Borrowed Money (part I)

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.

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.

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.

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.