Question

Marwick Corporation issues 8%, 5 year bonds with a par value of $1,200,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 6%. What is the bond's issue (selling) price, assuming the following Present Value factors:

Answer 1

Answer:

The selling price of the bonds is $1,302,362.43

Explanation:

Hi, in order to find the present value of the bonds, we need to use the following formula.

$Price=\frac{Coupon((1+Yield)^{n}-1) }{Yield(1+Yield)^{n} } +\frac{FaceValue}{(1+Yield)^{n} }$

Where:

Coupon = the semi-annual interest payment (1,200,000*(8%/2)=48,000)

Yield = Annual market rate (2.96%)

n = Number of semi-annual payments (5 years*2 = 10 semesters)

Let me show you how to convert an effective annual rate (annual market rate) into a semi-annual effective rate.

$r(semi-annual)=(1+r(annual))^{1/2} -1$

$r(semi-annual)=(1+0.06)^{1/2} -1=0.029563$

Everything should look like this.

$Price=\frac{48,000((1+0.029563)^{10}-1) }{0.029563(1+0.029563)^{10} } +\frac{1,200,000}{(1+0.029563)^{10} }$

Therefore, the price is $1,307,074.18

Best of luck