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.