A 18 year bond at YTM 6%, coupon rate of 9.215% face value of $1000, that was $1350.95. Called price $1120, called at 5 years at 12% premium over par for a realized yield of 3.675%? If you bought one of these bonds today, what would be your expected rate of return?

To determine the expected rate of return on the bond if purchased today, we need to evaluate a few key details. The bond has the following characteristics:

1. **Face Value (Par Value)**: $1,000
2. **Coupon Rate**: 9.215%
3. **Current Price**: $1,350.95
4. **Yield to Maturity (YTM)**: 6%
5. **Call Price**: $1,120
6. **Time to Call**: 5 years
7. **Realized Yield if Called**: 3.675%
8. **Call Premium**: 12% over par value (so $1,120 is the call price, which is $1,000 + $120)

To find the expected rate of return, we have to compare the yield to maturity (YTM) with the yield to call (YTC). The bond's expected rate of return will be the lower of the two because the bond might be called early by the issuer if it’s advantageous for them (e.g., interest rates drop).

### 1. **Yield to Maturity (YTM):**
The YTM is already given as 6%. This is the return you would expect if you held the bond until maturity (18 years).

### 2. **Yield to Call (YTC):**
To calculate the yield to call, we use the following information:
- **Price Paid**: $1,350.95
- **Call Price**: $1,120
- **Number of Years Until Call**: 5 years

We can calculate the YTC using the formula:

\[
YTC = \frac{C + \frac{(Call \, Price - Current \, Price)}{Years \, to \, Call}}{\frac{(Call \, Price + Current \, Price)}{2}}
\]

Where $ C $ is the annual coupon payment, which is calculated as:

\[
C = \text{Coupon Rate} \times \text{Face Value} = 9.215\% \times 1000 = \$92.15
\]

### Steps:
1. Calculate the annual coupon payment $ C = \$92.15 $.
2. Calculate the annualized capital loss due to the bond being called early:
\[
\text{Annualized Capital Loss} = \frac{(Call \, Price - Current \, Price)}{Years \, to \, Call} = \frac{(1120 - 1350.95)}{5} = -\$46.19
\]
3. Calculate the average price:
\[
\text{Average Price} = \frac{(Call \, Price + Current \, Price)}{2} = \frac{(1120 + 1350.95)}{2} = \$1235.475
\]
4. Substitute these into the formula for YTC:
\[
YTC = \frac{92.15 - 46.19}{1235.475} \approx 3.72\%
\]

The yield to call is approximately 3.72%, which is very close to the realized yield provided (3.675%). 

### Conclusion:
The expected rate of return if the bond is called is around **3.72%**. Since bonds are usually called if the call yield is lower than the yield to maturity, your expected rate of return is the **Yield to Call** (YTC), which is 3.72%.

### Do you want more details or have any questions? Here are some related questions:

1. How does bond pricing change when interest rates fluctuate?
2. What factors influence whether a bond is called before maturity?
3. How does the coupon rate impact the bond's attractiveness in the market?
4. What is the difference between Yield to Maturity (YTM) and Yield to Call (YTC)?
5. How do call provisions affect the risk and return of a bond?

**Tip:** Always compare the yield to maturity with the yield to call when evaluating callable bonds, as the issuer might call the bond if it becomes favorable to them.

Learn how to calculate the expected rate of return on a bond with given YTM and YTC values. Explore the differences between Yield to Maturity (YTM) and Yield to Call (YTC) using practical examples. Suitable for advanced finance students and professionals.

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