Lesson 10: Evaluation Involving Borrowed Money
Lesson 10: Evaluation Involving Borrowed Money jls164Introduction
Introduction jls164Most 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.
Learning Objectives
At the successful completion of this lesson, students should:
- be able to conduct a leveraged investment analysis;
- be familiar with joint venture analysis;
- be able to analyze a land investment with leverage; and
- understand the relationship between minimum rate of return and leverage.
What is due for Lesson 10?
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 10. |
|---|---|
| Assignments | Homework and Quiz 10. |
Questions?
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.
Borrowed Money (part I)
Borrowed Money (part I) jls164In 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” and “gearing.” 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:
- Interest on borrowed money is an additional operating expense tax deduction that must be accounted for each evaluation period that mortgage payments are made.
- Loan principal payments are additional non-tax deductible capital costs that must be accounted as after-tax outflows of money each evaluation period that mortgage payments are made.
Compounding
In order to compare different alternatives in an economic evaluation, they should have the same base (equivalent base). Compound interest is a method that can help applying the time value of money. For example, assume you have 100 dollars now and you put it in a bank for interest rate of 3% per year. After one year, the bank will pay you . Then, you will put the 103 dollars in the bank again for another year. One year later, you will have . If you repeat this action over and over, you will have:
Which can be written as:
In general:
The value of money after nth period of time can be calculated as:
(Equation 1-1)Which F is the future value of money, P is the money that you have at the present time, and i is the compound interest rate.
Example 1-1:
Assume you put 20,000 dollars (principal) in a bank for the interest rate of 4%. How much money will the bank give you after 10 years?
So the bank will pay you 29604.8 after 10 years.
Discounting
In economic evaluations, “discounted” is equivalent to “present value” or “present worth” of money. As you know, the value of money is dependent on time; you prefer to have 100 dollars now rather than five years from now, because with 100 dollars you can buy more things now than five years from now, and the value of 100 dollars in the future is equivalent to a lower present value. That's why when you take loan from the bank, the summation of all your installments will be higher than the loan that you take. In an investment project, flow of money can occur in different time intervals. In order to evaluate the project, time value of money should be taken into consideration, and values should have the same base. Otherwise, different alternatives can’t be compared.
Assume you temporarily worked in a project, and in the end (which is present time), you are offered to be paid 2000 dollars now or 2600 dollars 3 years from now. Which payment method will you chose?
In order to decide, you need to know how much is the value of 2600 dollars now, to be able to compare that with 2000 dollars. To calculate the present value of a money occurred in the future, you need to discount that to the present time and to do so, you need discount rate. Discount rate, i, is the rate that money is discounted over the time, the rate that time adds/drops value to the money per time period. It is the interest rate that brings future values into the present when considering the time value of money. Discount rate represents the rate of return on similar investments with the same level of risk.
So, if the discount rate is i=10% per year, it means the value of money that you have now is 10% higher next year. So, if you have P dollars money now, next year you will have and if you have F dollars money next year, your money is equivalent to dollars at present time.
Going back to the example, considering the discount rate of 10%:
We can calculate the present value of $2600 occurred 3 years from now by discounting it year by year back to the present time:
Value of 2600 dollars in the 2nd years from now
Value of 2600 dollars in the 1st years from now
Value of 2600 dollars at the present timeSo, it seems at the discount rate of i=10%, present value of 2600 dollars in 3 years equals 1953.42 dollars, and you are better off, if you accept the 2000 dollars now.
With the following fundamental equation, present value of a single sum of money in any time in the future can be calculated. It means a single sum of money in the future can be converted to an equivalent present single sum of money, knowing the interest rate and the time. This is called discounting.
Equation 1-2P: Present single sum of money.
F: A future single sum of money at some designated future date.
n: The number of periods in the project evaluation life (can be year, quarter or month).
i: The discount rate (interest rate).Example 1-2:
Assuming the discount rate of 10 %, present value of 100 dollars which will be received in 5 years from now can be calculated as:
You can see how time and discount rate can affect the value of money in the future. 62.1 dollars is the equivalent present sum that has the same value of 100 dollars in five years under the discount rate of 10%
Note:
The concept of compounding and discounting are similar. Discounting brings a future sum of money to the present time using discount rate and compounding brings a present sum of money to future time.
Figure 1-1: Compounding and DiscountingCredit: Farid TayariInvestment capital costs must be adjusted for borrowed money inflows of money each evaluation period that loans are made.
