How to Account for Convertible Bonds

Convertible bonds are hybrid securities that combine the features of both debt and equity. They are essentially bonds that can be converted into a predetermined number of the issuer’s equity shares. This conversion feature makes them attractive to investors who want the security of fixed interest payments with the potential upside of equity conversion. From an accounting perspective, convertible bonds present unique challenges due to their dual nature. This tutorial will provide a comprehensive guide on how to account for convertible bonds.

Understanding Convertible Bonds

Convertible bonds have two main components:

Debt Component: This represents the traditional bond aspect, which includes periodic interest payments (coupon) and the repayment of the principal at maturity.
Equity Component: This gives the bondholder the option to convert the bond into a fixed number of shares of the issuing company’s stock.

Because of this hybrid nature, accounting for convertible bonds involves separating these two components and recognizing them appropriately in the financial statements.

Initial Recognition

When a company issues convertible bonds, it must recognize both the debt and equity components separately. This separation is based on the fair value of each component at the time of issuance. The total proceeds from the issuance of the convertible bond are allocated between the debt and equity components based on their fair values.

Step 1: Determine the Fair Value of the Debt Component

The fair value of the debt component is determined using the market interest rate for similar debt instruments without the conversion option. This is done through the process of discounting the future cash flows (interest payments and principal repayment) at the market rate of interest.

For example, consider a company issuing a $1,000 convertible bond with a 5% coupon rate, payable annually, maturing in 5 years. If similar non-convertible bonds have a market interest rate of 7%, the present value of the debt component is calculated as follows:

$PV_{\text{Interest}} = \sum_{t=1}^{5} \frac{50}{(1+0.07)^t}$

$PV_{\text{Principal}} = \frac{1,000}{(1+0.07)^5}$

The sum of these present values gives the fair value of the debt component.

Step 2: Determine the Fair Value of the Equity Component

The equity component is the residual amount after deducting the fair value of the debt component from the total proceeds received from the bond issuance.

$latex \text{Equity Component} = \text{Proceeds from Bond} – \text{Fair Value of Debt Component} ]

For instance, if the total proceeds from the bond issuance are $1,000 and the fair value of the debt component is $920, the fair value of the equity component is:

$\text{Equity Component} = 1,000 - 920 = 80$

Step 3: Record the Initial Journal Entry

The initial journal entry to record the issuance of the convertible bond is as follows:

Debit Cash for the total proceeds received.
Credit Convertible Bonds Payable for the fair value of the debt component.
Credit Equity (Convertible Bond Equity Component) for the fair value of the equity component.

For our example:

$\text{Dr Cash} \quad 1,000$

$\text{Cr Convertible Bonds Payable} \quad 920$

$\text{Cr Equity (Convertible Bond Equity Component)} \quad 80$

Subsequent Accounting for the Debt Component

The debt component of the convertible bond is subsequently accounted for using the amortized cost method. This involves recognizing interest expense over the life of the bond using the effective interest rate method.

Step 1: Calculate the Effective Interest Rate

The effective interest rate is the market interest rate at the time of issuance, which is used to discount the cash flows of the debt component.

Step 2: Recognize Interest Expense

Interest expense is recognized in each period based on the carrying amount of the debt component and the effective interest rate. The carrying amount is adjusted for the interest expense recognized and the coupon payment made.

For example, using our earlier example with a 7% market rate and a 5% coupon rate, the interest expense for the first year is:

$\text{Interest Expense} = \\ \text{Carrying Amount of Debt Component} \times \\ \text{Effective Interest Rate}$

$\text{Interest Expense} = 920 \times 0.07 = 64.4$

The coupon payment is:

$\text{Coupon Payment} = 1,000 \times 0.05 = 50$

The difference between the interest expense and the coupon payment is the amortization of the bond discount, which is added to the carrying amount of the debt component.

