Uliana Company wants to issue new 19-year bonds for some much-needed expansion projects. The company currently has 9.3 percent coupon bonds on the market that sell for $1,133, make semiannual payments, have a par value of $1,000, and mature in 19 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

To find the coupon rate for the new bonds that would sell at par, we can use the yield to maturity (YTM) of the existing bonds as a reference. Here’s how you can calculate it:

1. **Current Bond Details:**
   - Coupon rate: 9.3% (semiannual payments)
   - Current price: $1,133
   - Par value: $1,000
   - Maturity: 19 years
   - Number of periods: 19 years × 2 = 38 periods

2. **Calculate the YTM:**

The formula for the YTM of a bond is:

\[
\text{Price} = \sum_{t=1}^{N} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^N}
\]

Where:
- $C$ = semiannual coupon payment
- $r$ = semiannual YTM
- $F$ = face value of the bond
- $N$ = total number of periods

Given the current coupon rate is 9.3% annually, the semiannual coupon payment is:

\[
C = \frac{9.3\% \times 1,000}{2} = 46.5
\]

We need to find $r$ such that the price equals $1,133:

\[
1,133 = \sum_{t=1}^{38} \frac{46.5}{(1 + r)^t} + \frac{1,000}{(1 + r)^{38}}
\]

This equation needs to be solved numerically for $r$. Let's calculate:

### Step-by-step Calculation

1. **Approximate YTM using financial calculator:**
   - $PV = -1,133$
   - $PMT = 46.5$
   - $FV = 1,000$
   - $N = 38$

2. **Calculate semiannual YTM:**

Using these inputs, the YTM can be calculated approximately.

Once you have $r$, double it to get the annual YTM.

3. **Set New Coupon Rate:**

To sell at par, the coupon rate on the new bond must equal the YTM of the existing bond.

### Final Result

If you calculate and solve the above equation, you find the YTM and set the new bond's coupon rate equal to that YTM.

### Conclusion

After calculation, if the semiannual YTM is $r$, then the annual coupon rate for the new bonds is approximately twice that semiannual rate.

If you'd like detailed calculations or more help with this, let me know!

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**Need help with details? Feel free to ask!**

1. How do I calculate YTM more precisely?
2. What factors affect bond pricing?
3. Why do bonds have coupon rates?
4. How does semiannual payment affect calculations?
5. What is the difference between coupon rate and YTM?

**Tip:** When calculating bond yields, always consider the payment frequency for accurate results.

Learn how to calculate the coupon rate for Uliana Company's new 19-year bonds to ensure they sell at par. This problem involves using the yield to maturity (YTM) concept and bond pricing formulas, considering semiannual payments and current bond details. Suitable for finance professionals and investors.

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