The University of California has two bonds outstanding. Both issues have the same credit rating, a face value of $1,000 and a coupon rate of 4%. Coupons are paid twice a year. Bond A matures in 1 year, while bond B matures in 30 years.

The market interest rate for similar bonds is 9%.

1. What is the price of bond A?
2. What is the price of bond B?
3. Now assume that yields increase to 12%. What is the price of bond A?
4. What is now the price of bond B?

1) price of Bond A=$953.18

2) price of Bond B=$484.05

3) price of Bond A= $ 926.66

4) price of Bond B= $ 353.54

Explanation:

According to the given data, we have two Bonds, Bond A and B with a face of value of $1,000 each of them, the coupon rate is of of 4%.

If The market interest rate for similar bonds is 9%, therefore the price of bond A and B would be calculated using the following formula:

PV(rate,nper,pmt,fv)

Hence, price of Bond A= PV(9%/2,1*2,40/2,1000)*-1

           1) price of Bond A=$953.18      

          price of Bond B= PV(9%/2,30*2,40/2,1000)*-1

          2) price of Bond B=$484.05

If that yields increase to 12%, therefore the price of bond A and B would be the following:

                  price of Bond A= PV(12%/2,1*2,40/2,1000)*-1

                  3) price of Bond A= $ 926.66

                 price of Bond B= PV(12%/2,30*2,40/2,1000)*-1

                 4) price of Bond B= $ 353.54

1. $953.18

2. $484.05

3. $926.66

4. $353.54

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Both of these cash flows discounted and added to calculate the value of the bond.

1.

Bond A

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 4% = $40 annually = $20 semiannually

Number of periods = n = 1 years x 2 = 2 period

Market Rate = 9% annually = 4.5% semiannually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = 20 x [ ( 1 - ( 1 + 4.5% )^-2 ) / 4.5% ] + [ $1,000 / ( 1 + 4.5% )^2 ]

Price of the Bond = $953.18

2.

Bond B

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 4% = $40 annually = $20 semiannually

Number of periods = n = 30 years x 2 = 60 period

Market Rate = 9% annually = 4.5% semiannually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = 20 x [ ( 1 - ( 1 + 4.5% )^-60 ) / 4.5% ] + [ $1,000 / ( 1 + 4.5% )^60 ]

Price of the Bond = $484.05

Now Change the Market Interest rate to 12%

3.

Bond A

Price of the Bond = 20 x [ ( 1 - ( 1 + 6% )^-2 ) / 6% ] + [ $1,000 / ( 1 + 6% )^2 ]

Price of the Bond = $926.66

4.

Bond B

Price of the Bond = 20 x [ ( 1 - ( 1 + 6% )^-60 ) / 6% ] + [ $1,000 / ( 1 + 6% )^60 ]

Price of the Bond = $353.54