EME 460
Geo-Resources Evaluation and Investment Analysis

Leasing Compared to Purchasing

PrintPrint

A Lease is a kind of rental agreement that allows the lessee (the renter) to use an asset for a specified time period without taking ownership. Decisions about leasing or purchasing are a secondary business assessment. This means that decisions about the economic necessity of acquiring the asset are already made, and in the next step we are going to decide whether to lease or purchase the asset due to economic, financial, and tax considerations.

Leasing and purchasing considerations:

Capital required to acquire the asset is much less for leasing compared to purchasing. So, when leasing, an investor can borrow less money and/or invest the extra money somewhere else.

A purchased asset can be depreciated and an investor can benefit from tax deductions. Besides, the interest paid for borrowed money is usually tax deductible. On the other hand, lease payments can be deductible as operating expenses for the lessee while the owner of the asset (lessor) receives depreciation deductions.

For publicly traded companies, leasing may have positive or negative impact on shareholder earnings depending on the magnitude of the operating lease payments to be expensed and the corresponding depreciation and interest deductions for a given year.

Types of lease

There are three types of lease:

Operating Lease

Operating Lease is a form of rental agreement that provides for the use of an asset by the lessee (user) for a period of time specified in the lease agreement. Operating lease payments are deductible in the full amount for tax purposes when these costs are incurred by the lessee. The lessor retains ownership and is therefore entitled to depreciate the asset over the MACRS specified life.

Capital Lease

Capital Lease (also called financial lease), differs from an operating lease in that it represents an alternative method of acquiring an asset, or effectively, it represents an installment loan to purchase the asset.

Financial Accounting Standards Board (FASB) statement number 13 outlines four criteria that classifies operating and capital lease (please read page 8 section “Criteria for Classifying Leases” of the statement).Please read the summary of this statement.

Leveraged Lease

Leveraged Lease includes a third party in the agreement.

In summary, the differences between operating and capital lease can be outlined as:

Operating Lease (Rental Agreement)

  • Lease payments may be expensed in their full amount when incurred.
  • Ownership is usually optional and subject to a buyout option upon completion of the lease period. Thus, salvage value may or may not be relevant depending on the service period being considered and other issues such as penalties regarding excessive use.
  • No depreciation is taken by the lessee.

Capital Lease (Installment Loan Purchase)

  • Lease payments are not deductible in the full amount when incurred.
  • The imputed interest component of the lease payment is an allowable deduction. (The imputed interest rate is based on rates for prevailing borrowed funds published by the IRS at the time the lease is initiated.)
  • The present value of the capital lease payments may be depreciated over the specified MACRS recovery period.
  • Salvage value at the end of the service period is always relevant since the investor will own the asset at the end of the capital lease.

More information about operating and capital lease can be found in the report Capital and Operating Leases: A Research Report.

Example 10-3

Suppose, as the manager, you want to decide whether to lease or purchase an asset for the company.

Purchase: The capital cost required to purchase the asset is $200,000 (at time zero) with a salvage value of $60,000 at the end of the 5th year. The purchased asset can be depreciated based on MACRS 5-year life depreciation with the half year convention (Table A-1 at IRS) over six years (from year 0 to year 5).

Lease (Operating): The asset can be leased for 5 years and annual lease payments (LP) of $50,000 should be paid from year 1 to year 5.

The asset would yield the annual revenue of $100,000 for five years (from year 1 to year 5) and operating cost for year 1 to 5 would be $20,000, $25,000, $30,000, $35,000, and $40,000.

Considering income tax of 40% and minimum ROR of 16%, calculate the ATCF for both alternative and incremental analysis and conclude which alternative is a better decision.

Purchase:

Year 0 1 2 3 4 5

Revenue 100,000 100,000 100,000 100,000 100,000
Salvage
60,000
- Operating cost
-20,000 -25,000 -30,000 -35,000 -40,000
-Depreciation
-40,000
-64,000
-38,400
-23,040
-23,040
-11,520

Taxable income
-40,000
16,000
36,600
46,960
41,960
108,480
- Income tax 40%
16,000
-6,400
-14,640
-18,784
-16,784
-43,392

Net Income
-24,000
9,600
21,960
28,176
25,176
65,088
+Depreciation 40,000 64,000 38,400 23,040 23,040 11,520
- Capital Cost -200,000

ATCF
-184,000
73,600
60,360
51,216
48,216
76,608

If asset is purchased, NPV at i* of 16% will be $20,221.

Lease:

Year 0 1 2 3 4 5

Revenue 100,000 100,000 100,000 100,000 100,000
- Operating cost -20,000 -25,000 -30,000 -35,000 -40,000
- Lease Operating cost -50,000 -50,000 -50,000 -50,000 -50,000

Taxable income 30,000 25,000 20,000 15,000 10,000
- Income tax 40% -12,000 -10,000 -8,000 -6,000 -4,000

Net Income 18,000 15,000 12,000 9,000 6,000

ATCF 18,000 15,000 12,000 9,000 6,000

If asset is leased, NPV at i* of 16% will be $42,180.

Incremental:

Year 0 1 2 3 4 5

Purchase ATCF
-184,000
73,600
60,360
51,216
48,216
76,608
Lease ATCF 18,000 15,000 12,000 9,000 6,000

Incremental ATCF -184,000
55,600
45,360
39,216
39,216
70,608

NPVPurchase-Lease at i* of 16% equals -$21,959.

Since NPV for lease is higher than purchasing, and incremental NPVPurchase-Lease is negative, we can conclude that leasing the asset is more economically satisfactory.

Note that because decision analysis is similar asset, revenue is similar in both alternatives and can be canceled out from both analysis. So, there is no need to have revenue as a known variable. NPV can be calculated without having revenue as known variable.

Lease, Types of Lease, and Lease/Purchase Decision Analysis part 1
Click for the transcript for Lease/Purchase Decision Analysis part 1

PRESENTER: In this video, I will explain lease and lease agreements.

There are two parties involved in a lease agreement-- lessor and lessee. Lessee is the person who uses the asset and pays the lease payments to the lessor. Lessor is the person who initially has the asset and gives it to lessee upon an agreement and for a specified period of time.

In this lesson, we are going to assume that a decision about leasing or purchasing are secondary business assessments. As meaning that we already assume that we are capable of taking a lease. So we are going to analyze whether it is good to take a lease, or it is better to purchase the property.

So when we lease an asset to use, it is going to require much less capital cost. If we purchase, we have to pay all the capital cost upfront. The purchase property can be depreciated. But when we lease the property upon the agreement-- I will explain later in the lesson that it might not be depreciable.

There are many types of lease. But in this lesson, I'm going to focus on just two of them. Two main types of lease. One is operating lease, and the other is the capital lease.

According to an operating lease agreement, lessor is allowed to use the asset for a defined period of time. Lessee is paying the lease payments, operating lease payments, to the lessor. These operating lease payments are deductible in full amount from revenue as tax deductions. They work similar to operating costs. In this type of lease, usually, the lessor holds the ownership of the assets. But it can be agreed that it can be optional for the lessee to take the ownership. But it is assumed, that in the operating lease, the lessor holds the ownership of the assets. And when the lease period is finished, lessee has to return the asset to the lessor.

So for the lessor, lessor can depreciate the asset. Because the asset is being used. Lessor can depreciate the asset according to MACRS method.

So the other type of lease is called capital lease. Capital lease is also called the financial lease. According to a capital lease agreement, the ownership of the asset is transferred from lessor to lessee upon the lease agreement. So the capital lease is somewhat similar to taking a loan, buying the assets by the loan, and then paying the loan installments-- paying the loan payments to pay off the loan.

So if you are interested to have more information about lease agreements, I'm going to put a link to Financial Accounting Standards Board that includes more information about lease agreements. And you can read more in this page.

