To solve these questions, let's break them down step by step.

Part a: Determine the yield to maturity (YTM) on the Vail bonds

The Yield to Maturity (YTM) is the rate of return earned on a bond if it is held until maturity, considering both the coupon payments and any capital gain or loss when the bond matures. To calculate the YTM, we need to use the following bond pricing formula:

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

Where:

• $P$ is the current price of the bond ($1090)
• $C$ is the annual coupon payment (14% of $1000 = $140)
• $F$ is the face value or par value of the bond ($1000)
• $T$ is the number of years to maturity (12 years)

We need to solve for the YTM. Since the YTM is not easily isolated in a simple formula, this often requires iterative methods or using a financial calculator or spreadsheet tool (like Excel or a financial calculator). However, I’ll walk you through the process conceptually:

1. Input the given data:

   • $P = 1090$
   • $C = 140$
   • $F = 1000$
   • $T = 12$

2. Solve for YTM using an iterative method or a financial calculator:

If you use Excel, you can use the YIELD function:

• =YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis]) Where:
• settlement = today's date (or purchase date)
• maturity = maturity date of the bond
• rate = coupon rate
• pr = current price of the bond ($1090)
• redemption = face value ($1000)
• frequency = 1 for annual payments

This process will give you the YTM for the bond, which should be around 11% (given that the market yield is 11% and the bond is priced above par, we expect the YTM to be lower than the coupon rate).

---

Would you like further details on how to calculate the YTM using a financial calculator or Excel?

---

Moving on to related questions:

1. How do you calculate the coupon payments for a bond?
2. What happens when a bond is priced above par (premium)?
3. How does the YTM compare to the coupon rate when the bond is priced at a premium?
4. What are the key factors that affect the price of a bond in the market?
5. How can you calculate the price of a bond if you know its YTM and other characteristics?

Tip: The YTM calculation requires you to account for both the coupon payments and the difference between the current price and the face value. If the bond is trading at a premium (price above par), the YTM will be lower than the coupon rate.