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.
Project Evaluation with Borrowed Money
PRESENTER: In this video, I'm going to explain how we can analyze a project considering borrowed money. In previous videos, we assumed that money required for the investment in a project is available in cash and the investor provides the entire money required for the investment without any cost. But in reality, it's very common that the project is funded by a combination of borrowed money-- loans-- and equity capital, or the money that the investor puts in the project.
So funding a project using borrowed money is called leverage or gearing. And the reason behind that is the higher portion of fund in the project coming from borrowed money, from loans, it is going to give the project higher profitability, and it is going to enhance the economics of the project.
So when an investor funds a project with borrowed money, two things have to be considered. First, the interest portion of borrowed money, similar to operating costs, can be expensed and deducted from revenue as tax deductions. And this is going to give leverage to the project and enhance the economics of the project because this is actually going to reduce the tax paid by the investor. The other difference is that the loan principal payments are non tax-deductible, and they can be deducted from the after-tax cash flow as similar to capital cost. But because they can be distributed over years, they can also contribute in enhancing the project's profitability and the economics of the project. I will work on an example in the following videos, and I will explain them later in this lesson.
So there are four main types of loans that I will explain in the following videos. The first one is a balloon payment loan; the second one is interest only loan; the third one is constant amortization loan; and the fourth one, which is the most common one, is the constant payment loan.
1. Balloon Payment Loan
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 | |||
| 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.
2. Interest Only Loan
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 |
| 0 | 1 | 2 | 3 | 4 |
Balloon Payment Loan and Interest Only Loan
So there are four main types of loan, balloon payment loan, interest only loan, constant amortization loan, constant payment loan. So the last one is the most common one, and I will explain it in the following videos. In this video, I'm going to explain the first two types.
Balloon payment loan. In this type of loan, the borrower receives the loan, takes the loan at the present time at year zero, and has to repay the loan in the end of the agreed period. The borrower has to pay the principal and interest for the loan in the end of the period.
So there is no installment. There is no monthly, or annual, or per period payments. The borrower takes the loan at the present time and repays the entire loan with interest in the end of the period.
So for example, if the borrower is going to take a loan of $1,000 at present time with 8%, let's say for four years, then the borrower doesn't need to pay anything at year one to three, but the borrower has to pay the entire loan with interest, the principal and interest, in the end of year four. So in order to calculate the money that the borrower has to pay to the lender, we have to multiply $1,000 of loan by the factor F over P, 8% of loan interest and after four years.
So this factor equals 1 plus 8 percent power 4, and the result is going to be $1,361. So from this $1,361, $1,000 is the principal and $361 is the interest of this loan. That has to be paid in the end of the period, which was year 4. So the borrower pays the principle of $1,000 plus $361 of interest to the lender in the end of the period.
The second type of loan is called interest only loan. In this type of loan, borrower takes the loan at present time, let's say $1,000. Then borrower returns this $1,000 in the end of their agreed period, but borrower has to pay equal amounts of annual interest to the lender.
So let's assume a borrower takes the loan of $1,000 with 8% interest at present time. Then, borrower has to pay $1,000, must apply 8%, which comes to $80 per year from year one to year four. Let's say four years is the time interval that is agreed between lender and borrower. And so borrower has to pay $80 per year from year one to year four to the lender. And also, the borrower has to pay the principal of $1,000 at the end of year four.
3. Constant Amortization Loan
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 |
| 0 | 1 | 2 | 3 | 4 |
Constant Amortization Loan
PRESENTER: So there are four types of loan-- balloon payment, loan interest on the loan, constant amortization loan, and constant payment loan. In the previous video, I explain the first two types-- balloon payment loan and interest on the loan.
In this video, I'm going to explain the constant amortization loan and in the next video, I'm going to explain the most common type of loan, which is constant payment loan.
In a constant amortization loan, borrower receives the loan, takes the loan let's say at the present time, and has to pay equal portion of principal per period, plus the interest that the interest is calculated based on the remaining balance.
So I'll explain constant amortization loan in an example. Let's assume an investor takes the loan of $1,000 that has an interest rate of 8%, and the loan has to be repaid over four years. And we are going to consider the constant amortization loan.
So in constant amortization loan, the principal paid in each period is constant, and it's not changing. So the first step is to calculate the principal.