So here are the differences between the operating lease and the capital lease. In the operating lease, or rental agreement, lease payments are deductible in full amount. They can be-- they can be expensed in full amount from the revenue. The ownership is usually not transferred to the lessee. So depreciation is not allowed for the lessee. Again, because we are assuming that the ownership stays with the lessor, depreciation is not allowed for the lessee. But the lessor-- who was the ownership-- can use the depreciation.

For the capital lease, or installment loan purchase, the ownership is transferred to the lessee. Lease payments are not deductible in full amount. But the interest portion of lease payments can be deducted from revenue as tax deductions. The lessee can use depreciation as tax deductions. Because lessee is going to have the ownership of the assets. I will explain this in a bit. Salvage value is applicable for the lessee. Again, because lessee's going to have the ownership of the asset.

So let's work on this example and see how the lease calculation works. Assume, as a manager, you want to decide whether to lease or purchase an asset. The asset-- the capital cost required for the asset is $200,000. At the present time, the salvage value is going to be $60,000. At the end of year five, the purchased asset is depreciable using the MACRS five year half year convention. If you lease the asset, you need to pay the lease payments of $50,000 from year one to year five. The asset is going to generate annual revenue of $100,000 from year one to year five. The operating costs from year one to year five are going to be 20, 25, 30, 35, and 40-- $40,000. The tax is going to be 40%. And the discount rate is going to be 16%.

Here we summarize the information that we have. So let's start with the purchase alternatives-- decision alternatives. We draw the time line. We start forming our table. We have five years. Revenue's $100,000 from year one to year five. And then we add salvage in year five-- $60,000. Then operating costs of 20, 25, 30, 35, and $40,000 from year one to year five. We deduct that from revenue. And then depreciation. We use-- we use half year MACRS for five years of depreciation. We extract the rates, and we multiply them by the value of asset-- which was $200,000, the capital cost required to buy the asset.

Then we calculate the taxable income. We make a summation over each column. The tax is 40%. So 40% of taxable income. And then we calculate the net income, which we deduct the income tax from the taxable income. Then we add back the depreciation. And the capital cost at the present time if we purchase the asset. And then we calculate the after tax cash flow. And, in the end, we will calculate the NPV for the decision alternative of purchasing the asset. So NPV at 16% discount rate is going to be $20,221.

Now, let's see how much will be the NPV if we lease the asset. So if we lease the asset, we are going to have the same revenue-- $100,000 per year from year one to year five. But there will be no salvage, because we as the lessee don't have the ownership of the asset. The operating cost is going to be the same. We add that to the table with a negative sign. The next is going to be the lease payments. So if we use the operating lease, we are allowed to deduct these lease payments in full amount in the year that it has happened. We can deduct them from revenue as tax deductions. So we deduct these as revenue.

We deduct the $50,000 per year of lease operating costs from revenue. Again, these lease payments are intuitively similar to operating costs. Then we calculate taxable income. 40% of tax. And then we calculate net income. Again, because we don't-- because we as the lessee don't own the property, we cannot depreciate. We cannot use the depreciation upon the operating lease agreement.

So we calculate the after tax cash flow. So here we don't need to pay the purchasing cost. And we are not benefiting from the depreciation and the salvage. And then we calculate the NPV of this after tax cash flow. Considering the 16% discount rate, which is going to be $42,180. And we can see this NPV is a much higher than the purchasing of the asset, so we can decide to lease this asset and not purchase it.

So I'm going to use a spreadsheet to work on this example quickly. So first, purchasing the asset, the revenue is going to be $100,000 per year. Then we are going to have salvage, which was $60,000 in year five. Then we are going to have the operating cost. Which was minus $20,000 minus $25,000 minus $30,000 minus $35,000 and minus $40,000.

And then we are going to have the depreciation. For the depreciation, I will go to table A1 MACRS half year convention in IRS website. These are the rates for five year half year convention. So I will just read them and enter them into the Excel spreadsheet. So I will calculate these here. I will say here. The rate was 20%.

