	22.64855	22.11772	21.59934	21.09311
sum of present values	1021.72
b) The YTM of this bond is 4.8%.
c) The first bond (Orange Ltd) is selling at a discount because the yield to maturity (5%) is greater than the coupon rate (4.9%).
The second bond (Pear Ltd) is selling at a premium because the yield to maturity (4.8%) is less than the coupon rate (5.1%).