Question

Problem E,

You are facing the following four Bonds which pay annual coupons:

Bonds                                             A                    B                    C                     D

Face ($)                                       1000              1000              1000                 1000

Present Price ($)                          1009.3458     1008.9778      993.5862          967.6028

Annual Coupon ($)                          80                 80                  80                    80  

Maturity                                        1 year             2 years         3 years               4 years        

Annual Yield Rate (%)                     7.00               7.50             ???                   9.00

The annual Yield Rate (%) for bond C is:

a. 8.25

b. 7.75

c. 9.00

d. 8.75

The Forward Rate of bond B for the second year is (%)

a. 8.00234

b. 7.50000

c. 7.70234

d. 8.30234

The discounted value of the face value of bond B at the end of the first year (beginning of the second year) should be

a. 927.2326

b. 923.9059

c. 925.9059

d. 930.2326

Answer 1

We will calculate internal rate of return on future inflows.

Time	Future Inflow	Discount factor @ 8.25%	Present value
Year 1	80	0.92379	73.9030
Year 2	80	0.85338	68.2707
Year 3	80	0.78834	63.0676
Year 3	1000	0.78834	788.3449
Total			993.5862

At 8.25% present value match the Investment amount.

Annual yield rate for the Bond C is 8.25%.

a. 8.25%

1 year yield rate = 7.00%

2 year yield rate = 7.50%

for 2 year bond yield rate = [(1.075 * 1.075) / 1.070] - 1

=(1.155625 / 1.07 ) - 1

=0.0800234

=8.00234%

option a. 8.00234 is correct

Forward rate of Bond B for the second year:

Face value after 2 years	1,000.0000
Discounting factor @ 7.5%	0.9302
(1/1+7.5%)
Discounting Value after 1 year	930.2326
(Face value * Discounting factor)

Option  d. 930.2326 is correct.