Chapter Thirteen: LongTerm Obligations
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Prior chapters illustrate notes payable of short duration. However, borrowers may desire a longer term for a loan. It would be common to find two, three, fiveyear, and even longer term notes. These notes may evidence a “term loan,” where “interest only” is paid during the period of borrowing and the balance of the note is due at maturity. To illustrate, assume that a $10,000, fiveyear, 8% term note, is issued on October 1, 20X3 :
Interest on the note must be accrued each December 31, with payment following on September 30.
The following entry is needed at maturity on September 30, 20X8:
With the term note illustration, it is easy to calculate interest of $800 per year, and observe the $10,000 balance due at maturity. Other loans may require level payments over their terms, so that the interest and principal are fully paid by the end of the loan. This type of arrangement is commonly used for real estate financing. The payment of the note is usually secured by the property, allowing the lender to take possession for nonpayment. Real estate notes thus secured are called “mortgage notes.” How are payments calculated? The first step is to learn about future value and present value calculations.
Let's start by thinking about how invested money can grow with interest. What will be the future value of an investment? If $1 is invested for one year, at 10% interest per year, it will grow to $1.10. This is calculated by multiplying the $1 by 10% ($1 X 10% = $0.10) and adding this $0.10 to the original dollar.
And, if the resulting $1.10 is invested for another year at 10%, it will grow to $1.21. That is, $1.10 X 10% = $0.11, which is added to the $1.10 value from the end of the first year. This process will continue year after year. The annual interest each year is larger than the year before because of “compounding.”
Compounding simply means that the investment is growing with accumulated interest and earning interest on previously accrued interest. The contrast to compound interest is simple interest. Simple interest does not provide for compounding, such that $1 invested for two years at 10% would only grow to $1.20.
The preceding observations lead to this compound interest calculation:
(1+i)^{n}
Where “i” is the interest rate per period and “n” is the number of periods
This calculation reveals how much an investment of $1 will grow to after “n” periods. If $1 was invested for 5 years at 6%, then it would grow to about $1.34 [(1.06)^{5} = 1.33823]. Of course, if $1,000 was invested for 5 years at 6%, it would grow to $1,338.23; this is determined by multiplying the derived factor times the amount invested at the beginning of the 5year period. This calculation is aptly termed the “future value of a lump sum amount.”
Future value amounts can always be calculated using the preceding formulation. However, spreadsheet software and business calculators frequently include builtin routines to return appropriate values. Another useful tool is a future value table (see principlesofaccounting.com supplements). These tables include values corresponding to various rates and periods. Use a table, spreadsheet, or business calculator to verify the 1.33823 factor for a 5period, 6% investment. Likewise, determine that $5,000, invested for 10 years, at 4%, will grow to $7,401.20 ($5,000 X 1.48024).
Present value is the opposite of future value, as it reveals how much a dollar to be received in the future is worth today. The math is simply the reciprocal of future value calculations:
1/(1+i)^{n}
Where “i” is the interest rate per period and “n” is the number of periods
For example, $1,000 to be received in 5 years, when the interest rate is 7%, is presently worth $712.99 [$1,000 X (1/(1.07)^{5})]. Stated differently, if $712.99 is invested today at 7%, it will grow to $1,000 in 5 years. Present value amounts are also determinable from spreadsheets, calculators, or tables. Verify that the present value of $50,000 to be received in 8 years at 8% is $27,013.50 ($50,000 X .54027).
Streams of level payments (i.e., the same amount each period) occurring on regular intervals are termed annuities. For example, if one invests $1 at the beginning of each year at 5% per annum, after 5 years it would accumulate to $5.80. This can be painstakingly calculated by summing the future value amount associated with each individual payment, as shown in the following calculations.
But, it is much easier to use spreadsheets, calculators, or annuity future value tables. The annuity table is simply the summation of individual factors. Verify the “5.80“ factor from the 5% row, 5year column of a table. These calculations are useful in financial planning. For example, one may wish to have a target amount accumulated by a certain age, such as with a retirement account. These factors help calculate the amount that must be set aside each period to reach the goal.
Conversely, one may be interested in the present value of an annuity which reveals the current worth of a level stream of payments to be received at the end of each period. Use a table, calculator, or spreadsheet to find the present value of $1,000 to be received at the end of each year for 5 years, if the interest rate is 8% per year. The 5year column, 8% row of the appropriate table shows a factor of 3.99271, indicating that the present value of the annuity is $3,992.71.
