Financial Accounting for Long-Term Debt
In the world of financial accounting, understanding how to account for long-term debt is essential, particularly when dealing with issuing bonds. Bonds represent a significant portion of a company's long-term debt and require a comprehensive understanding of various terms and concepts. This blog post will discuss key bond terminology and how companies carry out financial accounting for bonds.
Bond Terminology
Before we dive into the accounting aspect, it is crucial to familiarize ourselves with some commonly used bond terms:
- Par and Face Value: This refers to the amount that a bond issuer agrees to repay the bondholder upon the bond's maturity. It's typically a standard value, like $1,000 or $100.
- Maturity: Maturity signifies the date when the bond issuer is obligated to repay the face value to the bondholder.
- Coupon Bonds and Coupon Rate: A coupon bond pays regular interest payments, known as the coupon, to the bondholder. The coupon rate is the percentage of the bond's face value that is paid each period to the bondholder.
- Zero Coupon Bonds: These bonds do not pay any regular interest or coupons. They are issued at a discount to their face value and mature at par.
Market Rate, Spot Rates and Bond Pricing
The importance of market rate at the issuance of the bond is fundamental to understanding bond pricing. At issuance, if the market rate is higher than the coupon rate, the bond will be issued at a discount. Conversely, if the market rate is lower than the coupon rate, the bond will be issued at a premium. The market rate's impact on bond pricing continues even after issuance as the bond price fluctuates based on changes in the current market rates.
Par, Discount and Premium Bonds
- Par Bonds: A bond is considered to be at par when its market price is equal to its face value.
- Discount Bonds: A bond is at a discount when its market price is less than its face value. This typically happens when the coupon rate is lower than the market rate.
- Premium Bonds: A bond is at a premium when its market price is greater than its face value. This usually occurs when the coupon rate is higher than the market rate.
Spot Rates and Yield Curve
A spot rate, also known as a "zero rate" or "zero-coupon yield," is the interest rate required to discount a single future cash flow to its present value. It's the rate of interest earned on a zero-coupon bond that's bought today and held until its maturity.
The term "spot" refers to the fact that it's the rate effective immediately – as in "on the spot".
Spot rates for different maturities are typically not the same. They form what's called the term structure of interest rates, or the yield curve.
It's important to note that a spot rate for a particular term to maturity is the rate of return promised by a zero-coupon bond with that particular term to maturity. This rate is different from the yield to maturity of a coupon-bearing bond, since the cash flows of the two types of bonds are different.
For example, the 2-year spot rate is the discount rate that would be used to determine the present value of a cash flow to be received two years from now. It is the yield on a zero-coupon bond that matures in 2 years.The following image depicts the yield curve for 1-month, 3-months, 6-months, 1, 2, 3, 5, 7, 10, 20, and 30 year bonds. The data for this is from early 2023 and it can be seen that there was an inverted yield curve, where shorter term bonds had higher yield than longer term bonds.
Bond Effective Interest Rate
The effective interest rate (generally not the same as the coupon rate) and referred to above as the market rate of a bond at issuance is often calculated using the yield to maturity (YTM) at the time of issuance, which takes into account all the future cash flows (coupon payments and principal repayment) of the bond. The reason for this complexity is that coupon bonds are effectively a series of cash flows with varying durations. We could think of coupon bonds as a series of zero coupon discount bonds. Each of these most likely will have a different interest rate \(Y_1, Y_2, \dots\, Y_n\). These different interest rates are the sport rates of the yield curve (if a spot rate is known for a specific duration due to discount bond equivalent securities existing with enough market data being available for the given duration).
If spot rates for the entire maturity period are available, this method can be used to accurately calculate the bond's price at issuance using this equation:
\[P_{issue} = \frac{C_1}{(1+Y_1)} + \frac{C_2}{(1+Y_2)^2} + \ldots + \frac{C_n}{(1+Y_n)^n} + \frac{FV}{(1+Y_n)^n}\]Where C is the bond coupon cash flow, FV is the face value cash flow, n is the number of periods, and Y are the spot rates. This formula would need to be adjusted if the coupons are note paid annually.
