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CA Final · Advanced Financial Management · Security Valuation

Sagar Finance holds a bond with a current price of ₹1,000, yield to maturity 10% p.a. (annual compounding) and Macaulay duration of 4.5 years. Market yields suddenly rise by 50 basis points. Using modified duration, what is the approximate new price of the bond?

The approximate new price is ₹979.55. Modified duration is 4.5 divided by 1.10, or 4.0909. A 0.5% rise in yield reduces price by about 2.045%, roughly ₹20.45 on ₹1,000. Using Macaulay duration without adjustment overstates the fall.

  1. A₹979.55Correct
  2. B₹977.50
  3. C₹1,020.45
  4. D₹1,022.50

Explanation

Modified duration = 4.5/1.10 = 4.0909. Percentage price change ≈ −4.0909 × 0.5% = −2.045%, or about −₹20.45. New price ≈ 1,000 − 20.45 = ₹979.55. Using Macaulay duration directly (4.5 × 0.5% = 2.25%) gives ₹977.50, which is wrong because it omits dividing by (1+y). The options above ₹1,000 carry the wrong sign, since a yield rise lowers price.

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