To find the bond's nominal yield to maturity (YTM) and nominal yield to call (YTC), we can apply the following formulas and methods.

Yield to Maturity (YTM)

The YTM is the interest rate that equates the present value of the bond's cash flows to its current price. This involves solving the equation for YTM, where the price of the bond equals the present value of its coupon payments and face value.

For Bond D:

• Semiannual coupon = $45 (since 9% of $1,000 = $90 annually, divided by 2 = $45 every 6 months)
• Time to maturity = 9 years × 2 = 18 periods
• Face value = $1,000
• Current bond price = $1,150

We solve for $YTM$ using the following equation: $1150 = 45 \times \left(1 - \frac{1}{(1 + r)^{18}}\right) \div r + \frac{1000}{(1 + r)^{18}}$ Where $r$ is the semiannual yield, and multiplying the result by 2 gives the nominal annual yield to maturity.

Since solving this equation algebraically is complex, we use a trial-and-error or financial calculator approach to find that:

$YTM = 3.46\% \text{ semiannual yield}$

Multiplying by 2 to get the annual nominal yield:

$YTM = 3.46\% \times 2 = 6.92\%$

Thus, the nominal YTM is 6.92%.

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Yield to Call (YTC)

The YTC is the interest rate that equates the present value of the bond's cash flows to its call price if the bond is called after 6 years.

For Bond D:

• Call price = $1,080
• Time to call = 6 years × 2 = 12 periods
• Semiannual coupon = $45
• Current bond price = $1,150

We solve for $YTC$ using the following equation: $1150 = 45 \times \left(1 - \frac{1}{(1 + r)^{12}}\right) \div r + \frac{1080}{(1 + r)^{12}}$ Where $r$ is the semiannual yield to call, and multiplying the result by 2 gives the nominal annual yield to call.

After calculating using trial-and-error or a financial calculator:

$YTC = 3.02\% \text{ semiannual yield}$

Multiplying by 2 to get the annual nominal yield:

$YTC = 3.02\% \times 2 = 6.04\%$

Thus, the nominal YTC is 6.04%.

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Final Results:

• Nominal YTM = 6.92%
• Nominal YTC = 6.04%

Do you need any further details or have questions about the process?

Here are five related questions to deepen your understanding:

1. How does the callable feature affect a bond's price compared to a non-callable bond?
2. What factors influence whether a company decides to call a bond early?
3. What is the difference between current yield and yield to maturity?
4. How does an increase in market interest rates affect the price of a bond with a fixed coupon rate?
5. What are the risks associated with investing in callable bonds?

Tip: When comparing YTM and YTC, keep in mind that if interest rates fall, the issuer is more likely to call the bond, which means investors should focus on YTC.