How does one compute the payment on a typical loan that involves level periodic payments, with the final payment satisfying the remaining balance due? The answer to this question is found in the present value of annuity calculations. Remember that an annuity involves a stream of level payments, just like many loans. The payments on a loan are a series of level payments that cover both the principal and interest. The present value of those payments is the amount borrowed, in essence “discounting” out the interest component. This concept may still be a bit abstract, but can be further clarified mathematically with some equations:
Present Value of Annuity = Payments X Annuity Present Value Factor
A loan that is paid off with a series of equal payments is also an annuity, therefore:
Loan Amount = Payments X Annuity Present Value Factor
Thus, to determine the annual payment to satisfy a $100,000, 5year loan at 6% per annum:
$100,000 = Payment X 4.21236 (from table)
Payment = $100,000 / 4.21236 = $23,739.64
The five payments of $23,739.64 will exactly pay off the $100,000 loan plus all interest at a 6% annual rate. Simply stated, the payments on a loan are just the loan amount divided by the appropriate present value factor. To fully prove this point, look at the following typical loan amortization table. This table shows how each payment is applied to first satisfy the accumulated interest for the period, and then reduce the principal. Note that the final payment will extinguish any remaining principal.
The journal entries associated with the preceding loan would flow as follows:
Note that some scenarios may involve payments at the beginning of each period, while other scenarios might require endofperiod payments. Later chapters of this book include additional future and present value calculations for alternatively timed payment streams (e.g., present value of an annuity with payments at the beginning of each period).
Also note that payments may occur on other than an annual basis. For example, a $10,000, 8% per annum loan may involve quarterly payments over two years. The quarterly payment would be $1,365.10 ($10,000/7.32548). The 7.32548 present value factor is reflective of 8 periods (4 quarters per year for 2 years) and 2% interest per period (8% per annum divided by 4 quarters per year). This type of modification applies to annuities and lumpsum amounts. For example, the present value of $1 invested for 5 years at 10% compounded semiannually can be determined by referring to the 5% row, 10period factor.
As previously noted, spreadsheet software normally includes functions to help with fundamental present value, future value, and payment calculations. Following is a screen shot of one such routine:
Bonds payable result when a borrower splits a large loan into many small units. Each of these units (or bonds) is essentially a note payable. Investors will buy these bonds, effectively making a loan to the issuing company. Bonds were introduced, from an investor’s perspective, in Chapter 9.
The terms of a bond issue are specified in a bond indenture. In addition to making representations about the interest payments and life of the bond, the indenture may also address questions such as:
 Are the bonds secured by specific assets pledged as collateral to insure payment? If not, the bonds are said to be debenture bonds, meaning they do not have specific collateral but are only as good as the general faith and credit of the issuer.
 What is the preference in liquidation in the event of failure? Agreements may provide that some bonds are paid before others.
 To whom and when is interest paid? In the past, some bonds were coupon bonds, and those bonds literally had detachable interest coupons that could be stripped off and cashed in on specific dates. One reason for coupon bonds was to ease the record keeping burden on bond issuers. Companies merely issued coupons that were turned in for redemption.
However, in recent times, most bonds are registered to an owner. Computerized information systems now facilitate tracking bond owners, and interest payments are commonly transmitted electronically to the registered owner. Registered bonds are in contrast to bearer bonds, where the holder of the physical bond instrument is deemed to be the owner (bearer bonds are rare in today’s economy).
 Must the company maintain a required sinking fund? A sinking fund bond may sound bad, but it is actually not. In the context of bonds, a sinking fund is a required account into which monies are periodically transferred to insure that funds will be available at maturity to satisfy the bond obligation.
 Some companies will issue serial bonds. Rather than the entire issue maturing at once, portions of the serial issue will mature on select dates spread over time.
 Can the bond be converted into stock? Convertible bonds enable the holder to exchange the bond for a predefined number of shares of corporate stock. The holder may plan to be paid the interest plus face amount of the bond, but if the company’s stock explodes upward in value, the holder may benefit by trading the bonds for appreciated stock.
