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

• 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

Step-by-step 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