The spot rates or zero-coupon yield for each maturity are crucial in this calculation because they help us to determine the present value of each individual cash flow.
And then after determining the price of the bond that price could be used to numerically determine the effective interest rate by numerically solving the following to find the bond's yield to maturity (YTM). The YTM is equivalent in this context to what is referred to as the bonds effective interest rate at issuance.
\[P_{issue} = \frac{C_1}{(1+YTM)} + \frac{C_2}{(1+YTM)^2} + \ldots + \frac{C_n}{(1+YTM)^n} + \frac{FV}{(1+YTM)^n}\]In practice, however, spot rates for every maturity may not be available, especially for longer maturity bonds. If that is the case, certain simplifications or assumptions may need to be made to derive an effective interest rate, for example, assuming a flat yield curve (all spot rates are equal).
More details about pricing of fixed income securities can be found here.
In the following sections, we will explore how these concepts play out in the financial accounting for long-term debt.
Accounting for Bond Issuance at Par Value
Let's consider a $1000, three-year 5% coupon bond where the coupon is paid annually and the bond sells at par value. To account for this, we need to understand that the bond payable and cash will be affected at the time of issuance, at each interest payment, and upon repayment of the bond at maturity. Let's explore how this plays out in the balance sheet equation accounting method.
Balance Sheet Equation Accounting for Bond
Balance sheet equation accounting is based on the fundamental accounting equation: Assets = Liabilities + Equity. For the bond transaction, the primary changes will be reflected in Cash (an asset), Bond Payable (a liability), and Retained Earnings (a part of equity). Since the bond is issued at par, there will be no discount or premium, thus no 'Discount on Bonds Payable' account (represented as 'Discount(CL)' in the table) will be used in this case.
| Year | Cash | = Bond Payable | - Discount(CL) | R/E |
|---|---|---|---|---|
| Issuance | $1,000 | $1,000 | 0 | 0 |
| Year 1 | ($50) | 0 | 0 | ($50) |
| Year 2 | ($50) | 0 | 0 | ($50) |
| Year 3 | ($1,050) | ($1,000) | 0 | ($50) |
In the table above, you can see how the bond issuance and subsequent transactions are reflected in the balance sheet. At issuance, the company increases Cash (an asset) by $1000 and Bond Payable (a liability) also by $1000. Each year, the company pays the bond's annual coupon of $50, which decreases Cash and reduces Retained Earnings (a component of equity). In the final year, in addition to the coupon payment, the company repays the principal amount, which leads to a significant reduction in Cash and Bond Payable.
Accounting for Bond Issuance at a Premium
Let's consider a $1000, three-year 5% coupon bond where the coupon is paid annually and the bond sells at a premium due to the bond's effective interest rate at the time of issuance being 4%.
If the market interest rates were a flat yield curve at 4% at issuance, and were a flat 5% shortly before issuance, then the bond premium likely could be calculated as the difference between the present value of the future cash flows less the bond face value.
| Year | Bond Cash Flow |
PV 4% Flat Yield Curve |
PV 5% Flat Yield Curve |
PV 6% Flat Yield Curve |
|---|---|---|---|---|
| 1 | $50 | $48.077 | $47.619 | $47.170 |
| 2 | $50 | $46.228 | $45.351 | $44.500 |
| 3 | $1,050 | $933.446 | $907.029 | $881.600 |
| Total | $1,150 | $1,027.751 | $1,000.000 | $973.270 |
For a flat 4% yield curve, the present value of the cash flows that the bond would provide would be $1,027.751. So the bond premium would be that value less $1,000 which is $27.51.
For the bond transaction, the primary changes will be reflected in Cash (an asset), Bond Payable (a liability), and Retained Earnings (a part of equity). Since the bond is issued at a premium, there will be a Bond Premium(L) liability account used to account for the premium received at issuance.
