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#1

3.On 15 August 2023, 3M corporation 4.25% bonds maturing on 15 February 2026 were trading at $100.25 per $100 face value. These bonds pay semi-annual coupons of 4.25%/2, on 15 February 2024, 15 August 2024, 15 February 2025, 15 August 2025, and 15 February 2026.

Please compute the yield-to-maturity, assuming compounding two times per year.

#2

Hi @Jing_Liu !!
To compute the yield-to-maturity (YTM) for a bond, you can use the following formula:
image

Where:

  • C is the semi-annual coupon payment,
  • F is the face value of the bond,
  • P is the current market price of the bond,
  • n is the number of periods (semi-annual periods until maturity), and
  • t is the total number of periods until maturity.

Given the information provided:

  • Semi-annual coupon payment (CC) = 4.25%/2 = 0.0425/2 = 0.021254.25%/2=0.0425/2=0.02125
  • Face value (FF) = $100
  • Current market price (PP) = $100.25
  • Number of periods until maturity (tt) = 2 * 3 (since there are semi-annual periods, and the bond matures in 3 years)

Now, plug these values into the formula:

image
image662×760 25.6 KB

So, the approximate yield-to-maturity is -0.006, or -0.6%. The negative sign indicates that the bond is trading at a premium compared to its face value. Keep in mind that this is an approximate calculation and the actual YTM may vary depending on the exact number of days in each period and other factors.
I hope it helps. Happy Learning :blush: