Most major investment projects in the natural resource industry involve the economics of borrowed money. One can use a lever and fulcrum to get leverage to raise a heavy object such as a large rock, and business owners can borrow someone else’s money, and in addition to their own equity capital, leverage investment dollars to increase the profit that can be generated. In this lesson, we will learn how to handle the borrowed money in discounted cash flow rate of return analysis and net present value analysis of various types of geo-resource projects.
At the successful completion of this lesson, students should:
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 11 of the textbook and the lesson content in this website for Lesson 11. |
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Assignments | Homework and Quiz 10. |
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.
In all previous lessons, we assumed that the money required for the investment is available in cash at no cost. However, it’s very common that an investment project is funded by a combination of borrowed money and equity capital. This way of funding a project is called “leverage [1]” and “gearing [2].” The idea here is to try to increase (leverage) the profitability of the project by borrowing money. There are three main differences between funding an investment project by cash or borrowed money:
To explore the effect of borrowed money on the project, we need to study four methods of loan amortization. Suppose an investor takes a $1000 loan with fixed annual interest rate of 8% to be repaid over four years.
In this method, the loan will be repaid in full (future value) at the end of the period. The payment at the end is called a balloon payment.
Loan = $1000 with 8% interest |
Balloon Payment =1361 |
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0 | 1 | 2 | 3 | 4 |
So, in this case, the balloon payment equals $1361 at the end of year 4, with loan principal of $1000 and interest of $361.
In this method, loan interest is paid at each period and the principal is paid in full at the end:
Loan = $1000 with 8% interest |
Interest = $80 | Interest = $80 | Interest = $80 | Principal= $1000 Interest = $80 |
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0 | 1 | 2 | 3 | 4 |
In this method, an equal portion of the principal is paid at each period plus interest based on the remaining balance in the beginning of each period.
Payment at year 1:
Principal:
Interest:
Payment at year 2:
Principal:
Interest:
Payment at year 3:
Principal:
Interest:
Payment at year 4:
Principal:
Interest:
Loan = $1000 with 8% interest |
Principal= $250 Interest = $80 |
Principal= $250 Interest = $60 |
Principal= $250 Interest = $40 |
Principal= $250 Interest = $20 |
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0 | 1 | 2 | 3 | 4 |
This method is similar to what we learned in previous lessons, and equal annual payments, A, can be calculated based on Table 1-12 as:
Payment =
Interest
Principal
Balance
Payment
Interest
Principal
Balance
Payment
Interest
Principal
Balance
Payment
Interest
Principal
Balance
Year | 1 | 2 | 3 | 4 |
---|---|---|---|---|
Payment | 301.92 | 301.92 | 301.92 | 301.92 |
Interest | 80 | 62.25 | 43.07 | 22.36 |
Principal | 221.92 | 239.67 | 258.85 | 279.56 |
Balance | 778.08 | 538.41 | 279.56 | 0 |
Loan = $1000 with 8% interest |
Payment= $301.92 | Payment= $301.92 | Payment= $301.92 | Payment= $301.92 |
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0 | 1 | 2 | 3 | 4 |
These methods consider a fixed annual interest rate of 8%. But there are types of loans that have variable interest rates, also called Adjustable Rate Mortgage (ARM), and interest rate changes periodically.
Generally, borrowed money enhances the economics of investment projects. But note that the result of leverage investment analysis shouldn’t be compared to cash equity investment. It should be compared with other investment projects with similar levels of leverage.
Consider an investment project that requires capital cost of $1,000,000 to purchase a machine at time zero, which yields the annual revenue of $625,000 and annual operating cost of $220,000 for 4 years (year 1 to year 4). Depreciation will be based on MACRS 3-year life depreciation with the half year convention (Table A-1 at IRS [3]) from year 1 to year 4. The salvage value is zero and working capital will be $100,000, income tax 40% and minimum rate of return will be 10%.
Year | 0 | 1 | 2 | 3 | 4 |
|
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Revenue | 625,000 | 625,000 | 625,000 | 625,000 | |
-Operating Cost | -220,000 | -220,000 | -220,000 | -220,000 | |
-Depreciation |
-333,300
|
-444,500
|
-148,100
|
-74,100
|
|
-Working Capital Write-off |
-100,000
|
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|
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Taxable income |
71,700
|
-39,500
|
256,900
|
230,900
|
|
- Income tax 40% |
-28,680
|
15,800
|
-102,760
|
-92,360
|
|
|
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Net Income |
43,020
|
-23,700
|
154,140
|
138,540
|
|
+Depreciation | 333,300 | 444,500 | 148,100 | 74,100 | |
+Working Capital Write-off | 100,000 | ||||
- Working Capital | -100,000 | ||||
- Capital Cost | -1,000,000 | ||||
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ATCF | -1,100,000 |
376,320
|
420,800
|
302,240
|
312,640
|
ROR for such an investment can be calculated using the trial and error method as ROR = 11.33% and NPV at 10% minimum rate of return equals $30,492.
Now, assume the investor takes a $1,000,000 loan at time zero with annual interest of 8% to be paid over four years (from year 1 to year 4).
Please note that the interest portion of the loan (mortgage) annual payments is tax deductible. Therefore, similar to part 4 on the previous page (Constant Payment Loan), we need to calculate interest and principal parts of each annual payment.
Loan annual payments:
Year | 1 | 2 | 3 | 4 |
---|---|---|---|---|
Payment | 301,921 | 301,921 | 301,921 | 301,921 |
Interest | 80,000 | 62,246 | 43,072 | 22,365 |
Principal | 221,921 | 239,674 | 258,848 | 279,556 |
Balance | 778,079 | 538,405 | 279,556 | 0 |
Year | 0 | 1 | 2 | 3 | 4 |
|
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Revenue | 625,000 | 625,000 | 625,000 | 625,000 | |
-Operating Cost | -220,000 | -220,000 | -220,000 | -220,000 | |
-Depreciation | -333,300 | -444,500 | -148,100 | -74,100 | |
-Working Capital Write-off | -100,000 | ||||
- Loan interest | -80,000 | -62,246 | -43,072 | -22,365 | |
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Taxable income |
-8,300
|
-101,746
|
213,828
|
208,535
|
|
- Income tax 40% |
3,320
|
40,699
|
-85,531
|
-83,414
|
|
|
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Net Income |
-4,980
|
-61,048
|
128,297
|
125,121
|
|
+Depreciation | 333,300 | 444,500 | 148,100 | 74,100 | |
+Working Capital Write-off | 100,000 | ||||
- Working Capital | -100,000 | ||||
-Principal |
-221,921
|
-239,674
|
-258,848
|
-279,556
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|
- Capital Cost | -1,000,000 | ||||
+ Loan | 1,000,000 | ||||
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ATCF | -100,000 |
106,399
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143,778
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17,548
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19,665
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ROR for this After Tax Cash Flow will be 89.87%.
Note that the loan needs to be entered in the table at time zero with a positive sign. As you can see here, borrowing money at 8% interest rate leverages and improves the economics of the project and the interest paid is tax deductible. In this case, After Tax Cash Flow of the project borrowed money is considerably smaller than funding project with cash.
It can be concluded that using borrowed money is always economically desirable as long as the borrowed money is earning more than it costs on an after-tax basis. The optimum amount of leverage and leverage ratio [4] (Total debt / Total Equity) for an investment is really a financial decision. Generally, the cost of equity is higher than debt.
Joint venture [5] is another method to provide capital if a company doesn’t have enough equity to fund a project. Joint venture has some considerations to compare to debt and loan:
Following Example 10-1, assume a 50-50 joint venture that shares all the costs and benefits equally. Calculate the ROR and NPV at minimum rate of return 10%.
Year | 0 | 1 | 2 | 3 | 4 |
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Revenue |
312,500
|
312,500 | 312,500 | 312,500 | |
-Operating Cost | -110,000 | -110,000 | -110,000 | -110,000 | |
-Depreciation |
-166,650
|
-222,250
|
-74,050
|
-37,050
|
|
-Working Capital Write-off | -50,000 | ||||
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Taxable income |
35,850
|
-19,750
|
128,450
|
115,450
|
|
- Income tax 40% |
-14,340
|
7,900
|
-51,380
|
-46,180
|
|
|
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Net Income |
21,510
|
-11,850
|
77,070
|
69,270
|
|
+Depreciation | 166,650 | 222,250 | 74,050 | 37,050 | |
+Working Capital Write-off | 50,000 | ||||
- Working Capital | -50,000 | ||||
- Capital Cost | -500,000 | ||||
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ATCF | -550,000 |
188,160
|
210,400
|
151,120
|
156,320
|
So for this, After Tax Cash Flow
Please note that in this case (50-50 joint venture investment), ROR for each partner will be similar to the case that one investor provides the entire equity. However, NPV for each partner is half (partnership ratio); compared to one investor providing the entire equity case.
