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.
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 report Capital and Operating Leases: A Research 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.
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.
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] http://www.fasb.org/resources/ccurl/62/358/fas13.pdf
[8] http://www.fasb.org/summary/stsum13.shtml
[9] http://www.investopedia.com/terms/l/leveragedlease.asp?optm=sa_v2
[10] http://files.fasab.gov/pdffiles/combinedleasev4.pdf
[11] https://www.e-education.psu.edu/eme460/node/746