Discounted Cash Flow analysis, NPV, and ratios are the best techniques for evaluation of an investment project from any type of industry, especially for after-tax evaluation. These are methods and equations that require accurate, realistic and reliable data to generate reliable results. If these methods are fed with poor data and assumptions, generated results won’t be reliable. Input parameters such as tax, inflation, escalation, risk, salvage, loan and borrowed money, the minimum rate of return and more should be utilized properly. For example, if you are calculating After-Tax Cash Flow, you should apply the minimum rate of return with after tax considerations.
In this lesson, some other measures (such as payback period) will be explained that are helpful but not as important and useful as techniques that we have learned so far. These measures were more common before the 1960s and 1970s, and the disadvantage is they don’t properly consider the time value of money and tax effects.
We will also discuss after-tax decision methods and analysis including sell versus keep, general replacement, comparing the economics of leasing and purchasing, operating and capital leases. For an oil/gas or mining project, it is a common problem to analyze the economics of sell versus keep and replacing existing assets with new assets that are more capital intensive. Replacement analysis does not require any new engineering economy decision making techniques. We will use rate of return, net present value, and break even analysis to address this problem. It is frequently necessary to replace equipment, vehicles, piping systems, and other assets on a periodic basis. Another investment decision for a natural resource project is leasing or purchasing. We will also talk about operating and capital leases in this section.
At the successful completion of this lesson, students should be able to:
This lesson will take us one week to complete. Please refer to the Course Syllabus for specific time frames and due dates. Specific directions for the assignment below can be found within this lesson.
| Reading | Read Chapter 9 and 10 of the textbook and Lesson 9 in this website. |
|---|---|
| Assignments | Homework and Quiz 8. |
If you have any questions, please post them to our discussion forum, located under the Modules tab in Canvas. I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.
Payback period [1] is the time required for positive project cash flow to recover negative project cash flow from the acquisition and/or development years. Payback can be calculated either from the start of a project or from the start of production.
Payback period is commonly calculated based on undiscounted cash flow, but it also can be calculated for Discounted Cash Flow with a specified minimum rate of return. The intuition behind payback period measure is that the investor prefers to recover the invested money as quickly as possible.
One of the disadvantages of the payback period is that it doesn’t analyze the project in its lifetime; whatever happens after investment costs are recovered won’t affect the payback period. For example, if two investment alternatives have 10-year lifetimes, and investment alternatives A and B have 4 and 6 year payback periods, alternative A is more desirable from the payback period point of view, and it is not important how profitable alternative A would be after the 4th year and B after the 6th year.
Payback period can be useful when the investor has some time constraints and wants to know the fastest time that s/he can get her money back on the investment.
Calculate the payback period for an investment with following cash flow.
| C=$200 | C=$250 | I=$150 | I=$180 | I=$220 | I=$200 |
| 0 | 1 | 2 | 3 | 4 | 5 |
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
|---|---|---|---|---|---|---|
| ATCF | -200 | -250 | 150 | 180 | 220 | 200 |
| Cumulative ATCF | -200 | -450 | -300 | -120 | 100 | 300 |
As you can see, in year 4, the cumulative cash flow sign changes from negative to positive, meaning that at some point between year 3 and 4, costs (the summation of 200 at time zero and 250 dollars investments in year 1) would be recovered by generated profit. So, the payback period is somewhere in third year. To calculate the fraction, we can simply divide the 120 (cumulative cash flow in year 3) by 220 (cash flow in year 4). Therefore the payback period equals: .
Note that payback period can be reported from the beginning of the production. In this case, the payback period for the above example is after production begins, because production starts from year 2.
As explained, payback period can be calculated for discounted cash flow as well. The following example includes these calculations.
Calculate the discounted payback for the cash flow in example 9-1 considering a minimum rate of return of 15%.
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
|---|---|---|---|---|---|---|
| ATCF | -200 | -250 | 150 | 180 | 220 | 200 |
| DCF | -200 | -217.39 | 113.42 | 118.35 | 125.79 | 99.44 |
| Cumulative DCF | -200 | -417.39 | -303.97 | -185.62 | -59.83 | 39.60 |
Similar to the calculations in Example 9-1, the discounted payback period equals . And the discounted payback period from the beginning of production (year 2) equals 2.6 years.
Consider two mutually exclusive investments with the following cash flows. Which project is more economically satisfactory assuming a minimum rate of return of 15%?
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
|---|---|---|---|---|---|---|
| A | -$200 | $600 | ||||
| B | -$200 | $80 | $80 | $80 | $80 | $80 |
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
|---|---|---|---|---|---|---|
| ATCF | -200 | 0 | 0 | 0 | 0 | 600 |
| Cumulative ATCF | -200 | -200 | -200 | -200 | -200 | 400 |
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
|---|---|---|---|---|---|---|
| ATCF | -200 | 80 | 80 | 80 | 80 | 80 |
| Cumulative ATCF | -200 | -120 | -40 | 40 | 120 | 200 |
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| 0 | -80 | -80 | -80 | -80 | 520 |
For project A-B:
So, we can conclude that project A is more economically satisfactory than project B. Note that although project B has a lower payback period, project A is better for investment and has better return. It could be concluded by comparing the NPVs as well.
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.
PRESENTER: In this video, I'm going to talk about the payback period. Payback period is the earliest time that an investor can recover his or her investment-- his capital cost. Payback period is the time that is required for the positive cash flow, the earnings, to recover the negative cash flow, which was the investments, which was the capital cost.
Payback period can be calculated for undiscounted cash flow and also for discounted cash flow. And it can be calculated from the beginning of the project or from the start of the production. And obviously, the earlier-- the shorter-- the payback period is better for the investor. It is reflecting the time that the investor can get his or her money back.
A disadvantage of a payback period is the payback period is not reflecting any information about the performance of the project after the capital cost is recovered. So let's work on this example and see how we can calculate the payback period for a cash flow.
So this cash flow is an after-tax cash flow for a project. We are going to have the investment at the present time, at year 1, and we are going to have earnings from year 2 to year 5. The first step in calculating the payback period, is calculating the cumulative cash flow.
So in this row, I have calculated the cumulative cash flow for year 0, or present time, the cumulative cash flow equals the capital cost at present time. For year 1, the cumulative cash flow is the cumulative cash flow of the previous year plus the cash flow at year 1, which the summation is going to be $450.
Cumulative cash flow at year 2 is the summation of cash flow at year 2 and the cumulative cash flow at year 1, and so on. So as we can see here, the sign of cumulative cash flow changes between year 3 and year 4. So the payback period is going to be 3 plus something-- some fraction.
So the investor is going to recover the capital cost of $200 at present time and $250 at year 1. The investor is recovering this capital cost somewhere between year 3 and year 4. So the payback period is going to be 3-point-something. And, how do we calculate that fraction? The fraction is actually-- is 120 divided by this interval. The difference between these two numbers-- the cumulative cash flow at your 3 and the cumulative cash flow at year 4.
So 120 divided by this difference, which is going to be 220, is going to give us the fraction of the payback period. So the payback period for this investment is going to be 3 plus 120 divided by 220, which is going to be 3.55 years. And we can also calculate the payback period from the beginning of the production, as you can see here. The production, it starts from year 2.
So the payback period from the beginning of the project is going to be 3.55. And if you want to calculate the payback period from the beginning of the production, the production starts from year 2. So we have to deduct 2 years from the payback period that we calculated. So payback period from the beginning of the project minus 2, the production year, equals 1.55 for the payback period after the production.
Please note that the payback period is 3.55, and it is not going to consider any payments or project performance months after these-- year 4. So whatever happened in the project is not going to be reflected in the payback period.
So lets use an Excel spreadsheet to calculate the payback rate for this example. First step is calculating the cumulative cash flow. For the present time, the cumulative cash flow equals $200-- the capital cost at present time. Cumulative cash flow for the year 1 equals the cumulative cash flow of the previous year plus the cash flow at year 1. And we can apply these to the other cells, and we can calculate the cumulative cash flow for other years similarly.
So as you can see here, the sign of the cumulative cash flow changes from negative to positive between year 3 to year 4. So payback period is going to be 3 plus a fraction. And, how do we calculate the fraction? We have to calculate the 120 divided by the difference between these two numbers, which is 220. So it is 120 divided by 220, which is going to be 3.5.
I could also refer to the cells here, but be careful when you're referring to these cells-- this has a negative sign, so you need to add a negative sign to make sure the result is going to be positive. This number divided by this one minus this one. And again, please double-check. You have to include a negative sign here because this number has a negative, and you want to make sure your payback period is 3 plus something.
We can also calculate the payback period for discounted cash flow. And let's work on this example. Considering the 15% minimum rate of return or discount rate, and calculate a discounted payback period. First, we need to calculate the discounted cash flow. So we discount every year's cash flow by 15% and number of years.
And then we calculate the cumulative discounted cash flow, which is the summation of cumulative-- for present time, it equals the cash flow at the present time. For year 1, it equals the cumulative cash flow at year 0 plus the cash flow of year 1, and so on. Same for the other years.
So again, as you can see here, the cumulative discounted cash flow-- the sign of cumulative discounted cash flow changes from negative to positive between year 4 and 5. So the payback period for the discounted cash flow-- discounted payback period-- is 4 plus a fraction. How do we calculate the fraction? The fraction equals the cumulative cash flow at year 4, cumulative discounted cash flow, at year 4 divided by this difference. Divided by the difference between cumulative cash flow-- cumulative discounted cash flow-- of year 5 and year 4, which equals the cash flow at year 5.
So it is going to be 4 plus 59.83 divided by 99.44, which is going to be 4.6 years, discounted payback period. And again, we can calculate this from the beginning of the production, which is year 2. So we deduct 2 years from this 4.6, and report 2.6 as for the discounted payback period from the beginning of production.
So let's calculate the discounted payback period using an Excel spreadsheet. So I need to calculate-- the first thing is, I have to calculate the discounted cash flow.
So the discount rate was 15%, so I discount the cash flow by 1 plus 0.15, power, the year-- present time, capital cost doesn't need to be discounted. And the power is 0, so it has to be the same. And we apply that to the other years. And then, we have to calculate the cumulative discounted cash flow, which for the present time, equals the discounted cash flow for year 1-- equals the cumulative discounted cash flow of the previous year plus the cash flow of the current year.
So this is the cumulative discounted cash flow for year 1. And I will apply this to the other years. And as you can see here, the cumulative discounted cash flow-- the sign of cumulative discounted cash flow changes from negative to positive, somewhere between year 4 and year 5. Now I have to calculate a discounted payback period.
So discounted payback period equals 4 plus a fraction. To calculate the fraction, we have to divide 59.83 by the difference between the cumulative discounted cash flow of year 4 and year 5. This difference equals this one, so I can either use this number or I can calculate the difference. Again, because this number has a negative sign, please make sure that you include a negative sign for this number.
So I will say minus this, divided by this number minus this number. And it should be 4-something. So again, as you can see here, this is the discounted payback period-- it is 4.6, [AUDIO OUT]
Sunk costs are costs that have already been incurred in the past and that nothing we do now or in the future can affect.
These costs won’t affect the decision-making and economic analysis at present and in the future. A typical example for sunk cost in the oil and gas industry is the cost that has been spent on drilling a well. That well may have been producing for many years by the time a decision must be made for whether the well should be abandoned, but in this situation, drilling cost is sunk cost, and it’s irrelevant for the analysis. A similar concept is applicable to revenues from previous years and all its tax and commitments that have been paid.
Opportunity cost [2] is hidden or implied cost that is incurred when a person or organization forgoes the opportunity to realize positive cash flow from an investment in order to take a different investment course of action. A typical opportunity cost example is to sell a property or keep and develop it. If an investor forgoes realizing a sale value positive cash flow in order to keep and develop a property, an opportunity cost equal to the positive cash flow that could be realized from selling must be included in the analysis of development economics.
Also, as explained before, minimum rate of return used to analyze a project is actually the opportunity cost of capital (not the cost of borrowing money). Minimum rate of return is the return on capital that could be invested in other projects. Consequently, minimum rate of return is equivalent to opportunity cost of capital.
Break-even analysis includes calculating one unknown parameter (such as annual revenues, product selling prices, project selling prices, and break-even acquisition costs) based on all other known parameters under the condition that costs break even the profits. When calculating and analyzing the unknown parameters for after tax considerations, it is very important to apply the after tax values. For example, minimum rate of return applied to calculate after tax NPV should be the rate corresponding to after tax analysis of the project.
