# 4.7 Lease (Solution to Question #2)

First, take note that the solutions presented below will differ from the manner in which an accountant may record the leaseâs goings-on. We have ignored below the cash outflow emanating from the periodic lease payments. Similarly, we have ignored any cash inflows that will devolve from the productivity of the leased asset. We have done so in order to focus exclusively on the manner in which a lease will affect the firmâs leverage.

This is a two-part question concerning both 1. depreciation and 2. amortization.

1. Depreciation of Leased Asset

The straight-line deprecation is: \$2,076 Ăˇ15 = \$138.40

Therefore, the new asset value is: \$2,076 â 138 = \$1,938

Here are the relevant accounting book entries for the leaseâs deprecation â in the first year.

Income Statement / Depreciation Expense (dr)Â Â Â Â Â Â Â Â Â  \$138.40

Balance Sheet / Accumulated Depreciation (cr)Â  Â  Â  Â  Â \$138.40

The balance sheet will reflect the following:

Gross leased equipment Â Â Â Â Â Â Â Â  \$2,076

Accumulated DepreciationÂ Â Â Â  Â Â Â  (138)

Net Leased EquipmentÂ Â Â Â Â Â Â Â Â Â  \$1,938

2. Amortization of Lease Obligation

In order to calculate the amortization of the lease obligation, we must figure out how much of the annual payment is principal and how much is interest. The interest is: .05 Ă \$2,076 = \$103.80

Total annual (cash) payments on the lease are \$200. The income statement will reflect interest expense of \$104 (rounded off), leaving \$96 as amortization (reduction) of the principal. Therefore, the new lease obligation (liability) is: 2,076 â 96 = 1,980. In accounting terms, we credit cash \$200, and we debit both interest expense \$104 and amortization of the lease liability \$96.

Another way of looking at these calculations is to utilize the approach we used to calculate mortgages. A lease is amortized just like a mortgage. This calculation is illustrated in the following table:

 YearÂ PMT.Â InterestÂ AmortizationÂ BalanceÂ Credit to Cash Debit to Income Statement Debit to Balance Sheet 0 – – \$2,076 1 \$200 (.05)(\$2,076)= \$104 (200-204)= \$96 (\$2,076-96)= \$1,980

With this, one year into the lease, the balance sheet will look as follows.

(000)

 InceptionÂ A Year LaterÂ InceptionÂ A Year LaterÂ Current Assets \$200 \$200 Current Liabilities \$100 \$100 Leased Equipment 2,076 1,938 Lease Obligation 2,076 1,980 Fixed Assets 1,800 1,800 Long-term Debt 900 900 Equity 1,000 958 Total Assets \$4,076 \$3,938 Total Debt + Equity \$4,076 \$3,938 Debt Ratio 75.46% 75.67%

While the equipment and the obligation are depreciated and amortized at different rates, they will each sum out to zero at the horizon of the lease. In the first year of the lease, the âLeased Equipmentâ decreased by \$138, whereas the Lease Obligationâ decreased by \$96 and the Equity decreased by \$42 (i.e., 96 + 42 = 138).

The new equity may initially and incorrectly be thought of as a plug number, which is reconciled as per below. In this case, the plug number is a debit (accounting adjustment), representing the fact that the accumulated depreciation exceeds the lease obligation by that amount. At some point in the future, that relationship will reverse.

In fact, the firmâs net assets, calculated as assets minus liabilities, will have decreased by \$42. Here, the leased asset depreciated faster than the lease obligation was amortized. In this example, assets went down by \$2,076 – \$1,938 = \$138, while liabilities decreased by \$2,076 â \$1,980 = or \$96. This is a decrease in net assets of \$138 â \$96 = \$42, as assets decreased more than liabilities. Therefore, it is reasonable to reduce the equity, in this case by \$42, in order to match the net assetsâ reduction. If net assets decreased by \$42, the equity must decrease by the same amount due to the application of this slightly modified basic accounting equation:

â A â â L = â E

(\$138) â (\$96) = (\$42)

 Decrease in AssetsÂ Decrease in LiabilitiesÂ Decrease in Net Assets (A-L) Decrease in EquityÂ \$2,076 – \$1,938= \$138 \$2,076-\$1,980 = \$96 \$138- \$96= \$42 \$42

This analysis may be expressed differently in terms of debits and credits as follows:

 Reduction in leased asset – accumulated depreciation on balance sheet (credit) 138 Reduction in lease obligation- liability on balance sheet (debit) (96) Reduction in Equity – plug (debit) (42) Net 0

Summary Steps: Letâs review the steps we took in order to resolve the Leasing Exercise.

1. Calculate the Present Value of the lease payments. Insert this PV into both the Leased Asset and Lease Obligation cells at Inception.

Using the mortgage formula:

Lease (PV) = (x) (PVAF)

PV = (200) (10.3797) = \$2,076

2. Determine the Depreciation Expense. Subtract this expense form the Leased Assetâs balance at Inception. Insert the new number into the Asset balance âOne Year Later.â

Straight-line Depreciation Expense: \$2,076 Ăˇ15 = \$138

New Lease Balance: \$2,076 â 138 = \$1,938

3. Determine the Lease Obligation Expense by using the firmâs opportunity borrowing cost. Subtract this amount from the annual Lease Payments in order to determine the Amortization in the first year. Subtract the Amortization from the Lease Obligation. This is your Lease Obligation One Year Later.

Interest = (.05) (\$2,076) = \$104

Amortization = Payment less Interest: \$200 â 104 = \$96

New Lease Liability Balance: 2,076 â 96 = \$1,980

4. Adjust the Equity account. You can do this using the Basic Accounting Equation, or simply by plugging in a new Equity figure to force the Balance Sheet to balance.

Î (A â L) = Î E

(\$138) â (\$96) = (\$42)Â  Â  Â  Â Equity is reduced!