So in order to calculate the depreciation, we multiply the capital cost of $200,000 by these rates. And these are the depreciation from present time-- year zero to year five. And we add them to the table with the negative sign. And again, because this is the half year depreciation, it has actually six years of depreciation because we move everything six months ahead. So we are going to have, actually, six years of depreciation starting from present time.

Then we calculate the taxable income. Which is the summation over each column. We apply that to the five years. Then we calculate the tax, 40% of the tax. Which is going to be 40% of taxable income. I have to consider a negative sign here, too. And the net income, which is the summation over these, or we deduct the tax from taxable income.

So because I entered the tax with a negative sign, we are just going to make a summation. Then we add back the depreciation, which is going to be this depreciation with a positive sign. So it has a negative sign. I multiply it by a negative sign. And the capital cost with a negative sign. Which was $200,000.

And then we calculate after tax cash flow, which is the summation over this column. Then we calculate the NPV. So because we have a payment at the present time, we enter that manually. Plus using the NPV equation and entering the 16% off discount rates. And we are going to have the NPV of $20,221 for purchasing the asset.

So for leasing the asset, I will just write the table here. Lease the asset. So the revenue's going to be the same. So I copied from up here. We are going to have the operating cost, which is going to be similar. So I will just-- these are equal to these numbers.

And then we are going to have lease operating payments. Which is going to be $50,000 with a negative sign from year one to year five. Then we calculate the taxable income, which is the summation of this column. Then we calculate the tax-- 40% of tax.

Then we calculate the net income.

And because we don't have anything else here for the lease payment, this net income is going to be equal to after tax cash flow. Which is going to be exactly these numbers. And then we calculate the NPV. As we can see here, there is no payments at present time. So I don't need to enter anything manually. Or because this is zero, it is going to be zero. So I'll just directly use the NPV function-- 16% of discounting rates and this cash flow. We can conclude that this investment is going to have a better return if we lease the asset instead of purchasing the asset.

In the next video, I'm going to explain how we can calculate the capital lease and how we can evaluate the project considering capital lease.

Credit: Farid Tayari

Example 10-4

Calculate the NPV of leasing the asset for Example 10-3 assuming capital lease, annual lease payments of $60,000 from year 1 to year 5, with borrowed money at an effective annual interest rate of 10%.

Since depreciation needs to be calculated based on present value of the capital lease payments, first we need to calculate the present value of the all six annual lease payments:

PW=60,000( P/ A 10%,5 )= $227,447

And depreciation is calculated as:

Depreciation
Year 0 1 2 3 4 5
Rate 0.20 0.32 0.19 0.12 0.12 0.06
Depreciation 227,447*0.20 =45,489 227,447*0.32 =72,783 227,447*0.19 =43,670 227,447*0.12 =26,202 227,447*0.12 =26,202 227,447*0.06 =13,101

Now the imputed interest for each payment needs to be calculated:

Imputed Interest
Year Payment Imputed Interest
=0.1*Balance
Principal
=Payment - Interest
Balancen
=Balancen-1 - Principaln
227,447
1 60,000 22,745 37,255 190,192
2 60,000 19,019 40,981 149,211
3 60,000 14,921 45,079 104,132
4 60,000 10,413 49,587 54,545
5 60,000 5,455 54,545 0
Total 227,447

ATCF will be:

Year 0 1 2 3 4 5

Revenue 100,000 100,000 100,000 100,000 100,000
Salvage 60,000
- Operating cost -20,000 -25,000 -30,000 -35,000 -40,000
- Imputed interest
-22,745
-19,019
-14,921
-10,413
-5,455
-Depreciation
-45,489
-72,783
-43,670
-26,202
-26,202
-13,101

Taxable income
-45,489
-15,528
12,311
28,877
28,385
101,444
- Income tax 40%
18,196
6,211
-4,924
-11,551
-11,354
-40,578

Net Income
-27,294
-9,317
7,387
17,326
17,031
60,867
+Depreciation 45,489 72,783 43,670 26,202 26,202 13,101
- Capital Cost
-37,255
-40,981
-45,079
-49,587
-54,545

ATCF
18,196
26,211
10,076
-1,551
-6,354
19,422

Note that Principal should be entered as capital cost.