The principal is calculated as the loan divided by the number of period that has to be repaid. So the loan was $1,000, and the loan has to be repaid over four years. So the principal is going to be 1,000 divided by four years, which is going to give $250 per year. So the principal is going to be constant from year one to year four and is $250.
The next step is going to be calculating the interest and payments for each period. The interest is the balance multiply the interest rate of the loan.
So the balance at year one is $1,000, multiply the interest rate for the loan, which is going to give us $80. So the payment equals the principal plus interest. So the borrower has to pay $330 at year one to the lender.
And then we calculate the balance after this payment is paid, so $1,000 minus balance equals the balance of previous year, which was $1,000 minus the principal paid. From $330, $250 was the principal that we calculated here. So the remaining is $750, which is the balance, which is going to be applied for the calculation of year two.
So for year two, the interest equals balance multiply the interest rate. The balance is the balance that we calculated at year one after borrower paid $330, so the balance is $750. Multiply the interest rate is going to be $60, and it is the interest that the borrower has to pay. So in total, borrower has to pay $250 of principal plus $60 of interest, which comes to $310 at year two for this loan.
So then we are going to calculate the balance after the loan payment is paid. The balance is going to be $750, which is the balance of the previous year minus the principal, which is going to be $500.
And year three, the principal was constant $250. In order to calculate interest, we need to multiply the balance of the previous year by the interest rate, which was 8%. So $500 multiplied by 8% gives $40 of interest.
The payment that has to be paid by the borrower to the lender is $250. The principal plus the interest-- 40, which comes to $290 for year three.
And then we need to calculate the balance. Balance is the balance of previous-- the balance of previous year after the payment is paid, which was $500 minus the principal. And the principal is constant, and it is $250 per year. And the remaining is $250. So the balance at year three, after the payment is paid, the loan payment is paid is $250.
For year four, again, the principal is constant-- $250. The interest is the balance at the previous year is 250 multiplied the interest, 8%, which gives $20. And the payments at year four is the principal plus interest-- $250 plus $20 gives $270.
And here, the balance should equal zero. The balance is the balance of previous year-- $250 minus the principal that is paid at year four. So if we calculated everything correctly, the balance at the end of year four has to be zero.
So this is the summary of this loan. Borrower has received the loan of $1,000 at 8%, and borrower has to pay the constant principal of $250 per year plus the interest. That is calculated based on the remaining balance. And as you can see, the interest is $80, $60, $40, and $20 from year one to year four, but the principal is constant from year one to year four.
4. Constant Payment Loan
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:
Year 1:
Payment =
Interest
Principal
Balance
Year 2:
Payment
Interest
Principal
Balance
Year 3:
Payment
Interest
Principal
Balance
Year 4:
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 |
| 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.
Constant Payment Loan, Interest and Principle
PRESENTER: So there are four types of loan-- balloon payment loan, interest only loan, constant amortization loan, and constant payment load, which is the most common one. I explained the first three types in previous videos, and in this video I'm going to explain the constant payment loan.
So in the constant payment loan, the payments that are paid per period are constant. So let's work an example and see how we can do the calculations for the constant payment loan. Let's assume an investor takes a loan of $1,000, and the interest rate is 8%, and that the loan has to be repaid over four years. And we consider constant payment loan.
So the first step is to calculate equal annual payments, A. And we can use factor A over P, or capital recovery factor, for calculating these payments. And this is the equation. i is the interest rate, and n is the number of years, period, that the loan has to be repaid. And P is the loan. So $1,000 might multiply this equation, which gives us about $302 per year for this loan.
So the payments are going to be equal, $302 per year. Then we need to calculate the interest and principal portion of these payments of $302 for each year. The interest is the balance multiplied the interest rate, which was $1,000 multiply 8%, which gives us $80 of interest for year one.
For calculating the balance, we have to deduct the interest from the payment. And we are going to have $302 minus 80, which comes to almost $222. After this payment is paid, the balance is going to be the balance of previous year, which was $1,000, minus the principal portion of the payment, which is $222. And the remaining is the remaining balance, which is 778.
For year two, payment is constant, is what we calculated. The interest is the remaining balance, which was 778, multiply the interest rate, which is going to be $62.25. For the principal, we deduct the interest from the payment, and the remaining is going to be the principal at year two. So the remaining balance is the balance of the previous year, 778, minus the principal portion of the payment, which was 339.68. And this is the balance at year two when we pay this $302.