Interest Expense vs Interest Payable
Interest payable is the amount that is paid for each coupon payment. This is generally not the same as the interest expense.
The interest expense is calculated as the net bond payable multiplied by the bond's effective interest rate at bond issuance. The net bond payable is the sum of the bond payable and the bond premium(L) when the bond was sold at a premium. When the bond is sold at a discount the net bond payable is the sum of the bond payable and the bond discount(CL) (discussed further below).
Balance Sheet Entry
Similar to the par bond scenario, the fundamental equation is A = L + S/E. However, accounting entry in this instance becomes:
\[\text{Cash} = \text{Bond Payable} + \text{Bond Premium(L)} + \text{R/E}\]Where Bond Premium(L) is the premium that is added to bond payable to determine net bond payable. As mentioned above, interest expense is calculated as net bond payable multiplied by the effective interest rate of the bond when it was issued.
\[\text{Bond Interest Expense} = \text{Net Bond Payable} \times \text{Effective Interest Rate}\]Where the effective interest rate is the interest rate that was used to price the bond at issuance.
When the bond is issued, the cash received is recorded to the cash account, the bond payable is incremented by the face value of the bond and the Bond Premium(L) account or the Discount(L) account are updated if the bond was sold at a premium or a discount.
For each period we will record the interest expense in R/E, the cash paid out for interest payable, and the bond premium(L) account will be reduced by the difference between interest payable and interest expense. The following table shows how this can be done for our above described example.
| Year | Cash | = Bond Payable | + Bond Premium(L) | + R/E |
|---|---|---|---|---|
| Issuance | $1,027.751 | $1,000 | 27.751 | |
| Year 1 | ($50) | 0 | ($8.89) | ($41.11) |
| Year 2 | ($50) | 0 | ($9.25 | ($40.75) |
| Year 3 | ($1,050) | ($1,000) | ($9.62) | ($40.38) |
The above table shows how the balance sheet entries are recorded in that:
- At issuance, the cash account is incremented by the amount of the bond sale.
- The bond payable is incremented to the amount of the face value of the bond.
- The Bond Premium(L) liability account is incremented by the amount of the bond premium.
- In each period the interest expense is calculated as net bond payable multiplied by the market rate at issuance of the bond and is record in retained earnings R/E.
- In each period, the interest payable is deducted from the cash account.
- The difference between interest payable and interest expense is deducted from the Bond Premium(L) liability account. At bond maturity, the Bond Premium(L) account portion allocated to the bond will be depleted.
- When the bond matures, the bond face value is paid back from the cash account and is also cleared out of the bond payable account.
If the bond sold at a premium, then instead of subtracting Discount(CL) we would add to the Bond Premium(L) account:
\[\text{Cash} = \text{Bond Payable} + \text{Bond Premium(L)} + \text{R/E}\]3-Year Zero-Coupon Bond Example
Shifting our attention to the accounting process of a 3-year zero-coupon bond with a face value of $1,000, we start again at the issuance.
Similar to the par bond scenario, the fundamental equation is A = L + S/E. The accounting entry in this instance becomes:
\[\text{Cash} = \text{Bond Payable} - \text{Discount(CL)} + \text{R/E}\]Where Discount(CL) signifying the discount on bond payable.
If the bond payable or face value is $1,000, but at issuance the market spot rate for a 3-year bond is 5%, then it is issued for \(\frac{$1,000}{(1+5\%)^3} = $863.838\), the discount amounts to \($1,000 - $863.838 = $136.162\). The $863.838 received goes to the company issuing the bond and signifies a loan to the company. This loan, along with accumulated interest, will total $1,000 at the end of three years. This impending payment is the net bond payable, which is calculated by the formula \($863.838 \times (1+5\%)^3\).
Understanding Discount(CL) and Amortization
The Discount(CL) account, a contra liability account, holds the discount that will be gradually expensed over time, a process known as amortization. Here's how it works:
- At issuance, the company "owes" the bondholder the $863.838 that they received.
- As time passes, the discount is amortized, decreasing the Discount(CL) account and increasing the net obligation.
- At maturity, the company will pay the bondholder the face value of $1,000, which equals the initial amount plus the accumulated interest.
Interest Expense vs Interest Payable
Now, let's define Interest Expense and Interest Payable. The former is calculated by multiplying the market interest rate at the bond issuance time by the net bond payable. The latter, on the other hand, is derived by multiplying the coupon rate by the bond's par value.
The distinction between Interest Expense and Interest Payable is essentially the amount amortized against the bond discount/premium account. Over time, as the Discount(CL) account diminishes, the book value of the bond converges with its face value.
The Impact on Financial Statements
Understanding these accounting entries and adjustments is paramount as they directly influence the company's financial statements:
- Income Statement: The interest expense is recognized on the income statement, impacting the net income of the company.
- Balance Sheet: The bond payable and the discount or premium on the bond payable affect the liabilities section, while the cash affects the assets section. Long-term debt that is due in the next 12-months is recorded under current liabilities. The remainder of long-term debt is recorded under non-current liabilities.
- Cash Flow Statement: The cash received from the issuance and the cash paid for interest payments impact the financing and operating activities sections, respectively.
The statement of cash flows will include:
- Operations - The operations section will include accruals for interest not yet paid that are added back to get cash flow from operations (CFO).
- Financing - The proceeds from issuing bonds and the reduction for payments to retire bonds are recorded under the financing section.
- Supplemental Disclosure - Discloses how much cash was used for interest payments.
By exploring these mechanisms, we attain a priceless understanding of the process of long-term debt accounting. Such knowledge forms the cornerstone of financial analysis and corporate decision-making.
The following table shows the balance sheet equation entries over the lifetime of the zero coupon bond described above. In this example, the bond is issued at the end of year 0 and at the end of year 1, 2, and 3 the other transactions are recorded.
| Year | Cash | = Bond Payable | - Discount(CL) | R/E |
|---|---|---|---|---|
| Issuance | $863.838 | $863.838 | 136.162 | 0 |
| Year 1 | ($43.192) | ($43.192) | ||
| Year 2 | ($45.351) | ($45.351) | ||
| Year 3 | ($1,000) | ($1,000) | ($47.619) | ($47.619) |
The following table provides a more clear picture of how the interest expense is amortized over time to increase the net bond payable to equal the bond payable. The most insightful columns here the discount balance and the net bond payable. The interest expense is calculated as the market interest rate at bond issuance multiplied by the net bond payable. This market rate is also referred to as the effective interest rate on financial statements.
| Year | Beginning Balance | Cash Interest Paid | Interest Expense | Discount Amortization | Discount Balance | Net Bond Payable |
|---|---|---|---|---|---|---|
| 0 | $136.162 | $863.838 | ||||
| 1 | $863.838 | $0.00 | $43.192 | $43.192 | $92.971 | $907.029 |
| 2 | $907.029 | $0.0 | $45.351 | $45.351 | $47.619 | $952.381 |
| 3 | $952.381 | $0.00 | $45.351 | $45.351 | $0.00 | $1,000 |
The Implications of Early Bond Retirement
Changes in a firm's financial health that impact its credit quality or changes in macroeconomic factors can sometimes lead to a shift in the strategic handling of its issued bonds. Circumstances such as a rise in interest rates or a heightened perception of risk associated with the bonds can depreciate their market value to such a degree that the firm may find it beneficial to repurchase the bonds.
Consider, for example, our previously discussed zero-coupon bond issued when market rates were 5%. Suppose market rates ascend to 6%. The bond's present value is likely to diminish as investors anticipate higher returns commensurate with the current market conditions. Thus, under a flat yield curve of 6%, the bond's market value at the end of year one would be \(\frac{$1,000}{(1 + 6\%)^2} = $889.996\), given that is the present value of $1,000 received in two years from that date. If the yield curve had remained flat at 5%, the bond would be worth \(\frac{$1,000}{(1 + 5\%)^2} = $907.029\).
