On 4 February 2010 a company issued a bond with a face value of $250,000 that matures exactly 25 years later. The coupon rate is 8% p.a. compounded half-yearly. What is the bond's value on 4 February 2021 assuming the market yield is 5% p.a. compounded half-yearly. Group of answer choices $199,648.89 $324,239.81 $293,840.92 $324,868.33 $187,513.51
Question
On 4 February 2010 a company issued a bond with a face value of $250,000 that matures exactly 25 years later. The coupon rate is 8% p.a. compounded half-yearly. What is the bond's value on 4 February 2021 assuming the market yield is 5% p.a. compounded half-yearly.
Group of answer choices
$199,648.89
$324,239.81
$293,840.92
$324,868.33
$187,513.51
Solution
To calculate the bond's value, we need to calculate the present value of the bond's cash flows, which are the semi-annual coupon payments and the face value payment at maturity.
Step 1: Calculate the semi-annual coupon payment The coupon rate is 8% per annum, compounded semi-annually, so the semi-annual coupon rate is 8%/2 = 4%. The semi-annual coupon payment is 4% of the face value, which is 0.04 * 10,000.
Step 2: Calculate the present value of the coupon payments The bond was issued on 4 February 2010 and it's now 4 February 2021, so there are 25 - 11 = 14 years left until maturity. Since the coupon payments are semi-annual, there are 14 * 2 = 28 periods left. The market yield is 5% per annum, compounded semi-annually, so the semi-annual market yield is 5%/2 = 2.5%. The present value of the coupon payments is 199,648.89.
Step 3: Calculate the present value of the face value payment The face value payment is a single payment of 250,000 / (1 + 0.025)^28 = $124,590.92.
Step 4: Add the present values of the coupon payments and the face value payment The bond's value is the sum of the present values of its cash flows, which is 124,590.92 = $324,239.81.
So, the bond's value on 4 February 2021 is $324,239.81.
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