For year three, the payment is constant, similar to year one and year two. The interest is the remaining balance, which is 538.41, the remaining balance that we have here, multiply the interest rate, and it is going to give us $43.07. And this is the interest portion of this payment.
The remaining is the principal portion. So we deduct the interest from the payment, and the remaining is going to be the principal portion of this payment. In order if we calculate the remaining balance, we deduct the principal from the balance of the previous year, which was here. So the balance of previous year minus the principle that we paid this year gives us the remaining balance.
For year four, payment is constant. The interest is the remaining balance multiply interest rate of 8%, which is going to be 22.36. And the principal is going to be the payment minus the interest. The remaining is 279.56. And if we calculate everything correctly, this number this principle for the last year, should be exactly same as the remaining, which means that we're going to have zero balance at year 4 after we pay the payments.
So we can summarize these loan calculations as-- so a loan is taken at 8%-- a loan of $1,000 is taken at with 8% at present time, and the payments of almost $302 is paid to repay the loan from year one to year four.
Borrowed Money (part II)
Borrowed Money (part II) jls164Generally, 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.
Example 10-1
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) 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 |
| 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 | ||||
| Taxable income | 71,700 | -39,500 | 256,900 | 230,900 | |
| - Income tax 40% | -28,680 | 15,800 | -102,760 | -92,360 | |
| 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 | ||||
| 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.
Example 10-2
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 |
| 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 | |
| Taxable income | -8,300 | -101,746 | 213,828 | 208,535 | |
| - Income tax 40% | 3,320 | 40,699 | -85,531 | -83,414 | |
| 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 | |
| - Capital Cost | -1,000,000 | ||||
| + Loan | 1,000,000 | ||||
| ATCF | -100,000 | 106,399 | 143,778 | 17,548 | 19,665 |
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 (Total debt / Total Equity) for an investment is really a financial decision. Generally, the cost of equity is higher than debt.
Project Evaluation with Loan (Borrowed Money)
PRESENTER: So there are four types of loan, balloon payment loan, interest only loan, constant amortization loan, and constant payment loan, which is the most common one. I explained the first three types in previous videos, and in this video, I'm going to explain the constant payment loan. Now let's work on an example and see how we can apply the loan calculation, how we can apply these principles and calculations to a project with borrowed money.
First, let's assume the simple case that there is no borrowed money and consider an investment of a project that records the capital cost of a million dollar. The capital cost is depreciable over four years using MACRS-3 year half convention. The capital-- the machine is going to generate annual revenue of $625,000, and the operating cost is going to be $220,000 from year one to year four. The discount rate is going to be 10% and tax will be 4%. And we are going to consider the working capital of $100,000.
So we summarized this example, as in this slide. The project life is four years, capital cost $1 million, annual revenue $625,000 and operating costs of $220,000 from year one to year four. Depreciation using MACRS-3 year half year convention. A zero salvage, capital cost-- working capital of $100,000, and income tax is 40%, and discount rate or minimal rate of return is going to be 10%.
So we draw our table. First, I enter the revenue of $625,000 from year one to year five. Then we deduct the operating cost of $220,000 depreciation. We multiply the capital cost of $1 million by depreciation rates that we read from table one from IRS website. And we enter the depreciation from year one to year four here. The other item is working capital write-off. Well, this is tax deductible so we enter that with a negative sign. $100,000 we deducted from revenue as tax deduction.
Taxable income, which is a summation over each column, income tax of 40% and net income. Then we add depreciation-- add back the depreciation, which equals to this row, but with a positive sign. Then we add back the working capital write-off, because it was deductible from revenue as tax deduction, so we need to add them back-- add that back again with a positive sign. Then we start adding the costs and capital costs, so working capital of $100,000 at present time with a negative sign. And capital costs of $1 million as present time with a negative sign. We calculate after tax cash flow and rate of return and NPV of the project as 11.33% for rate of return and NPV at a discount rate of 10% of $30,492.
Now, let's assume the investor takes a loan of $1 million at time zero with annual interest of 8% that has to be paid over four years. So the first step is calculating the equal annual payments. We use a capitol recovery factor or A over P factor, 8% and four years, and we calculate the annual payment of $301,921 that has to be paid for each year from year one to year four.
So then we need to calculate the interest and principal portion of each payment for each year. Payments are equal from year one to year four. For year one, we have to calculate interest. Interest equals balance multiply interest rate. Balance of $1 million multiply interest rate of 8%, which gives $80,000. And then principal equals payment minus interest, which gives us the principal at year one and that balance equals the balance of previous year minus the principal that is paid, which gives us the remaining balance.