$\text{Amortization} = 64.4 - 50 = 14.4$

The carrying amount of the debt component at the end of the first year is:

$\text{Carrying Amount} = 920 + 14.4 = 934.4$

The journal entry to record the interest expense and coupon payment is:

$\text{Dr Interest Expense} \quad 64.4$

$\text{Cr Convertible Bonds Payable} \quad 14.4$

$\text{Cr Cash} \quad 50$

This process is repeated for each period until the bond matures or is converted.

Subsequent Accounting for the Equity Component

The equity component of the convertible bond remains unchanged after initial recognition. It is not remeasured subsequently. However, if the bond is converted into equity, the carrying amount of the equity component is transferred to share capital and share premium (additional paid-in capital).

Conversion of Convertible Bonds

When bondholders exercise their option to convert the bonds into equity, the carrying amounts of both the debt and equity components are transferred to share capital and share premium.

For example, suppose a bondholder converts a $1,000 bond when the carrying amount of the debt component is $950 and the equity component is $80. The journal entry to record the conversion is:

$\text{Dr Convertible Bonds Payable} \quad 950$

$\text{Dr Equity (Convertible Bond Equity Component)} \quad 80$

$\text{Cr Share Capital} \quad (Par value of shares issued)$

$\text{Cr Share Premium} \quad (Balancing figure)$

Redemption of Convertible Bonds

If convertible bonds are redeemed before they are converted, the accounting treatment is similar to that for any other bond redemption. The carrying amount of the debt component is removed from the books, and any difference between the redemption price and the carrying amount is recognized as a gain or loss in the income statement.

For example, if a $1,000 convertible bond is redeemed for $1,050 when the carrying amount of the debt component is $980, the journal entry is:

$\text{Dr Convertible Bonds Payable} \quad 980$

$\text{Dr Loss on Redemption of Bonds} \quad 70$

$\text{Cr Cash} \quad 1,050$

Disclosure Requirements

Accounting standards require extensive disclosures about convertible bonds to provide users of financial statements with a clear understanding of their nature and financial impact. Key disclosures include:

Description of Convertible Bonds:

Terms and conditions of the conversion feature.
Maturity date, coupon rate, and other relevant terms.

Carrying Amounts of Debt and Equity Components:

Separate disclosure of the carrying amounts of the debt and equity components.

Interest Expense:

Effective interest rate and interest expense recognized for the period.

Conversion Details:

Number of shares issued upon conversion and the impact on share capital and share premium.

Redemption Details:

Details of any bonds redeemed and the financial impact of such redemption.

Example Case Study

Let’s walk through a detailed example to illustrate the accounting for convertible bonds.

Issuance of Convertible Bonds

ABC Corporation issues $500,000 of convertible bonds on January 1, 2024. The bonds have a 4% coupon rate, payable annually, and mature in 5 years. The market interest rate for similar non-convertible bonds is 6%. The bonds are convertible into 10,000 shares of ABC Corporation’s common stock.

Calculate the Fair Value of the Debt Component:

The present value of the interest payments:

$PV_{\text{Interest}} = \sum_{t=1}^{5} \frac{20,000}{(1+0.06)^t}$

$PV_{\text{Interest}} = \frac{20,000}{1.06} + \frac{20,000}{(1.06)^2} + \frac{20,000}{(1.06)^3} + \frac{20,000}{(1.06)^4} + \frac{20,000}{(1.06)^5}$

$PV_{\text{Interest}} \approx 18,868 + 17,800 + 16,792 + 15,839 + 14,936$

$PV_{\text{Interest}} \approx 84,235$

The present value of the principal repayment:

$PV_{\text{Principal}} = \frac{500,000}{(1.06)^5}$

$PV_{\text{Principal}} \approx 373,501$

The fair value of the debt component:

$\text{Fair Value of Debt Component} = 84,235 + 373,501 \approx 457,736$

Calculate the Fair Value of the Equity Component:

$\text{Equity Component} = \text{Proceeds from Bond} - \\ \text{Fair Value of Debt Component}$

$\text{Equity Component} = 500,000 - 457,736 = 42,264$

Record the Initial Journal Entry:

