Question

Consider three bonds with 6.8% coupon rates, all making annual coupon payments and all selling at a face value of $1,000. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years. a.What will be the price of each bond if their yields increase to 7.8%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 4 Years 8 Years 30 Years Bond price$ $ $ b.What will be the price of each bond if their yields decrease to 5.8%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 4 Years 8 Years 30 Years Bond price$ $ $

Answer 1

Answer:

• a. What will be the price of each bond if their yields increase to 7.8%?

4 Years :  $966,73  (see example)

8 Years :  $942,09  

30 Years : $885,26  

• b. What will be the price of each bond if their yields decrease to 5.8%?

4 Years :  $1,034.81 (see example)

8 Years :  $1,062.59

30 Years : $1,140.64

Explanation:

Principal Present Value  =  F /  (1 + r)^t      

Coupon Present Value   =  C x [1 - 1/(1 +r)^t] / r      

This is an example for 4 years, 7,8%, to the others years only change "t".

The price of this bond it's $740,50 + $226,23 = $966,73      

Present Value of Bonds $740,50 = $1,000/(1+0,0780)^4        

Present Value of Coupons $226,23 =  $68 (Coupon) x 3,33      

3,33 =   [1 - 1/(1+0,0780)^4 ]/ 0,0780      

This is an example for 4 years, 5,8%, to the others years only change "t".

The price of this bond it's $798,10 + $236,71 = $1,034.81      

Present Value of Bonds $798,10 = $1,000/(1+0,0580)^4        

Present Value of Coupons $236,71 =  $68 (Coupon) x 3,48      

3,48 =   [1 - 1/(1+0,0580)^4 ]/ 0,0580