And these are the numbers for year one. We repeat the calculations for year two. We calculate the interest as the remaining balance, which we calculated here multiplied by interest rate. The principal equals the payment, which we calculated here, minus the interest. And the balance equals the balance of previous year, which is here, minus the principal which we calculated here. And this is the remaining balance.
We repeat the calculation for year three. Interest equals remaining balance of the previous year multiplied interest rates, and the principal equals the payment, which is up here, minus the interest, which we calculated here, and it gives us the principal. And remaining balance equals the balance minus the principal that we calculated here, which gives us the remaining balance at year three.
We repeat the equation for the last year. Interest equals remaining balance multiplied interest rate. Principal equals the payment minus the interest, and if we calculate everything correctly, the principal in the last year should equal the balance, the remaining balance-- the last remaining balance, and it should gives us the zero remaining balance for the last year.
So we are going to need these two rows of interest and principal portions of each payment, and let's see how we have to enter them into the table for our calculations. So the revenue, operating cost, and depreciation in working capital are the same. And the other item that we have to enter to the table as an amount that has to be deducted from the revenue as tax deduction is the principal portion of these annual payments. So this loan interest is the interest that we paid that we calculated here.
This is the row-- we entered this row, the interest row, as the amount that has-- that have to be deducted from-- deducted from revenue as tax deductions. And we calculate the taxable income. We calculate the tax. We calculate net income. We add back the depreciation working capital write-off and working capital with a negative sign. So very important point here, because we [INAUDIBLE] need to enter the principal portion of those annual payments. So the principal portion of the loan that we calculated here, we extract these and we entered them to the table.
So these are the principal of loan. Then we enter the capital cost, which was $1 million and the loan. So here, as you notice that, because we take $1 million exactly equal to the capital cost, these two cancel out, but still-- but we still keep them in a table. This is because you keep them organized, because there might be cases that your loan might be lower than the capital cost that you need.
For example, let's say you're going to take the loan of $400,000 or $600,000. So in that case, you will need the capital costs, then you will need to write the entire money record for the capital cost, and you say, OK, I got $400,000 or $600,000, a loan for that. And we calculate the rate of return and NPV. So, again, note that when we have borrowed money in our projects, we need to be very careful. The interest portion of annual payments are deductible from revenue as tax deductions, and principal portion of those annual payments should be entered in the table with a negative sign.
So, again, you still need to write the capital cost with a negative sign and the loan with a positive sign. If they are equal, they cancel out. But if they are not equal, if the loan that you are getting is lower than the capital cost that you are needing, then they won't cancel out. And so we calculate the after tax cash flow, and we calculate the rate of return as almost 90%. And you can see that how this project is leveraged after we took the loan.
Project Evaluation with Loan Using Excel Spreadsheet
PRESENTER: So there are four types of loan-- balloon payment loan, interest only loan, constant amortization loan, and constant payment loan, which is the most common one. I explained the first three types in previous videos. And in this video, I'm going to explain the constant payment loan. So let's work on this example, using Excel spreadsheet, a briefly explained example.
The life of the project is four years. The capital cost record is $1 million, annual revenue of $625,000, annual operating cost of $220,000 from year 1 to year 4. The depreciation method is MACRS 3-year half year convention, salvage zero, working capital of $100,000, income tax of 40%, and discount rate of 10%.
So the first is revenue. So revenue is $625,000 from year 1 to year 4. And then we are going to have the operating cost, with a negative sign, of -$220,000 from year 1 to year 4. Then we are going to have the depreciation from year 1 to year 4. So I extracted the rates here, and I'm just going to apply them with the negative sign-- $1 million of capital cost. Multiply these rates from year 1 to year 4.
Then we are going to have working capital write-off, write-off. So it is going to be-- working capital can be deducted from revenue as tax deductions. So this was $100,000. And then we are going to calculate the taxable income, which is a summation of each column.
Then we calculate the tax, which was 40%. So we multiply the taxable income by 40%. And we can enter, with a negative sign, then net income, which equals this plus tax with a negative sum plus taxable income. Then we add back the depreciation, with positive sign. So it is negative.
I multiply it with a negative sign, to which I get a positive sign. The other is working capital write-off. This here was with a negative sign. I have to enter it with a positive sign here-- I just use abbreviation-- then the capital cost in the working capital.