$\text{Dr Cash} \quad 500,000$

$\text{Cr Convertible Bonds Payable} \quad 457,736$

$\text{Cr Equity (Convertible Bond Equity Component)} \quad 42,264$

Subsequent Accounting for the Debt Component

First Year Interest Expense Calculation:

$\text{Interest Expense} = 457,736 \times 0.06 = 27,464$

$\text{Coupon Payment} = 500,000 \times 0.04 = 20,000$

$\text{Amortization} = 27,464 - 20,000 = 7,464$

Carrying Amount at End of First Year:

$\text{Carrying Amount} = 457,736 + 7,464 = 465,200$

Journal Entry to Record Interest Expense:

$\text{Dr Interest Expense} \quad 27,464$

$\text{Cr Convertible Bonds Payable} \quad 7,464$

$\text{Cr Cash} \quad 20,000$

This process is repeated for each subsequent year until maturity or conversion.

Conversion of Convertible Bonds

On January 1, 2028, a bondholder converts a $50,000 bond into 1,000 shares of ABC Corporation’s common stock.

Carrying Amounts of Debt and Equity Components:

Assume the carrying amount of the debt component is $46,520, and the equity component is $4,226.

Journal Entry to Record Conversion:

$\text{Dr Convertible Bonds Payable} \quad 46,520$

$\text{Dr Equity (Convertible Bond Equity Component)} \quad 4,226$

$\text{Cr Share Capital} \quad (Par value of 1,000 shares)$

$\text{Cr Share Premium} \quad (Balancing figure)$

Redemption of Convertible Bonds

If ABC Corporation redeems $100,000 of bonds for $105,000 when the carrying amount of the debt component is $93,040:

Journal Entry to Record Redemption:

$\text{Dr Convertible Bonds Payable} \quad 93,040$

$\text{Dr Loss on Redemption of Bonds} \quad 11,960$

$\text{Cr Cash} \quad 105,000$

Practice Exercises and Solutions

Practice Exercise 1: Issuance of Convertible Bonds

ABC Corporation issues $1,000,000 of convertible bonds with a 5% coupon rate, payable annually, maturing in 10 years. The market interest rate for similar non-convertible bonds is 8%. The bonds are convertible into 50,000 shares of ABC Corporation’s common stock. Calculate the fair value of the debt and equity components and prepare the initial journal entry.

Step 1: Calculate the Fair Value of the Debt Component

The present value of the interest payments (annuity):

$PV_{\text{Interest}} = \sum_{t=1}^{10} \frac{50,000}{(1+0.08)^t}$

$PV_{\text{Interest}} = \frac{50,000}{1.08} + \frac{50,000}{(1.08)^2} + \frac{50,000}{(1.08)^3} + \cdots + \frac{50,000}{(1.08)^{10}}$

$PV_{\text{Interest}} = 46,296 + 42,867 + 39,689 + 36,749 + 34,027 + 31,512 + 29,197 + 27,079 + 25,148 + 23,394$

$PV_{\text{Interest}} \approx 336,958$

The present value of the principal repayment:

$PV_{\text{Principal}} = \frac{1,000,000}{(1.08)^{10}}$

$PV_{\text{Principal}} \approx 463,193$

The fair value of the debt component:

$\text{Fair Value of Debt Component} = 336,958 + 463,193 \approx 800,151$

Step 2: Calculate the Fair Value of the Equity Component

$latex \text{Equity Component} = \text{Proceeds from Bond} – \text{Fair Value of Debt Component} ]

$\text{Equity Component} = 1,000,000 - 800,151 = 199,849$

Step 3: Record the Initial Journal Entry

$\text{Dr Cash} \quad 1,000,000$

$\text{Cr Convertible Bonds Payable} \quad 800,151$

$\text{Cr Equity (Convertible Bond Equity Component)} \quad 199,849$

Practice Exercise 2: Interest Expense Calculation

For the bond issued in Exercise 1, calculate the interest expense and carrying amount of the debt component at the end of the first year. Prepare the journal entry to record the interest expense.