This situation presents an opportunity. If the company has sufficient cash reserves and wishes to retire the debt early, it could repurchase the debt now for $889.996 which is $17.033 less than it would have been worth if market interest rates were still at 5%. Essentially, this strategy would be equivalent to investing the $889.996 cash it could have used to pay off the bond at a 6% return at the end of year one, and then utilizing the resultant $1,000 at the end of year three to pay off the bond.
Accounting for Early Retirement of Bonds
If a company opts for an early bond retirement, it will need to account for any resultant gain or loss, which in turn will impact retained earnings. Applying the above scenario, the accounting would be structured as follows:
Firstly, the cash paid to retire the bond is recorded. Subsequently, the bond payable is entered, along with the residual value of the contra liability account discount. The final step involves calculating the gain or loss that is subsequently recorded in retained earnings (R/E).
By understanding the mechanisms and implications of early bond retirement, a company can make informed decisions that strategically leverage market conditions and optimize its long-term financial health.
In the above example this would look like the following where we enter the cash paid to retire the bond, bond payable, remaining contra liability account discount value and then solve for the gain or loss that is recorded in retained earnings (R/E):
| Year | Cash = | Bond Payable | - Discount(CL) | + R/E |
|---|---|---|---|---|
| 1 | ($889.996) | ($1,000) | $92.971 | $17.033 |
Understanding the 'Mark-to-Market' Approach for Debt
There exist circumstances where a company may decide to adopt the mark-to-market accounting technique to assess the value of its debt. This may transpire when, for instance, the company's debt is perceived as riskier due to the firm underperformed and the perceived likelihood of bankruptcy increases. In such a scenario, the company's borrowing market rate would escalate, the market value of the bond would shrink, while the bond's coupon rate remains steady.
Let's revert to our earlier three-year zero-coupon bond example. Suppose that at the end of the first year (first day of the new fiscal year 2), the company opts to mark-to-market the bond, prompted by the market rate hiking to 6%. In such a case, the company would adjust the contra liability account, Discount(CL) by the amount of the decrease in bond value.
Following our previous scenario, if the interest rate escalated from 5% to 6%, the bond's worth would diminish by $17.033. This value would then be appended to the Discount(CL) account at the commencement of year 2. The outcome of this adjustment is an elevation in the other comprehensive income (OCI), a key component of shareholders' equity that captures unrealized gains and losses.
| Year | Cash = | Bond Payable | - Discount(CL) | + OCI |
|---|---|---|---|---|
| 2 | $17.033 | $17.033 |
All firms are required by FASB (Financial Accounting Standards Board) to include a footnote in their financial statements that shows the fair market value of their debt. Firms are not required to mark-to-market their debt, but they are required to show what the value of their debt would be if it were marked-to-market.
Conclusion
As we've explored the complexities of financial accounting in the context of long-term debt, we've uncovered the mechanisms that govern these financial instruments. We’ve dissected the accounting principles associated with bond issuance at par and discount, the implications of early retirement, and the impact of marking debt to market. These concepts may seem daunting, but their understanding is integral to a thorough financial analysis, particularly for those involved in quantitative research and portfolio management.
Quantitative researchers/analysts/developers and portfolio managers alike can immensely benefit from a strong foundation in financial accounting. Not only does it provide crucial insight into a company's financial standing, but it also enriches the analytical toolkit used in strategic decision-making. Every aspect of a company's financial statement— from cash flow to retained earnings— tells a story. And as we've discovered, these stories can significantly influence investment decisions and portfolio management strategies.
The fusion of financial accounting with quantitative research creates a powerful combination for portfolio management. It equips you with the ability to discern the financial strength of a company and make well-informed, strategic decisions.
Continue this path of seeking knowledge, enhance your quantitative analysis skills, and unlock new horizons in your portfolio management strategies. Remember, in the ever-evolving financial landscape, the power lies in understanding the numbers and the stories they tell.