Question

A corporate bond has 22 years to maturity, a face value of $1,000, a coupon rate of 4.6% and pays interest semiannually. The annual market interest rate for similar bonds is 3.3%.
Required:
a. What is the price of the bond Intro A bond has an annual coupon rate of 3.4%, a face value of $1,000, a price of $883.61, and matures in 10 years.
b. What is the bond's YTM?
c. What is the current yield?

Answer 1

Answer:

a. The answer is: $1,008.40

b. The bond's YTM is 3.343%

c. The current yield is 3.826%

Explanation:

a. Bond price formula: ∑(C* / (1+YTM)$n$ )

The price of the bond Intro A with i=1,2...10 is:

∑($1,000 x 3.4% / (1 + 3.3%)$i$ ) = $1,008.40

b.  The price of the corporate bond which has 22 years to maturity is: $1,202.20

Given that the bond is trading at par value, the bond's YTM is:

[Annual Interest Payment + ((Face Value – Current Price) / (Years to Maturity))] / ( ( Face Value + Current Price ) / 2 )

= [$1,000 x 4.6% + (($1,000 - $1,202.20) /  22)]  / (($1,000 + $1,202.20) /2)

= 3.343%

c. The bond's current yield is:

Annual Interest Payment / Current Price = $46 / $1,202.2 = 3.826%