Question

Find the value of the following two corporate bonds:

	Bond 1	Bond 2
Time to Maturity (Years)	16	16
Coupon Frequency (a year)	2	2
Coupon Rate (Annual)	4%	8%
Face Value	$1,000	$1,000
Required Return (Annual)	7%	7%

b) How does the value of each bond change when the time to maturity changes? Construct a data table that shows the bond value as the maturity declines from 16 years down to zero in one-year increments. You can present one data table for both bonds or two data tables separately – one for each bond. (5 points) Answer in writing – what trend in value do you see for each bond? What is the bond value as maturity approaches zero? Why?

c)Graph the values of the two bonds on one graph with maturity as X axis and bond value as Y axis.

Answer 1

Given:

	Bond 1	Bond 2
Time to Maturity (Years)	16	16
Coupon Frequency (a year)	2	2
Coupon Rate (Annual)	4%	8%
Face Value	$1,000	$1,000
Required Return (Annual)	7%	7%

Coupon Payment and Required Return Rate per Period are:

Coupon payment = Copun rate per period * Bond Face Value

Required rate of return per period = Rate of return / Coupon frequency

	Bond 1	Bond 2
Annual coupon (per period)	$20	$40
Required return (per period)	0.035	0.035

Bond Value Vs. Time to maturity :

Bond Value is the present value of all the future cashflows from the bond and can be calculated using the PV formula in excel as follows:

Time to maturity	Bond 1 Value	Bond 2 Value
16	713.97	1095.34
15	724.12	1091.96
14	734.99	1088.34
13	746.64	1084.45
12	759.12	1080.29
11	772.49	1075.84
10	786.81	1071.06
9	802.15	1065.95
8	818.59	1060.47
7	836.19	1054.60
6	855.05	1048.32
5	875.25	1041.58
4	896.89	1034.37
3	920.07	1026.64
2	944.90	1018.37
1	971.50	1009.50
0	1000.00	1000.00

The formula used for above calculations are:

The trend we observe is that, In case of Bond 1,  As the time to maturity is decreasing, the Bond Value is increasing and in the Year 0, the Bond Value is equal to its face value.

In case of Bond 2,  As the time to maturity is decreasing, the Bond Value is also decreasing and in the Year 0, the Bond Value is equal to its face value.

In case of Bond 1, the Value of the bond is below its Par value (for year 16) and is increasing with decrease in maturity as the Coupon rateis less than the required rate of return.

In case of Bond 2, the value of Bond is greater than its par value (Year 16) and is decreasing with the decrease in maturity as its required rate of return is lower than its coupon rate.

Graph the values of the two bonds on one graph with maturity as X axis and bond value as Y axis:

The graph is plotted using data given above in Excel.