A company wishes to issues bonds with a coupon rate of 5%. The company wishes to raise 100 million dollars net of commissions (5% of total sales). Each bond has a face value of $1,000 and matures in 10 years. Interest is to be paid semi-annually. Using the following conditions, please determine how many bonds the company has to sell in order to raise the necessary capital:

Question

A company wishes to issues bonds with a coupon rate of 5%. The company wishes to raise 100 million dollars net of commissions (5% of total sales). Each bond has a face value of $1,000 and matures in 10 years. Interest is to be paid semi-annually. Using the following conditions, please determine how many bonds the company has to sell in order to raise the necessary capital:

Answer 1

To determine how many bonds the company needs to sell in order to raise the necessary capital, we can follow these steps:

Step 1: Calculate the total capital required
The company wishes to raise 100 million dollars net of commissions, which means the total capital required can be calculated as follows:
Total Capital = Desired Net Proceeds / (1 - Commission Rate)
Total Capital = 100,000,000 / (1 - 0.05)

Step 2: Calculate the total face value of bonds needed
Each bond has a face value of $1,000, so the total face value of bonds needed can be calculated as follows:
Total Face Value = Total Capital / Face Value of One Bond
Total Face Value = Total Capital / $1,000

Step 3: Calculate the number of bonds needed
Since we know that interest is paid semi-annually, and the bonds mature in 10 years, we need to calculate the number of semi-annual periods in 10 years:
Number of Semi-annual Periods = Maturity Period in Years / Number of Bond Payments per Year
Number of Semi-annual Periods = 10 years / 2

Now, we can calculate the number of bonds needed:
Number of Bonds = Total Face Value / Number of Semi-annual Periods

Let's plug in the given values and calculate the result:

Total Capital = 100,000,000 / (1 - 0.05) = 105,263,158.33 (rounded to two decimal places)

Total Face Value = Total Capital / $1,000 = 105,263,158.33 / 1,000 = 105,263.16 (rounded to two decimal places)

Number of Semi-annual Periods = 10 years / 2 = 5

Number of Bonds = Total Face Value / Number of Semi-annual Periods = 105,263.16 / 5 = 21,052.63 (rounded to two decimal places)

Therefore, the company needs to sell approximately 21,053 bonds in order to raise the necessary 100 million dollars net of commissions.