Why would a company issue convertibles? First, investors may prefer these securities and are usually willing to accept lower interest rates than must be paid on bonds that are not convertible. Another factor is that the company may contemplate its stock going up; by initially borrowing money and later exchanging the debt for stock, the company may actually get more money for its stock than it would have had it issued the stock on the earlier date.
 Is the company able to call the debt? Callable bonds provide a company with the option of buying back the debt at a prearranged price before its scheduled maturity. If interest rates go down, the company may not want to be saddled with the higher cost obligations and can escape the obligation by calling the debt.
Sometimes, bonds cannot be called. For example, suppose a company is in financial distress and issues high interest rate debt (known as junk bonds) to investors who are willing to take a chance to bail out the company. If the company is able to manage a turnaround, the investors who took the risk and bought the bonds don’t want to have their “high yield” stripped away with an early payoff before scheduled maturity.
 Bonds that cannot be paid off earlier are sometimes called nonredeemable. Be careful not to confuse nonredeemable with nonrefundable. Nonrefundable bonds can be paid off early, so long as the payoff money is generated from business operations rather than an alternative borrowing arrangement. Some specialized securities may be legally
structured as equity instruments, but nonetheless possess mandatory redemption
features. These attributes make the securities more like longterm debt, and the
accounting should mirror this economic substance.
Note that convertible bonds will almost always be callable, enabling the company to force a bond holder to either cash out or convert. The company will reserve this call privilege because they will want to stop paying interest (by forcing the holder out of the debt) once the stock has gone up enough to know that a conversion is inevitable.
Bonds are potentially complex financial instruments. Who enforces all of the requirements for a company’s bond issue? Within the bond indenture agreement should be a specified bond trustee. This trustee may be an investment company, law firm, or other independent party. The trustee is to monitor compliance with the terms of the agreement and has a fiduciary duty to intervene to protect the investor group if the company runs afoul of its covenants.
A bond payable is just a promise to pay a series of payments over time (the interest component) and a fixed amount at maturity (the face amount). Thus, it is a blend of an annuity (the interest) and lump sum payment (the face). To determine the amount an investor will pay for a bond, therefore, requires present value computations to determine the current worth of the future payments. Assume that Schultz Company issues 5year, 8% bonds. Bonds frequently have a $1,000 face value and pay interest every six months. Using these assumptions, consider the following three alternative scenarios:
The following table shows calculations of the price of the bond under different scenarios:
To further explain, the interest amount on the $1,000, 8% bond is $40 every six months. Because the bonds have a 5year life, there are 10 interest payments (or periods). The periodic interest is an annuity with a 10period duration, while the maturity value is a lumpsum payment at the end of the tenth period. The 8% market rate of interest equates to a semiannual rate of 4%, the 6% market rate scenario equates to a 3% semiannual rate, and the 10% rate is 5% per semiannual period.
The present value factors are taken from the present value tables (annuity and lumpsum, respectively). Take time to verify the factors by reference to the appropriate tables, spreadsheet, or calculator routine. The present value factors are multiplied by the payment amounts, and the sum of the present value of the components would equal the price of the bond under each of the three scenarios.
Note that the 8% market rate assumption produced a bond priced at $1,000, the 6% assumption produced a bond priced at $1,085.30 (which includes an $85.30 premium), and the 10% assumption produced a bond priced at $922.78 (which includes a $77.22 discount).
These calculations are not only correct theoretically, but are very accurate financial tools. However, one point is noteworthy. Bond pricing is frequently to the nearest 1/32nd. That is, a bond might trade at 103.08. One could easily misinterpret this price as $1,030.80. But, it actually means 103 and 8/32. In dollars, this would amount to $1,032.50 ($1,000 X 103.25). Having learned the financial mechanics of bonds, it is now time to examine the correct accounting.
If Schultz issued 100 of its 5year, 8% bonds at par, the following entries would be required :
One simple way to understand bonds issued at a premium is to view the accounting relative to counting money! If Schultz issues 100 of the 8%, 5year bonds when the market rate of interest is only 6%, then the cash received is $108,530 (see the previous calculations). Schultz will have to repay a total of $140,000 ($4,000 every 6 months for 5 years, plus $100,000 at maturity).
Thus, Schultz will repay $31,470 more than was borrowed ($140,000  $108,530). This $31,470 must be expensed over the life of the bond; uniformly spreading the $31,470 over 10 sixmonth periods produces periodic interest expense of $3,147 (not to be confused with the actual periodic cash payment of $4,000).
