Chartered Financial Analyst Level 1

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A three-year, semiannual-pay bond with a $100 par value and a 5% coupon rate is purchased for$ 108. One year later, if the yield to maturity has decreased by 100 basis points, the change in the bond's value is closest to:

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Explanation:

The correct answer is A ($0.57). The value of a bond is calculated using the present value formula:

PV = [PMT / (1 + r)^1] + [PMT / (1 + r)^2] + ... + [(PMT + FV) / (1 + r)^N]

where:

Calculation Steps:

Initial Yield: Using the calculator inputs (N = 6, PMT = $2.5, FV =$ 100, PV = $108), the yield is 1.114% semiannually (2.228% annually).
New Yield: After a 100 bps decrease, the new yield is 0.614% semiannually.
New Price: With N = 4, PMT = $2.5, FV =$ 100, and r = 0.614%, the new price is $107.43.
Change in Value: $108.00 -$ 107.43 = $0.57.

Why Not B or C?

B ($1.52) incorrectly fails to annualize the interest rate before computing the change.
C ($3.08) incorrectly uses the same time to maturity without adjusting for the passage of one year.