Setrakian Industries needs to raise $48.5 million to fund a new project. The company will sell bonds that have a coupon rate of 5.56 percent paid semiannually and that mature in 10 years. The bonds will be sold at an initial YTM of 6.13 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds?

Multiple Choice

48,500 bonds

24,250 bonds

64,243 bonds

25,317 bonds

31,646 bonds

To determine how many bonds Setrakian Industries must sell, we need to find the price of each bond based on the given information and then calculate how many bonds would be required to raise $48.5 million.

Here’s the step-by-step process:

1. **Given Data**:
   - Coupon rate: 5.56% (paid semiannually, so semiannual coupon = 5.56%/2 = 2.78%)
   - Par value: $2,000
   - Time to maturity: 10 years (20 semiannual periods)
   - Yield to maturity (YTM): 6.13% annually (semiannual YTM = 6.13%/2 = 3.065%)
   - Required funds: $48.5 million

2. **Price of the Bond**:
   The price of a bond can be calculated using the present value of its coupon payments and the present value of its par value (face value).

   The formula for the price of a bond is:
   \[
   P = C \times \left(1 - \frac{1}{(1 + r)^t}\right) / r + \frac{F}{(1 + r)^t}
   \]
   where:
   - $ C $ is the semiannual coupon payment ($ C = \frac{5.56\%}{2} \times 2000 = 55.60 $),
   - $ r $ is the semiannual YTM ($ r = \frac{6.13\%}{2} = 3.065\% = 0.03065 $),
   - $ t $ is the number of semiannual periods ($ t = 10 \times 2 = 20 $),
   - $ F $ is the face value ($ F = 2000 $).

Now, let's calculate the price of one bond.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you want, I can walk you through the manual calculation process to estimate the bond price and determine the number of bonds needed. Would you like to proceed with that?

Here are five questions to expand on the topic:

1. What are the key differences between coupon rate and yield to maturity (YTM)?
2. How does the bond price fluctuate with changes in the YTM?
3. Why is the YTM expressed semiannually in bond calculations?
4. What factors can affect the bond's price before its maturity?
5. How does raising capital through bonds compare with raising it through equity?

**Tip:** When dealing with bonds, always differentiate between annual and semiannual rates for accurate calculations.

Setrakian Industries needs to raise $48.5 million to fund a new project. The company will sell bonds that have a coupon rate of 5.56 percent paid semiannually and that mature in 10 years. The bonds will be sold at an initial YTM of 6.13 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds?

Learn how to calculate the number of bonds Setrakian Industries must sell to raise $48.5 million. This finance problem involves key concepts such as bond pricing, coupon payments, present value, and yield to maturity (YTM). Suitable for college-level finance or economics students.

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