So, assuming capital lease, NPV at minimum ROR of 16% will be $53,024.

Lease, Types of Lease, and Lease/Purchase Decision Analysis part 2
Click for the transcript for Lease/Purchase Decision Analysis part 2

PRESENTER: In the previous video, I explained the lease, type of lease, and I explained how we can evaluate a project with a operating lease. In this video, I'm going to explain the capital lease and the project assessment considering the capital lease. First, I'm going to review the lease and type of lease.

So lease is an agreement between a lessee and the lessor. A lessee is the person who uses the property. Lessor is the person who gives the property to the lessee to be used by lessee.

In previous video, I explained that there are two main types of lease-- operating lease and capital lease. The major differences between these two lease is in the operating lease, lease payments are allowed to be expensed in full amount. They can be deductible in full amount from revenue as tax deductions. We assume that in the operating lease, the ownership of the property stays with the lessor. So in the end of the period of lease, the lessee returns the property to the lessor. Because the ownership is not transferred, a lessee cannot use the depreciation for the asset, and salvage is not applicable to lessee.

The other type of lease agreement is the capital lease. In this type of lease, the ownership is transferred from lessor to lessee. The interest portion of lease payments can be deductible from revenue as tax deductions. Not the whole of that. Depreciation. Because the ownership is transferred to the lessee, lessee can use depreciation to take advantage of tax deductions. Lessee can use MACRS method. And again, because the ownership is transferred to the lessee, lessee can salvage values applicable to the lessee project assessment.

So let's work on this example, that in previous video, we calculated the project assessment for the operating lease. Here, we are going to calculate-- We are going to evaluate the project based on the capital lease. So assume, as a manager, you want to decide whether lease or purchase asset. If you purchase the asset, you need to pay $200,000 at present time. The salvage value is going to be $60,000.

This asset is going to generate revenue from year one to year five with $100,000 of revenue from year one to year five. The asset is depreciable using MACRS five-year half year convention. So depreciation can be applied in table from year zero to year five.

If you decide to lease this property using the capital lease method, the annual lease payments are going to be $60,000 from year one to year five, and the interest, the annual interest for the lease is going to be 10%. So this is the summary of the problem. The capital cost is going to be $200,000 if you buy the asset. A salvage value of $60,000. Annual revenue is going to be $100,000 from year one to year five, and the operating costs are going to be $20,000, $25,000, $30,000, $35,000, and $40,000 from year to year five.

Tax is going to be 40%, and a minimum discount rate is going to be 16%. The effective annual interest rate for the lease is going to be 10%, and capital lease payments are going to be $60,000 per year from year one to year five.

So this is the table if-- This is the project assessment if we purchase the asset. I explain that in detail in the previous video. If we purchase the asset, the NPV is going to be $20,221. Now, let's see how we can evaluate the project considering the capital lease.

So the first step in evaluating a project with capital lease is calculating the present value of all capital lease payments. So we have five capital lease payments from year one to year five, and the lease interest is going to be 10%. So we can use factor P/A, or this equation, to calculate the present value of all these five payments of $60,000 at the lease interest rate of 10%.

So the present value is going to be $227,447. Then, after calculating the present value of lease payments, we can calculate the depreciation. So this amount, this present value of lease payments, is going to be, actually, intuitively, is going to be the present value of the capital cost that we pay for the asset. So if we multiply that by the depreciation rate that we read from table A-1, MACRS method, five years depreciation half year convention. These are the rates that we read from the table, and we multiply it.

In order to calculate the depreciation for each year, we multiply these rates by the present value of capital lease payments that we pay. So we multiply, for example, for the present time, we multiply this present value by the 20%. This is the depreciation at present time. Same method for year one to year five. Present value of capital lease payments multiplied by the rate, and this is the depreciation for year one and so on.

