Answer-first summary for fast verification
Answer: $100.97
A floating-rate note with a margin equal to the required credit spread is approximately worth par after each reset date. Here, however, the **first coupon is fixed at 3.20%**, while the current required floating rate is based on the new reference rate: \[ \text{Current required annual rate} = 0.50\% + 2.00\% = 2.50\% \] So the note is worth slightly **above par** because the first coupon of 3.20% is higher than the current required rate of 2.50%. Using semiannual compounding: - Discount rate per half-year = \(2.50\%/2 = 1.25\%\) - First coupon amount = \(3.20\%/2 \times 100 = 1.60\) - Subsequent coupons are approximately \(2.50\%/2 \times 100 = 1.25\) each - Time to first coupon = 0.25 years = 0.5 semiannual periods Discounting all remaining cash flows gives a value of about: \[ P \approx 100.9 \] So the nearest answer is **D. $100.97**. If one quoted a clean price, it would be close to par; the small premium comes from the above-market first coupon.
Author: Manit Arora
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Question-505.2. Three months ago, a US corporation issued a floating-rate note (FRN) that pays its first coupon in three months and matures in five years. The index (aka, reference rate; eg, six-month LIBOR) was 1.20% at the time of issuance but has dropped to its current level of 0.50%. The index is quoted per annum with semiannual compounding. The quoted margin on the note is 200 basis points, such that the first coupon pays 3.20% = 1.20% reference + 2.00% margin. Assume three months equals 0.25 years and assume the quoted margin equals the required margin; i.e., the margin is appropriate compensation for credit risk. Which is nearest to the note's current value?
A
$97.35
B
$99.13
C
$100.00
D
$100.97
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