Question

Bond A and Bond B are both annual coupon, five-year, 10,000 par value bonds bought to yield an annual effective rate of 4%.

1. Bond A has an annual coupon rate of r%r%, a redemption value that is 10% below par, and a price of P.

2. Bond B has an annual coupon rate of (r+1)%(r+1)%, a redemption value that is 10% above par, and a price of 1.2P.

Calculate r%

1. 5.85%

2. 6.85%

3. 7.85%

4. 8.85%

5. 9.85%

Answer 1

6.85% is the required rate

We use an excel solver to solve this problem

Initially, we input any random rate r in the rate column ( Here, taken 5% initially)

r	6.85%
		1/(1.04^Year)	Bond A	Bond B
	Year	PV Factor	Cash-flows	PV of cash-flows	Cash-flows	PV of cash-flows
	1	0.961538462	684.6271146	658.2953025	784.627115	754.4491487
	2	0.924556213	684.6271146	632.9762524	784.627115	725.4318737
	3	0.888996359	684.6271146	608.6310119	784.627115	697.5306478
	4	0.854804191	684.6271146	585.2221269	784.627115	670.702546
	5	0.821927107	684.6271146	562.7135835	784.627115	644.9062942
	5	0.821927107	9000	7397.343961	11000	9041.198174
			Bond Price	10445.18224		12534.21868

Bond cash-flows are chalked out for 5 years

Bond A price = 10% below par = 90%*10000 = 9000

Bond B price = 10% above par = 110%*10000 =11000

Coupon payment of Bond A = (r)% *10000

Coupon payment of Bond B = (1+r)% *10000

Input the following constraints in a solver,

Here the constraint is Price of Bond B should be 1.2 times that of Bond A

And the rate cell should be changed to get the required rate

Solving we get,

Hence, 6.85% is the required rate.