In the next step, we have to calculate the interest portion of each annual lease payment. This part might be a little bit tricky, but this is not hard at all. This is the equation that we use to calculate the interest and the principal portion of each payment, each annual payment, that we pay for that lease. So every year, we pay $60,000 of capital lease payments for the asset, and in the end, we are going to have the ownership of the asset. So a portion, some part of the $60,000, is the interest, and some part of that is the principal.

So this is the equation that we calculate, this interest and principal portion. This is very important, because interest portion is deductible from the revenue as tax deductions, and the principal portion is the amount that we put as the capital cost for each year after we calculate the tax. Let's start calculating and see how it works.

So for the year zero, we don't have any payment. Payments are starting from year one, so the balance is going to be $227,447 that we had as the present value of these five payments of $60,000. So for year one, we are going to pay $60,000. In order to calculate the interest portion of the $60,000, we need to multiply the lease interest, which was 10%, multiply the balance of the previous year. So this is the balance of the previous year, which was $227,447. So 10% multiply this equals to $22,745 of interest for year one.

So from $60,000, $20,745 is the interest portion, and the rest is the principal. So in order to calculate the principal portion of this $60,000, we deduct interest from the payment. So $60,000 of payments minus $20,000 something of interest that we calculated equals $37,255 of principal for year one. And the balance equals the balance of the previous year minus the principal that we calculated here, and the remaining is the balance for year one.

Let's repeat this calculation for year two. So in year two, again, the payment is going to be constant, $60,000. The interest, the interest portion of this $60,000, is going to be 10%. The lease interest multiply the balance of the previous year, which was $190,192. 10% of that equals to this $19,000, almost $20. This is the interest portion of the $60,000 at year two. If we deduct this interest from the payment, the remaining is the principal. So payment, $60,000, minus the interest that we calculate here gives us the principal portion of the $60,000.

In order to calculate the balance, balance equals the balance of previous year multiply the principal, the principal that we calculated here. The remaining is the balance for year two. We do this calculation for year three, year four, and year five, and we have this table. Please note that if you calculate everything correctly, in year five, you must have the balance of zero. So if this is not zero, you should check your calculation. Something is wrong.

Another double-check mechanism is the summation of all principal should be exactly same as the balance that you initially had. And it makes sense, because you are paying off this lease, this loan. They should be exactly the same.

Now, let's enter this data in the table and evaluate the project assuming the capital lease. So year present time to year five, revenue $100,000 from year one to year five, and the salvage is going to be $60,000 in the end of year five. The operating cost is going to be $20,000, $25,000, $30,000, $35,000, and $40,000 from year one to year five.

The interest. So these interests, these interest portions, are the ones that we calculated in this table. So these are the interest portion of the lease payments of $60,000. So these are deductible from revenue as tax deductions. So going back to table. These are the interest portions. These are the interest portion of the $60,000 of lease payments that we have.

Then, we add the depreciation that we calculated before using the present value of lease payments. Then we calculate the taxable income, income tax, and net income. We add back the depreciation with positive sign. And another important point here, please note that the capital cost is the principal portion of the lease payments. So going back to the table, so this column is the principal portion of the $60,000. So we have to enter these as the capital cost for each year if we have capital lease.

Please note that in the purchasing alternative, we had the capital cost. We entered that at the present time. But here, we add this capital cost, which was the principal portion of the lease payments, to this row as the capital cost from year one to year five. And another double-check, the summation of these capital costs, this principal portion, and the interest portion should be equal to the $60,000 of the lease payments.

And then we calculate the after-tax cash flow. And again, please note that for the $60,000 of capital, annual capital lease payments, we break that down into two portions-- the interest portion and the principal portion. The interest portion is deductible from revenue as tax deduction, and the principal portion has to be entered in the table as the capital cost.