Since more borrowed money enhances the economics of the project and makes it look economically better, it might be misleading for the decision makers to know how much actual return on the project would be.
However, for leveraged NPV results to be valid for decision-making purposes, the minimum DCFROR used in NPV calculations must be based on the same or a similar amount of leverage as the project being analyzed. This means that you need a different minimum DCFROR for every NPV calculation based on different amounts of borrowed money.
Since the minimum DCFROR represents the analysis of other opportunities for the investment of capital, it should be evident that it is desirable and necessary for valid economic analysis to evaluate the “other opportunities” on the same leverage basis as the project or projects being analyzed.
The opportunity cost that defines the after-tax minimum rate of return is a function of the leverage proportion associated with the investment. Because the use of leverage will increase the project DCFROR, the minimum rate of return that the project investment must equal or exceed for acceptance must also be increased to reflect the increased leverage incorporated in the investment. If the minimum DCFROR is not increased to reflect the increased leverage proportion, almost any project can be made to look economically attractive simply by increasing the proportion of borrowed money devoted to the project.
A company can sometimes be viewed as simply a set of investment projects. Similarly, an individual project can be viewed as being equivalent to a company with one single activity. Weighted Average Cost of Capital (WACC) is a common method to calculate the company’s required rate of return based on its capital structure. This method can also be used to determine the minimum rate of return (discount rate) for the projects that company is involved in.
Capital structure: A company (or a project) can be financed from two sources: owners’ money and borrowed money. This combination (proportion of debt and equity) forms the capital structure. So, company’s financial resources (assets) can be written as:
Borrowed money, also called liabilities, comes from debt, loan, etc. Liabilities are typically subject to paying interest. Owners’ money is called equity. For example, for a company, equity comes from the shareholders’ contribution. Company issues shares, investors buy them, become shareholders, and participate in the ownership. In return, shareholders expect to benefit from the business activities and receive some return (interest) on their investments. This expectation is reflected into the cost of equity for the company.
WACC method finds the minimum rate of return based on the weighted average of costs of financing from debt and equity. Weights are calculated according to the capital structure, the proportion of project that is financed through debt and equity.
The cost of debt is what lenders charge as interest. For example, interest that has to be paid on a loan. The cost of debt is dependent on how likely or unlikely the lender is to be paid back (think of this as having high versus low credit score. If loan is approved, the one with higher credit score will be charged less interest compared to the person with low credit score).
The cost of equity is the rate of return that investors demand and it represents the "opportunity cost." When equity investors (like potential holders of stock) invest in the company, they forego the returns that they could have earned from some other investment opportunities. Therefore, those foregone returns represent opportunity cost of their investment in the company. Cost of debt depends on many factors, such as type of investment, market, industry, and risk.
In general, a lower WACC indicates a financially healthy business that’s capable of attracting investors at a lower cost. Whereas higher WACC shows that investors expect to be compensated with higher return due to the higher risk and more challenges associated with the project.
Example 10-4: Assume an oil company financing a project with 20% debt and 80% equity. Where the cost of debt is 6% and cost of equity is 10% and tax rate is 35%. Weighted average cost of capital can be calculated as:
WACC = 0.2×0.06×(1−0.35)+0.8×0.1 = 0.0878 or 8.78%
Example 10-5: Assume a project that requires capital cost of 10 million dollars, where 4 million dollars is financed through loan and the rest through equity. Calculate the WACC (expected minimum rate of return) if the loan interest is 4%, cost of equity of equity 8%, and tax is 30%.
WACC = (4/10)×0.04×(1−0.30)+(6/10)×0.08 = 0.0592 ~ 6%
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.
This lesson focused on leverage and borrowed money. Using examples and solving illustrative problems, we have learned:
The rule of leverage we have learned is to never borrow money when you have a sufficient treasury to finance investments on a 100% equity basis unless the portion of your treasury equal to the borrowed money amount can be put to work at a DCFROR, which is more than the after-tax cost of borrowed money.
You have reached the end of Lesson 11! Double-check the to-do list on the Lesson 10 Overview page [6] to make sure you have completed all of the activities listed there before you begin Lesson 12.
Links
[1] http://www.investopedia.com/terms/l/leverage.asp
[2] http://www.investopedia.com/terms/g/gearing.asp
[3] https://www.irs.gov/publications/p946/ar02.html
[4] http://www.investopedia.com/terms/l/leverageratio.asp
[5] http://www.investopedia.com/terms/j/jointventure.asp
[6] https://www.e-education.psu.edu/eme460/node/753