Step 1: Calculate the Interest Expense

$\text{Interest Expense} = \\ \text{Carrying Amount of Debt Component} \times \\ \text{Effective Interest Rate}$

$\text{Interest Expense} = 800,151 \times 0.08 = 64,012$

Step 2: Calculate the Coupon Payment

$\text{Coupon Payment} = 1,000,000 \times 0.05 = 50,000$

Step 3: Calculate the Amortization of the Bond Discount

$\text{Amortization} = \text{Interest Expense} - \text{Coupon Payment}$

$\text{Amortization} = 64,012 - 50,000 = 14,012$

Step 4: Calculate the Carrying Amount at the End of the First Year

$\text{Carrying Amount} = \text{Initial Carrying Amount} + \\ \text{Amortization}$

$\text{Carrying Amount} = 800,151 + 14,012 = 814,163$

Step 5: Record the Journal Entry

$\text{Dr Interest Expense} \quad 64,012$

$\text{Cr Convertible Bonds Payable} \quad 14,012$

$\text{Cr Cash} \quad 50,000$

Practice Exercise 3: Conversion of Convertible Bonds

A bondholder converts $200,000 of bonds issued in Exercise 1 into 10,000 shares of ABC Corporation’s common stock. Assume the carrying amount of the debt component is $184,000 and the equity component is $16,000. Prepare the journal entry to record the conversion.

Step 1: Record the Conversion

$\text{Dr Convertible Bonds Payable} \quad 184,000$

$\text{Dr Equity (Convertible Bond Equity Component)} \quad 16,000$

$\text{Cr Share Capital} \quad (Par value of 10,000 shares)$

$\text{Cr Share Premium} \quad (Balancing figure)$

Assuming the par value of each share is $1:

$\text{Cr Share Capital} \quad 10,000$

$\text{Cr Share Premium} \quad 190,000$

Practice Exercise 4: Redemption of Convertible Bonds

ABC Corporation redeems $300,000 of bonds issued in Exercise 1 for $315,000 when the carrying amount of the debt component is $276,000. Prepare the journal entry to record the redemption.

Step 1: Calculate the Loss on Redemption

$\text{Loss on Redemption} = \text{Redemption Price} - \\ \text{Carrying Amount of Debt Component}$

$\text{Loss on Redemption} = 315,000 - 276,000 = 39,000$

Step 2: Record the Journal Entry

$\text{Dr Convertible Bonds Payable} \quad 276,000$

$\text{Dr Loss on Redemption of Bonds} \quad 39,000$

$\text{Cr Cash} \quad 315,000$

By working through these exercises, you gain practical experience in the accounting treatment of convertible bonds, enhancing your understanding of the concepts discussed in the tutorial.

Understanding Convertible Bonds

Initial Recognition

Step 1: Determine the Fair Value of the Debt Component

Step 2: Determine the Fair Value of the Equity Component

Step 3: Record the Initial Journal Entry

Subsequent Accounting for the Debt Component

Step 1: Calculate the Effective Interest Rate

Step 2: Recognize Interest Expense

Subsequent Accounting for the Equity Component

Conversion of Convertible Bonds

Redemption of Convertible Bonds

Disclosure Requirements

Example Case Study

Issuance of Convertible Bonds

Subsequent Accounting for the Debt Component

Conversion of Convertible Bonds

Redemption of Convertible Bonds

Practice Exercises and Solutions

Practice Exercise 1: Issuance of Convertible Bonds

Step 1: Calculate the Fair Value of the Debt Component

Step 2: Calculate the Fair Value of the Equity Component

Step 3: Record the Initial Journal Entry

Practice Exercise 2: Interest Expense Calculation

Step 1: Calculate the Interest Expense

Step 2: Calculate the Coupon Payment

Step 3: Calculate the Amortization of the Bond Discount

Step 4: Calculate the Carrying Amount at the End of the First Year

Step 5: Record the Journal Entry

Practice Exercise 3: Conversion of Convertible Bonds

Step 1: Record the Conversion

Practice Exercise 4: Redemption of Convertible Bonds

Step 1: Calculate the Loss on Redemption

Step 2: Record the Journal Entry

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