Consider a fairly old producing machine. As a manager, you have two alternatives:
A) Sell the machine: You can sell the machine in the market now for $500,000 with zero book value and pay the tax of 35%.
B) Keep the machine: You can decide to keep the machine, but an overhaul cost of $800,000 is required to repair and improve the machine. The overhaul cost is depreciable from time 0 to year 3 (over four years) based on MACRS 7-year life depreciation with the half year convention (Table A-1 at IRS [3]). After overhaul, the machine would be able to produce and generate equal annual revenue for three years (year 1 to 3). In the end of year 3, salvage value of the machine will be 100,000 dollars (zero book value). The operating cost of the machine for year 1, 2, and 3 will be $300,000,$400,000 and $500,000.
Assuming 35% income tax rate and after-tax minimum ROR of 18%, calculate the minimum annual revenue that the machine has to generate to break-even the selling with NPV of keeping the machine.
| Revenue of selling | 500,000 |
| - Book value | 0 |
|
|
|
| Taxable income | 500,000 |
| - income tax 35% | -175,000 |
|
|
|
| Net Income | 325,000 |
| Book value | 0 |
|
|
|
| ATCF | 325,000 |
Note that because in this case the machine would be sold at time zero, the NPVselling the machine = $325,000.
In this case, the annual revenue is the unknown variable (X).
Depreciation rate based on method MACRS 7-year life with the half year convention for year 0, 1, and 2 will be 0.1429, 0.2449, and 0.1749. And for year 3 we apply the remaining:
| Year | 0 | 1 | 2 | 3 |
|
|
||||
| Revenue | X | X | X | |
| + Salvage | 100,000 | |||
| - Operating cost | -300,000 | -400,000 | -500,000 | |
| - Depreciation | -114,320 | -195,920 | -139,920 | -349,840 |
|
|
||||
| Taxable income | -114,320 | X - 495,920 | X - 539,920 | X - 749,840 |
| - Income tax 35% |
+40,012
|
-0.35X + 173,572
|
-0.35X + 188,972 | -0.35X + 262,444 |
|
|
||||
| Net Income |
-74,308
|
0.65X - 322,348
|
0.65X - 350,948
|
0.65X - 487,396
|
| + Depreciation | 114,320 | 195,920 | 139,920 | 349,840 |
| - Repair Cost | -800,000 | |||
|
|
||||
| ATCF |
-759,988
|
0.65X - 126,428
|
0.65X - 211,028
|
0.65X - 137,556
|
NPV for this After Tax Cash Flow can be calculated as:
In order to calculate the minimum annual income of X, we have to equate the NPVKeeping the machine and NPVselling the machine.
So, the minimum revenue equals $1,010,000 for year 1 to year 3.
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.
A common economic decision is whether to replace an existing asset with a new costly asset that can help enhance the economics of the project. This decision is made: to increase the capacity, to improve the quality of products, to reduce the costs, to increase the production efficiency, or to make a product that can meet the market demands better. The old asset usually has lower capital and higher operating cost than the new asset.
In such decision making processes, the old and new assets are also called “defender” and “challenger.” The economics of the project is the key to making replacement decisions. An asset should be replaced if to do so improves the economics, and this decision shouldn’t depend on physical deterioration of the asset. Financial and intangible considerations should be taken into consideration for the final decision. Also, risk and uncertainty can be included in the evaluation. The old asset, already in place, usually has lower risk than the new one. Methods explained in previous lessons such as present worth cost, annual cost, incremental NPV or ROR analysis can be applied for replacement decisions. Please note that since tax deductions for two alternatives are different, evaluations should be based on after-tax considerations to give the correct answer.
Assume, as a manager, you have two alternatives: to keep the existing machine or replace it with a new one. The capital cost required for the new machine is $500,000 that needs to be paid at time zero and is depreciable from time 0 to year 4 (over five years) based on MACRS 7-year life depreciation with the half year convention (Table A-1 at IRS [3]). The new machine produces similar products with the same rate as the existing machine, so the revenue of selling product would be the same. But the new machine operates at lower operating costs of 80,000, $90,000, 100,000, and 110,000 dollars years 1, 2, 3 and 4. The operating cost of the existing machine is 320,000, $330,000, $340,000, and 350,000 dollars for year 1, 2, 3 and 4. Salvage value of both machines would be zero at the end of the 4th year. Consider the income tax of 40% and minimum after-tax ROR is 18%. Evaluate the project using Incremental ROR Analysis and conclude which alternative would be more economically satisfactory.
