Problem Breakdown:

Given:

• Coupon rate: 4.8% annually, with semi-annual coupon payments.
• Bond price: $98.51 (quoted as a percentage of par).
• Callable at par: After 2 years (at par value of $100).
• Maturity: 3 years.
• Coupons: Semi-annual payments, so $N = 6$ periods (3 years * 2).

Part 1: Yield to Maturity (YTM)

To find the YTM, we can use the formula for the bond price:

$P = \sum_{t=1}^{N} \frac{C}{(1 + \frac{YTM}{2})^t} + \frac{F}{(1 + \frac{YTM}{2})^N}$

Where:

• $P$ is the price of the bond ($98.51).
• $C$ is the semi-annual coupon payment: $C = \frac{4.8\% \times 100}{2} = 2.40$.
• $F$ is the face value (par value) = $100.
• $N$ is the number of periods = 6 (since 3 years with semi-annual payments).
• $YTM$ is the yield to maturity (annual).

We will solve for $YTM$ by iteration or using financial calculator functions.

Part 2: Yield to Call (YTC)

For the YTC, the bond can be called at par in 2 years. Thus, the number of periods to call is 4 (2 years * 2). The formula is similar:

$P = \sum_{t=1}^{N_{call}} \frac{C}{(1 + \frac{YTC}{2})^t} + \frac{F}{(1 + \frac{YTC}{2})^{N_{call}}}$

Where:

• $N_{call} = 4$ (since the bond can be called after 2 years).
• The rest of the parameters remain the same, but we solve for YTC.

Part 3: Yield to Worst (YTW)

The YTW is the minimum of the YTM and the YTC. This means we compare the yield to maturity and the yield to call, and the lower of the two is the yield to worst.

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Let me calculate both YTM and YTC first.### Results:

• Yield to Maturity (YTM): 5.34% (rounded to two decimal places).
• Yield to Call (YTC): 5.60% (rounded to two decimal places).

Part 3: Yield to Worst (YTW)

The yield to worst is the lower of the yield to maturity and the yield to call, which is:

• Yield to Worst (YTW): 5.34%.

Would you like further details on how these values were calculated or need additional clarification?

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Here are some follow-up questions for deeper understanding:

1. What are the differences between YTM and YTC in callable bonds?
2. How does the bond's price relate to its yield?
3. What factors influence the decision to call a bond early?
4. How does semi-annual coupon payment impact the yield calculations?
5. How do market interest rates affect the bond's callability?

Tip: For callable bonds, always calculate both YTC and YTM to assess the yield under different scenarios, as the issuer can decide to call the bond depending on market conditions.