And after tax cash flow, which is going to be the summation of these numbers. And then I'm going to calculate the rate of return for this project, using the IR function. And then the NPV, which was-- I have a payment at present time, plus NPV of 10% and the other.
Now, let's assume we are going to take a loan of $1 million at present time with 8% of interest. And we want to see how it is going to affect the project. So the first thing is we have to calculate the payments, so from year 1, 2, 3, 4. The payment equals this $1 million. Multiply the factor A/P, or capital recovery factor, which is I multiply 1 plus I power 4 years, divided by 1 plus I power 4 minus 1.
So it is going to give us almost $302,000 per year. And they are equal for year 1 to year 4. Then we need to calculate the interest. The interest equals the balance multiply the interest rate. The balance for year 1 is $1 million. Multiply the interest. And the principal is the payment minus the interest. The principal equals payment minus interest. And the balance equals the balance of previous year, which was $1 million minus the principal that is paid at-- the principal portion of the payment that is paid at year 1.
For year 2, the interest equals the balance of the previous year minus multiply the interest rate, which was 8%. And the principal equals payment minus the interest rate. And the balance equals the balance of previous year minus the principal portion that is paid. So I can just apply this to the other years. And as you can see here, if we calculate everything correctly, the balance of the principal of the last year should equal exactly same as the last remaining balance.
Now, we need to draw our table. First, start with year 1, 2, 3, 4-- sorry, we start at present time-- 1, 2, 3, 4. We start with revenue, which was, starting at the year 1, $625,000. And it was from year 1 to year 4; then the operating cost, with the negative sign. Then I will add depreciation. I can extract rates from the table and write them here. So depreciation equals minus $1 million. Multiply these rates. Then we add the working capital write-off-- I just use that abbreviation-- which was minus $100,000.
And the important part here is the interest portion of these annual payments, loan annual payments, are deductible from revenue as tax deductions. So I will enter them with the negative sign. So this is the interest. Then I will calculate taxable income, which is the summation over this column, and the tax, which is 40% of this number, and net income.
Then we add back the depreciation, with positive sign, equals this amount; then the working capital write-off, which is a positive sign here. And then we have to enter the loan principal, with a negative sign, here. So this is the loan principal from year 1 to year 4. Then we enter the capital cost, with a negative sign. And then we enter the loan, with the positive sign.
And we are going to have. And then we calculate the after-tax cash flow, which is the summation of this part. Sorry, I missed the working capital in the table, working capital, with the negative $100,000, and after-tax cash flow, and rate of return, and the NPV.
Joint Venture Analysis
Joint Venture Analysis jls164Joint venture 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:
- In most cases, if a project fails, any bank loans and debt have to be repaid (depending on the loan agreement). But in a joint venture, the money doesn’t need to be repaid.
- Equity dilutes the ownership. In a joint venture, the profit will be shared between partners (based on their partnership), but the original investor can keep the entire profit, if she or he takes a loan instead of forming a joint venture.
- Debt and borrowed money may impose financial and non-financial restrictions on the investor (depending on the loan agreement).
- Depending on the performance of the project, the cost of equity may change over time, but cost of debt and loan are usually fixed.
- The interest portion of repaid money for the borrowed money and debt are deductible from tax, but the sum of money paid to the shareholders (dividend) is not.
Example 10-3
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 |
|---|---|---|---|---|---|
| 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 | ||||
| Taxable income | 35,850 | -19,750 | 128,450 | 115,450 | |
| - Income tax 40% | -14,340 | 7,900 | -51,380 | -46,180 | |
| 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 | ||||
| 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.
Minimum Rate of Return and Leverage
Minimum Rate of Return and Leverage jls164Since 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.
Weighted Average Cost of Capital (WACC)
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.
Summary and Final Tasks
Summary and Final Tasks jls164Summary
This lesson focused on leverage and borrowed money. Using examples and solving illustrative problems, we have learned:
- how to conduct a leveraged investment analysis;
- the concept and organization of a joint venture;
- how to analyze land/real estate investment with leverage; and
- the relationship between the minimum rate of return and leverage.
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.
Reminder - Complete all of the Lesson 10 tasks!
You have reached the end of Lesson 11! Double-check the to-do list on the Lesson 10 Overview page to make sure you have completed all of the activities listed there before you begin Lesson 12.