Another way to illustrate this problem is to note that total borrowing cost is reduced by the $8,530 premium, since less is to be repaid at maturity than was borrowed up front. Therefore, the $4,000 periodic interest payment is reduced by $853 of premium amortization each period ($8,530 premium amortized on a straightline basis over the 10 periods), also producing the periodic interest expense of $3,147 ($4,000  $853).
This topic is inherently confusing, and the journal entries are actually clarifying. Notice that the premium on bonds payable is carried in a separate account (unlike accounting for investments in bonds covered in a prior chapter, where the premium was simply included with the Investment in Bonds account).
Study the following illustration, and observe that the Premium on Bonds Payable is established at $8,530, then reduced by $853 every interest date, bringing the final balance to zero at maturity.
On any given financial statement date, Bonds Payable is reported on the balance sheet as a liability, along with the unamortized Premium balance (known as an “adjunct” account). To illustrate, the balance sheet disclosures would appear as follows on December 31, 20X3 and 20X4:
The income statement for all of 20X3 would include $6,294 of interest expense ($3,147 X 2). This method of accounting for bonds is known as the straightline amortization method, as interest expense is recognized uniformly over the life of the bond. Although simple, it does have one conceptual shortcoming. Notice that interest expense is the same each year, even though the net book value of the bond (bond plus remaining premium) is declining each year due to amortization.
As a result, interest expense each year is not exactly equal to the effective rate of interest (6%) that was implicit in the pricing of the bonds. For 20X1, interest expense can be seen to be roughly 5.8% of the bond liability ($6,294 expense divided by beginning of year liability of $108,530). For 20X4, interest expense is roughly 6.1% ($6,294 expense divided by beginning of year liability of $103,412).
Accountants have devised a more precise approach to account for bond issues called the effectiveinterest method. Be aware that the more theoretically correct effectiveinterest method is actually the required method, except in those cases where the straightline results do not differ materially. Effectiveinterest techniques are introduced in a following section of this chapter.
If Schultz issues 100 of the 8%, 5year bonds for $92,278 (when the market rate of interest is 10%), Schultz will still have to repay a total of $140,000 ($4,000 every 6 months for 5 years, plus $100,000 at maturity). Thus, Schultz will repay $47,722 ($140,000  $92,278) more than was borrowed. Spreading the $47,722 over 10 sixmonth periods produces periodic interest expense of $4,772.20 (not to be confused with the periodic cash payment of $4,000).
Another way to consider this problem is to note that the total borrowing cost is increased by the $7,722 discount, since more is to be repaid at maturity than was borrowed initially. Therefore, the $4,000 periodic interest payment is increased by $772.20 of discount amortization each period ($7,722 discount amortized on a straightline basis over the 10 periods), producing periodic interest expense that totals $4,772.20.
Like bond premiums, discounts are also carried in a separate account. The following entry is needed to record the initial bond issuance:
The following entries reflect periodic interest and repayment at maturity:
Carefully study this illustration, and observe that the Discount on Bonds Payable is established at $7,722, then reduced by $772.20 on every interest date, bringing the final balance to zero at maturity. On any given financial statement date, Bonds Payable is reported on the balance sheet as a liability, along with the unamortized Discount that is subtracted (known as a “contra” account). The illustration below shows the balance sheet disclosure as of June 30, 20X3. Note that the unamortized discount on this date is determined by calculations revealed in the table that follows:
Each yearly income statement would include $9,544.40 of interest expense ($4,772.20 X 2). The straightline approach suffers from the same limitations discussed earlier, and is acceptable only if the results are not materially different from those resulting with the effectiveinterest technique.
The theoretically preferable approach to recording amortization is the effectiveinterest method. Interest expense is a constant percentage of the bond’s carrying value, rather than an equal dollar amount each year. The theoretical merit rests on the fact that the interest calculation aligns with the basis on which the bond was priced.
Interest expense is calculated as the effectiveinterest rate times the bond’s carrying value for each period. The amount of amortization is the difference between the cash paid for interest and the calculated amount of bond interest expense.
