To calculate the yield to call (YTC), we need to use the following key inputs for the bond pricing formula:

1. Current bond price: This is the price at which the bond is currently selling.
2. Coupon rate: The bond pays an 8.4% coupon rate annually, or 4.2% per half-year.
3. Number of periods until call: This depends on the call date.
4. Call price: This is the price at which the bond will be called (redeemed early).
5. Coupon payment: The coupon payment is based on the coupon rate applied to the face value of the bond.

We’ll break down the three scenarios you asked for:

1. Yield to Call (YTC) with Call Price of $1,120 in Six Years

Given:

• Coupon rate: 8.4% annual (or 4.2% per half-year).
• Call price: $1,120.
• Number of periods until call: 6 years = 12 periods (semiannual).
• Current bond price: We are not explicitly told, but we assume it’s at par value (or use the yield to maturity as reference).

Let's calculate the YTC using an iterative process, solving for the interest rate in the following bond pricing formula:

$P = \sum_{t=1}^{12} \frac{C}{(1 + r/2)^t} + \frac{M}{(1 + r/2)^{12}}$ Where:

• $P$ is the current bond price.
• $C$ is the semiannual coupon payment (based on 8.4% of the bond's face value, so $C = \frac{8.4\%}{2} \times 1,000 = 42$).
• $M$ is the call price ($1,120).
• $r$ is the yield to call (what we are solving for).

Since the bond currently sells at a yield to maturity (YTM) of 7.4%, we can expect the YTC to be slightly different.

Steps:

1. Approximate or solve iteratively for the YTC using the formula by trial and error or financial calculator.
2. For simplicity, we use a financial calculator or software to compute the exact YTC.

2. Yield to Call with Call Price of $1,070 in Six Years

In this scenario, the only change is the call price, which is now $1,070.

Using the same bond pricing formula, we substitute the call price $M$ as $1,070 instead of $1,120. Everything else remains the same. Solving for $r$, this will give a slightly different YTC, as the call price affects the terminal value of the bond.

Steps:

1. Recalculate with the new call price ($1,070) to find the updated YTC.

3. Yield to Call with Call Price of $1,120 but Callable in Three Years

In this scenario, the call price reverts to $1,120, but the bond can now be called in three years instead of six.

• Number of periods: 3 years = 6 periods (semiannual).
• Call price: $1,120.

Steps:

1. Substitute the number of periods as 6 instead of 12.
2. Recalculate the YTC with this updated timeline.

Conclusion:

The YTC changes based on both the call price and the time to call. Generally:

• A higher call price results in a lower YTC (since the bondholder is receiving more at the call).
• A shorter time to call usually results in a higher YTC, as the bondholder has less time to earn interest from the bond.

Would you like the detailed step-by-step calculation for each scenario?

Five relative questions:

1. What is the difference between YTC and YTM in bond valuation?
2. How does the coupon rate influence the bond's market price when interest rates change?
3. What factors influence a bond issuer's decision to call a bond?
4. How does bond convexity impact its yield calculations?
5. Can a bond's price exceed its call price, and what does this signify?

Tip:

The yield to call (YTC) assumes the bond will be called as soon as it becomes callable. Always compare YTC and YTM when evaluating callable bonds.