Step 1: Understanding the Concept:
When a company settles a purchase liability (purchase consideration) by issuing its own securities (shares or debentures), the primary goal is to determine the exact number of units to be issued so that the total value matches the debt owed.
The number of debentures depends on two factors:
1. The Purchase Consideration: The total amount agreed upon for the asset purchased.
2. The Issue Price per Debenture: This is the value at which the debenture is offered to the seller.
The "Issue Price" is not always equal to the "Face Value" (the value printed on the certificate). Debentures can be issued at:
- Par: Issue Price = Face Value.
- Premium: Issue Price = Face Value + Extra Amount.
- Discount: Issue Price = Face Value - Discounted Amount.
The coupon rate (e.g., 12%) is the interest rate the company will pay annually and is irrelevant for the calculation of the number of units issued.
Step 2: Key Formula or Approach:
The universal formula to find the number of securities to be issued is:
\[ \text{Number of Debentures} = \frac{\text{Purchase Consideration}}{\text{Issue Price per Debenture}} \]
In this specific problem, since the debentures are issued "at par," the Issue Price is equal to the Face Value (\( 100 \)).
Step 3: Detailed Explanation:
Let us break down the components of the transaction to reach the final count:
1. The value of the machinery purchased is \( 5,00,000 \). This is the total amount the company owes to the vendor.
2. The company decides to pay this debt by issuing 12% Debentures.
3. The Face Value of each individual debenture is \( 100 \).
4. The problem specifies the issue is "at par."
5. Therefore, the Issue Price per debenture = \( 100 \).
6. Using the formula to calculate the quantity:
\[ \text{Number of Debentures} = \frac{5,00,000 \text{ (Debt to be settled)}}{100 \text{ (Value per unit)}} \]
7. Performing the division:
\[ 5,00,000 / 100 = 5,000. \]
8. This means the company will hand over 5,000 physical certificates (or electronic credits) of debentures to the vendor to satisfy the \( 5,00,000 \) debt.
9. If the company were to issue them at a premium of 25%, the denominator would be 125, and the number of debentures would be 4,000. But for "at par," it remains 5,000.
Step 4: Final Answer:
The total number of debentures issued to the vendor is 5,000. This results from dividing the machinery's cost of 5,00,000 by the par issue price of 100.