Watson Co is a tech firm that hasn't figured out their product yet. They have bonds which have a face value of $1,000. The bonds carry a 4 percent semi-annual coupon, and mature in 16 years. What is the current price of these bonds if the yield to maturity (the going market rate, rd) is 5 percent?
$1327.74 |
||
$525.92 |
||
$934.72 |
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$891.62 |
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$890.75 |
Price of a bond is present value of all cash flows associated with the bond - namely coupons and maturity value. It is mathematically represented as:
where P is price of a bond, with periodic coupon C, periodic YTM i, n periods to maturity and M face value.
For our question, C = 4% * 1000/2 = $20 (semi-annual coupon)
i = 5%/2 = 2.5% (semi-annual YTM)
n = 16 * 2 = 32 semi-annual periods
P = 20 * 21.8492 + 453.7706 = 436.9836 + 453.7706
P = $890.75 ---> Answer
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