Question

Seaside issues a bond that has a stated interest rate of 10%, face amount of $50,000, and is due in 5 years. Interest payments are made semi-annually. The market rate for this type of bond is 12%. What is the issue price of the bond

Answer 1

Answer:

$46300

Explanation:

interest that earned will be $50,000×10%=$5000

Since payments are made semi-annually, a payment of  $2,500 is made every six months

market rate for the bond is 12%, which implies 6% for every 6 months since the payment is semi-annually.

using the Present Value Factor Table, find out the Present Value Factor of the bond.

using 6% interest for 10 terms of six month each, the Present Value Factor is 0.558.

using the Present Value of an Annuity Factor Table,  the Present Value of an Annuity Factor is 7.36.

current value of interest payments = 7.36 * $2,500 =  $18400

current face value of bond= 0.558 * $50,000 =  $27900

current price of bond =  $27900 + $18400 = $46300

Answer 2

Answer:

The issue price of the bond is $46,320

Explanation:

Given;

Face value = $50,000

stated interest rate = 10%

period of duration =  5 years

market rate = 12%

Interest payments are made semi-annually

Price of Bond =  (Present value of face) + (Present value of coupons)

$Present \ value \ of \ face= \frac{50000}{(1.06)^{10}} =27,919.7$

Coupon payments is given as

annual payment = 10% of 50,000  =   $5,000

semi - annual payment = ¹/₂ × $5,000 = $2,500

$Present \ value \ of \ coupons= \frac{2500}{0.06}*(1-\frac{1}{(1.06)^{10}}) =18,400.2$

Price of Bond = $27,919.7 + $18,400.2

                       = $46,320

Therefore, the issue price of the bond is $46,320