The following table displays the cost and revenue as it occurred for each decision alternative.
| R1 | R2 | R3 | R4 | |||
| C=$500,000 | OC=$80,000 | OC=$90,000 | OC=$100,000 | OC=$110,000 | ||
| New Machine: |
|
|||||
| Year | 0 | 1 | 2 | 3 | 4 | |
| R1 | R2 | R3 | R4 | |||
| OC=$320,000 | OC=$330,000 | OC=$340,000 | OC=$350,000 | |||
| Existing Machine |
|
|||||
| Year | 0 | 1 | 2 | 3 | 4 | |
The following table displays the incremental cost and revenue for New Machine - Existing Machine. Since questions assume similar production rate for new and old machines, they cancel out from incremental analysis. So, we can deduct the operating costs.
| New Machine - Existing Machine | C=$500,000 | S=$240,000 | S=$240,000 | S=$240,000 | S=$240,000 | |
|
|
||||||
| Year | 0 | 1 | 2 | 3 | 4 | |
R: Revenue, C: Capital Cost, OC: Operating cost, S: Saving
Note that since operating costs for the new machine are less than for the old one, the difference between the operating costs for the old and new machines is the savings due to installing the new machine. This saving implies that more income will be generated by installing the new machine.
| Year | 0 | 1 | 2 | 3 | 4 |
|
|
|||||
| Saving (Income) | 240,000 | 240,000 | 240,000 | 240,000 | |
| -Depreciation |
-71,450
|
-122,450
|
-87,450
|
-62,450
|
-156,200
|
|
|
|||||
| Taxable income |
-71,450
|
117,550
|
152,550
|
177,550
|
83,800
|
| - Income tax 40% |
+28,580
|
-47,020
|
-61,020
|
-71,020
|
-33,520
|
|
|
|||||
| Net Income |
-42,870
|
70,530
|
91,530
|
106,530
|
50,280
|
| +Depreciation | 71,450 | 122,450 | 87,450 | 62,450 | 156,200 |
| - Capital Cost | -500,000 | ||||
|
|
|||||
| ATCF |
-471,420
|
192,980
|
178,980
|
168,980
|
206,480
|
Depreciation rate based on method MACRS 7-year life with the half year convention for year 0, 1, 2, and 3 will be 0.1429, 0.2449, 0.1749, and 0.1249. And, for year 4, we apply the remaining:
Year 0 depreciation:
Year 1 depreciation:
Year 2 depreciation:
Year 3 depreciation:
Year 4 depreciation:
The incremental NPV at 18% minimum ROR for this ATCF equals 30,010. And with the trial and error method, incremental ROR will be 21.2%. These results indicate that replacing the existing machine with the new one is economically satisfactory.
Consider Example 9-5 and assume each machine produces 10,000 units per year. Calculate the cost per unit of the product and conclude which decision is more economically satisfactory.
Here we assume price of each unit of product equals X, then revenue in each year equals number of goods produced multiplied by the price. New machine break even analysis for price per unit of production will be:
| Year | 0 | 1 | 2 | 3 | 4 |
|
|
|||||
| Revenue | 10,000X | 10,000X | 10,000X | 10,000X | |
| - Operating cost | -80,000 | -90,000 | -100,000 | -110,000 | |
| -Depreciation | -71,450 | -122,450 | -87,450 | -62,450 | -156,200 |
|
|
|||||
| Taxable income | -71,450 | 10,000X - 202,450 | 10,000X - 177,450 | 10,000X - 162,450 | 10,000X - 266,200 |
| - Income tax 40% | +28,580 | -4,000X+80,980 | -4,000X + 70,980 | -4,000X+64,980 | -4,000X+106,480 |
|
|
|||||
| Net Income | -42,870 | 6,000X - 121,470 | 6,000X - 106,470 | 6,000X - 97,470 | 6,000X - 159,720 |
| +Depreciation | 71,450 | 122,450 | 87,450 | 62,450 | 156,200 |
| - Capital Cost | -500,000 | ||||
|
|
|||||
| ATCF | -471,420 | 6,000X + 980 | 6,000X - 19,020 | 6,000X - 35,020 | 6,000X - 3,520 |
Now we have to find the X that makes the NPV equal to zero.
