Question

Grossnickle Corporation issues 20-year, noncallable, 7.1% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 19 years to maturity

Answer 1

Answer:

Price of bond= $1,185.72

Explanation:

The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.

These cash flows include interest payment and redemption value

The price of the bond can be calculated as follows:

Step 1

PV of interest payment

annual coupon rate = 7.1%

Annual Interest payment =( 7.1%×$1000)= $71

Annual yield = = 5.5%

PV of interest payment  

= A ×(1- (1+r)^(-n))/r

A- interest payment, r- yield - 5.5%, n- no of periods -19 periods

= 71× (1-(1.055)^(-19))/0.055)

= 71× 11.60765352

= 824.143

Step 2  

PV of redemption value (RV)

PV = RV × (1+r)^(-n)

RV - redemption value- $1000, n- 19, r- 5.5%  

= 1,000 × (1+0.055)^(-19)

= 361.579

Step 3

Price of bond = PV of interest payment + PV of RV

$824.143 +  $361.579

Price of bond= $1,185.72