And we calculate the NPV using the discount rate of 16%, which is going to be $53,000. And as you notice, it has the highest NPV among their purchasing, operating lease, and capital lease.

So let me use a XLS spreadsheet and work on this example in the spreadsheet and see how we can formulate such example. So I have the purchase alternative already here. I'm going to follow with the capital lease analysis. So the revenue salvage operating costs are going to be exactly the same. So I will just copy them here, and I will say capital lease.

So now I have to calculate interest and principal portion of these lease payments. First, I have to calculate the present value of all these five capital lease payments of $60,000. So year one, year two, three, four, and five. Each year, we are going to pay $60,000. So in order to calculate the present value of these five payments, I can just use the NPV function. Present value equals NPV. The interest rate for the lease was 10%. There is no payment at present time. I start from year one. So this is the present value of all these payments.

Now, we have to calculate the interest and principal portion of these payments. So let me write the year here. So it is year zero, one, two, three, four, five. So this is going to be the payment, which we start paying at $60,000 from year one to year five. Then, the interest. Then, the principal and balance.

So balance at year zero equals the present value of these lease payments, the capital lease payments that we calculate. Then we go to the year one. The interest portion of the $60,000 equals the 10% of the capital lease interest multiply the balance. The principal equals the payment minus the interest, and the balance equals the balance of previous year minus the principal.

For year two, same method. So 10% multiply by the balance of previous year. The principal equals the payment minus interest, and the balance equals the balance of previous year minus the principal. And same for year three and so on. So we can just apply this equation. We can just apply this equation to the other years. And again, this cell is the double-check cell. If we calculate everything correctly, the balance of the last year should equal zero. And if I calculate the summation of all these principals, it should be exactly same as the balance of the first balance, the present value of all these payments.

So next, I'm going to calculate the depreciation. Again, I don't have much space here. I will write year zero, one, two, three, four, five. The depreciation is going to be equal the present value of these payments, which you see here-- I will fix that-- multiply the rates that I had. I had it from the table. So these are the depreciation from year one, from present time, to year five. And then I'll start adding them to the table.

So the interest portion of the annual lease payments are deductible from the revenue as tax deductions. So for year zero, we didn't have any payments. For year one, it is equal to this value. For year two, this value. For year three, equals this value, and so on. Year four and year five. And then I will enter the depreciation, which is negative sign. With starting from year zero, I refer to this year. And then I will calculate the taxable income.

Taxable income, which is the summation of this row. Then, we will calculate the tax, which was 40%. And then net income, which is the summation of these two. I add back the depreciation. Depreciation with the positive sign, so I will multiply this with a negative sign. So I'm going to-- This one.

And for the capital cost, as I explained-- So we have to enter the principal portion of these payments as capital cost. So there is nothing at year zero, because we didn't have any payment at year zero. For year one, negative sign. The principal portion of the lease payment is the capital cost that we pay. For year two, the principal portion at year two. For year three, the principal portion at year three. Four year four, the principal portion at year four. And four year five, the principal portion at year five.

So there is a very important-- Please note that from year one to year five, your interest portion reduces and your principal portion increases. So your interest portion decrease, your principal portion increase from year to year five. So this has a very positive impact on the project. So as you can see here, these interests are being deducted from the revenue. Big interests are being deducted from revenue as tax reductions in early years, and the principal, because it is increasing-- So we are paying less principal. We are paying less capital cost for the property in early years.

So because these higher capital costs are farther away from the present time, they are going to have less effect and the total effect-- Because these negative numbers are far from present, it is going to have a very good and positive impact on the project. So let me calculate the after-tax cash flow. So after-tax cash flow is going to be equal the summation of these three rows and the NPV.

In the end, we calculate the NPV here. Because we have a payment at present time, we have to enter that manually. We can use the NPV function for the rest 16% of interest. And we use the NPV function for the cash flow from year one to year five. We can see here, this has the highest NPV among the other three alternatives that we had for the purchase, for the operating lease, and for the capital lease.

Credit: Farid Tayari