Company issues 5%, 5-year bonds with a par value of $1,000,000 and semiannual in

Question

Company issues 5%, 5-year bonds with a par value of $1,000,000 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 factors:

n=

i=

Present Value of an Annuity

Present value of $1

5

5

%

4.3295

0.7835

10

3

%

8.7521

0.7812

5

6

%

4.2124

0.7473

10

3

%

8.5302

0.7441

A) $957,355

B) $1,000,000

C) $1,250,000

D) $786,745

E) $1,213,255

n=

i=

Present Value of an Annuity

Present value of $1

5

5

%

4.3295

0.7835

10

3

%

8.7521

0.7812

5

6

%

4.2124

0.7473

10

3

%

8.5302

0.7441

Explanation / Answer

A.$957,355.

bonds selling price = present value of annuity factor *(interest payments) + present value factor *(face value)

here,

relevant present value of annuity factor will be => 6% / 2 =>3%.....(since we have semi annual payment of interest)

and 5 year * 2 semi annual periods =>10 semi annual periods.

=> i=3% and n=10 , present value of annuity factor = 8.5302.

interest payment = face value of bonds * (stated rate) *(6/12)

=> $1,000,000 * 5% *(6/12)

=>$25,000..

present value factor will be =3% for 10th period =>0.7441

maturity value = $1,000,000.

now,

price of bond = (8.5302)*($25,000) + (0.7441) *($1,000,000)

=>$213,255 + $744,100

=>$957,355.

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