On 4 September 2012 a company issued a bond with a face value of $500,000 that matures exactly 20 years later. The coupon rate is 7% p.a. compounded half-yearly. What is the bond's value on 4 September 2018 assuming the market yield is 4% p.a. compounded half-yearly. Group of answer choices $655,301.73 $749,945.95 $663,832.88 $659,609.54 $705,166.09
Question
On 4 September 2012 a company issued a bond with a face value of $500,000 that matures exactly 20 years later. The coupon rate is 7% p.a. compounded half-yearly. What is the bond's value on 4 September 2018 assuming the market yield is 4% p.a. compounded half-yearly.
Group of answer choices
$655,301.73
$749,945.95
$663,832.88
$659,609.54
$705,166.09
Solution
To calculate the bond's value, we need to calculate the present value of the bond's cash flows. The bond's cash flows consist of semi-annual coupon payments and the face value of the bond that will be paid back at maturity.
Step 1: Calculate the semi-annual coupon payment The coupon rate is 7% per annum, compounded semi-annually, so the semi-annual coupon rate is 7%/2 = 3.5%. The semi-annual coupon payment is 3.5% of the face value of the bond, which is 500,000 * 3.5% = $17,500.
Step 2: Calculate the present value of the coupon payments The bond was issued on 4 September 2012 and it's now 4 September 2018, so 12 periods (6 years * 2) have passed. There are 20 years * 2 - 12 = 28 periods left until the bond matures. The market yield is 4% per annum, compounded semi-annually, so the semi-annual market yield is 4%/2 = 2%. The present value of the coupon payments is 374,972.95.
Step 3: Calculate the present value of the face value The present value of the face value is 375,973.00.
Step 4: Calculate the bond's value The bond's value is the sum of the present value of the coupon payments and the present value of the face value. So, the bond's value is 375,973.00 = $750,945.95.
So, the bond's value on 4 September 2018 is 749,945.95.
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