Recall that when Schultz issued its bonds to yield 6%, it received $108,530. Thus, effective interest for the first six months is $108,530 X 6% X 6/12 = $3,255.90. Of this amount, $4,000 is paid in cash and $744.10 ($4,000  $3,255.90) is premium amortization. The premium amortization reduces the net book value of the debt to $107,785.90 ($108,530  $744.10). This new balance would then be used to calculate the effective interest for the next period. This process would be repeated each period, as shown in the following table:
The initial journal entry to record the issuance of the bonds, and the final journal entry to record repayment at maturity would be identical to those demonstrated for the straightline method. However, each journal entry to record the periodic interest expense recognition would vary and can be determined by reference to the preceding amortization table.
The following entry would record interest on June 30, 20X3:
The following balance sheet disclosure would be appropriate as of June 30, 20X3:
Recall that when Schultz issued its bonds to yield 10%, it received only $92,278. Thus, effective interest for the first six months is $92,278 X 10% X 6/12 = $4,613.90. Of this amount, $4,000 is paid in cash, and $613.90 is discount amortization. The discount amortization increases the net book value of the debt to $92,891.90 ($92,278.00 + $613.90). This new balance would then be used to calculate the effective interest for the next period. This process would repeat each period as shown:
Each journal entry to record the periodic interest expense recognition would vary, and can be determined by reference to the preceding amortization table. For instance, the following entry would record interest on June 30, 20X3, and result in the balance sheet disclosure below:
Bonds issued between interest dates are best understood in the context of a specific example. Suppose Thompson Corporation proposed to issue $100,000 of 12% bonds, dated April 1, 20X1. However, despite the April 1 date, the actual issuance was slightly delayed, and the bonds were not sold until June 1. Nevertheless, the covenant pertaining to the bonds specifies that the first 6month interest payment date will occur on September 30 in the amount of $6,000 ($100,000 X 12% X 6/12). In effect, interest for April and May has already accrued at the time the bonds are actually issued ($100,000 X 12% X 2/12 = $2,000). To be fair, Thompson will collect $2,000 from the purchasers of the bonds at the time of issue, and then return it within the $6,000 payment on September 30. This effectively causes the net difference of $4,000 to represent interest expense for June, July, August, and September ($100,000 X 12% X 4/12). The resulting journal entries are:
Notice that interest was paid in full through September 30. Therefore, the December 31 yearend entry must reflect the accrual of interest for October through December:
When the next interest payment date arrives on March 31, the actual interest payment will cover the previously accrued interest, and additional amounts pertaining to January, February, and March:
If these bonds had been issued at other than par, endofperiod entries would also include adjustments of interest expense for the amortization of premiums or discounts relating to elapsed periods.
Early retirements of debt may occur because a company has generated sufficient cash reserves from operations, and the company wants to stop paying interest on outstanding debt. Or, interest rates may have changed, and the company wants to take advantage of more favorable borrowing opportunities by “refinancing.”
Whether the debt is being retired or refinanced in some other way, accounting rules dictate that the extinguished obligation be removed from the books. The difference between the old debt’s net carrying value and the amounts used for the payoff should be recognized as a gain or loss.
For instance, assume that Cabano Corporation is retiring $200,000 face value of its 6% bonds payable on June 30, 20X5. The last semiannual interest payment occurred on April 30. The unamortized discount on the bonds at April 30, 20X5, was $6,000, and there was a 5year remaining life on the bonds as of that date. Further, Cabano is paying $210,000, plus accrued interest to date ($2,000), to retire the bonds; this “early call” price was stipulated in the original bond covenant. The first step to account for this bond retirement is to bring the accounting for interest up to date:
Then, the actual bond retirement can be recorded, with the difference between the uptodate carrying value and the funds utilized being recorded as a loss (debit) or gain (credit). Notice that Cabano’s loss relates to the fact that it took more cash to pay off the debt than was the debt’s carrying value of $194,200 ($200,000 minus $5,800).
Be aware that bonds can change in value. Remember that the value of a bond is a function of the bond’s stated rate of interest in relation to the going market rate of interest. If market interest rates rise, look for a market value decline (reflecting a lower present value based on the higher discount rate) and vice versa. Companies are permitted, but not required, to recognize changes in value of such liabilities. Entities that opt for this approach are to report unrealized gains and losses in earnings at each reporting date, and the balance sheet will be revised to reflect the fair value of the obligation.