NPV = 0
X = 31.44 dollar per unit
n analysis for price per unit of production for existing machine:
| Year | 0 | 1 | 2 | 3 | 4 |
|
|
|||||
| Revenue | 10,000X | 10,000X | 10,000X | 10,000X | |
| - Operating cost | -320,000 | -330,000 | -340,000 | -350,000 | |
|
|
|||||
| Taxable income | 10,000X - 320,000 | 10,000X - 330,000 | 10,000X - 340,000 | 10,000X - 350,000 | |
| - Income tax 40% | -4,000X+128,000 | -4,000X +132,000 | -4,000X+136,000 | -4,000X+140,000 | |
|
|
|||||
| Net Income | 6,000X - 192,000 | 6,000X - 198,000 | 6,000X - 204,000 | 6,000X - 210,000 | |
|
|
|||||
| ATCF | 6,000X - 192,000 | 6,000X - 198,000 | 6,000X - 204,000 | 6,000X - 210,000 | |
dollar per unit
Since the new machine breaks even at a lower unit price, we can conclude that replacing the existing machine with the new one is a better economic decision.
A Lease [4] 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.
There are three types of lease:
Operating Lease [5] 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 [6] (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 [7] 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 [8].
Leveraged Lease [9] includes a third party in the agreement.
In summary, the differences between operating and capital lease can be outlined as:
More information about operating and capital lease can be found in the extract of report [10].
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 [3]) 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.
| 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.
| 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.
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.
Calculate the NPV of leasing the asset for Example 9-7 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:
And depreciation is calculated as:
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Rate | 0.20 | 0.32 | 0.19 | 0.12 | 0.12 | 0.06 |
| Depreciation |
Now the imputed interest for each payment needs to be calculated:
| 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.
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.
In this lesson, we have learned the payback period analysis and after-tax investment decision methods and their applications including sell versus keep, general replacement, comparing the economics of lease versus purchasing, operating and capital leases. Also, we have introduced the difference between opportunity cost and sunk cost.
It is very important to explicitly understand the assumptions related to all economic analysis calculations to properly interpret and apply the results for investment decision making. Break-even calculations are no exception. Several key assumptions may have a significant effect on proper economics analysis, such as related to before-tax or after-tax, the cash flows are in escalated or constant dollars, with or without risk adjustment, and on a cash investment or leveraged basis. There is no substitute for understanding the calculation mechanics and the meaning of relevant discounted cash flow analysis assumptions in order to be able to apply evaluation results properly for economic decision-making.
You have reached the end of Lesson 9! Double-check the to-do list on the Lesson 9 Overview page [11] to make sure you have completed all of the activities listed there before you begin Lesson 10.
Links
[1] http://www.investopedia.com/terms/p/paybackperiod.asp
[2] http://www.econlib.org/library/Enc/OpportunityCost.html
[3] https://www.irs.gov/publications/p946/ar02.html
[4] http://www.investopedia.com/terms/l/lease.asp?optm=sa_v2
[5] http://www.investopedia.com/terms/o/operatinglease.asp?optm=sa_v2
[6] http://www.investopedia.com/terms/c/capitallease.asp?optm=sa_v2
[7] https://www.e-education.psu.edu/eme460/sites/www.e-education.psu.edu.eme460/files/Lesson09/FAS_13.docx
[8] https://www.fasb.org/page/PageContent?pageId=/reference-library/superseded-standards/summary-of-statement-no-13.html&bcpath=tff
[9] http://www.investopedia.com/terms/l/leveragedlease.asp?optm=sa_v2
[10] https://www.e-education.psu.edu/eme460/sites/www.e-education.psu.edu.eme460/files/Lesson09/Extract_Capital%20and%20operating%20leases.docx
[11] https://www.e-education.psu.edu/eme460/node/746