Specific rules dictate the process and judgment for determining fair value. If a company's debt is traded in a public market, the valuation would be based on its observable price ("Level 1"). If the debt does not have a clearly determinable market, pricing would be tied to similar securities ("Level 2"). Management may develop their own pricing models in the rare case where the value is not otherwise observable ("Level 3").
Careful analysis is essential to judge an entity’s financial health. One form of analysis is ratio analysis where certain key metrics are evaluated against one another. The “debt to total assets” ratio shows the percentage of total capitalization that is provided by the creditors of a business:
Debt to Total Assets Ratio = Total Debt / Total Assets
A related ratio is “debt to equity” that compares total debt to total equity:
Debt to Equity Ratio = Total Debt / Total Equity
The debt to asset and debt to equity ratios are carefully monitored by investors, creditors, and analysts. The ratios are often seen as signs of financial strength when “small,” or signs of vulnerability when “large.” Of course, small and large are relative terms. Some industries, like the utilities, are inherently dependent on debt financing but may, nevertheless, be very healthy. On the other hand, some hightech companies may have little or no debt but be seen as vulnerable due to their intangible assets with potentially fleeting value. In short, one must be careful to correctly interpret a company’s debtrelated ratios. One must also be careful to recognize the signals and trends that may be revealed by careful monitoring of these ratios.
Another ratio, the “times interest earned ratio,” demonstrates how many times the income of a company is capable of covering its unavoidable interest obligation.
Times Interest Earned Ratio = Income Before Income Taxes and Interest / Interest Charges
If this number is relatively small, it may signal that the company is on the verge of not generating sufficient operating results to cover its mandatory interest obligation. While ratio analysis is an important part of evaluating a company’s financial health, one should be careful to not place undue reliance on any single evaluative measure.
A company may enter into a variety of longterm agreements. For example, a company may agree to buy a certain quantity of supplies from another company, agree to make periodic payments under a lease for many years to come, or agree to deliver products at fixed prices in the future. There is effectively no limit or boundary on the nature of these commitments and agreements. Oftentimes, such situations do not result in a presently recorded obligation, but may give rise to an obligation in the future.
This introduces a myriad of accounting issues, and a few generalizations are in order. First, footnote disclosures are generally required for the aggregate amount of committed payments that must be made in the future (with a year by year breakdown). Second, changes in the value of such commitments may require loss recognition when a company finds itself locked into a future transaction that will have negative economic effects. These observations should make it clear that an evaluation of a company should not be limited to just the numbers on the balance sheet.
A previous chapter introduced the idea of a "capital lease." Such transactions enable the lessee to acquire needed productive assets, not by outright purchase, but by leasing. It may be helpful to review the discussion in Chapter 10. The economic substance of capital leases, in sharp contrast to their legal form, is such that the lessee effectively assumes the risks and rewards of owning the asset. Further, the accompanying obligation for lease payments is akin to a note payable. That is, the lessee is under contract to make a stream of payments over time that substantively resembles the stream of payments that would have occurred had the lessee purchased the asset by a promissory note. Accounting rules attempt to track economic substance ahead of legal form. When an asset is acquired under a capital lease, the initial recording is to establish both the asset and related obligation on the lessee's balance sheet.
Assume that equipment with a fiveyear life is leased on January 1, 20X1, and the lease agreement provides for five endofyear lease payments of $23,739.64 each. At the time the lease was initiated, the lessee’s incremental borrowing rate (the interest rate the lessee would have incurred on similar debt financing) is assumed to be 6%. The accountant would discount the stream of payments using the 6% interest rate and find that the present value of the fixed noncancelable lease payments is $100,000. Therefore, the following entry would be necessary to record the lease:
After the initial recording, the accounting for the asset and obligation take separate paths. Essentially, the leased asset is accounted for like any other owned asset of the company. The asset is typically depreciated over the lease term (or useful life, depending on a variety of conditions). The depreciation method might be straightline or an accelerated approach. The Obligation Under Capital Lease liability is accounted for like a note payable. In the lease example, the amounts correspond to those illustrated for the mortgage note introduced earlier in the chapter. The first lease payment would be accounted for as follows:
Notice that this entry results in recording interest expense, not rent. This strategy would be applied for each successive payment, until the final payment extinguishes the Obligation Under Capital Lease account. The accounting outcome is virtually identical to that associated with the mortgage note illustrated earlier in the chapter.