Calculating the Present Value of a Fixed Principal Loan

Unlike “normal” loans that have a fixed payment, fixed principal loans are characterized by a declining payment amount.

With normal loans, the portion of each payment applied to principal increases over time as the interest portion decreases. This occurs because the loan balance decreases with each payment. With fixed principal loans, the amount applied to principal does not change. However, because the balance declines over time, the interest due with each payment also decreases. Therefore, the fixed principal amount plus the declining interest amount results in a declining periodic payment.

As a result, finding the present value of a fixed principal loan is often tedious because the payment amounts change. Normally, you would have to enter each individual payment manually into a calculator. With the Ultimate Financial Calculator, this is not necessary. This tutorial demonstrates how to use analytical calculations to discount any cash flow.

All users should work through the more detailed first tutorial to understand the Ultimate Financial Calculator’s (UFC) basic concepts and settings.

To calculate the present value of a fixed principal loan with two interest-only payments, follow these steps:

1. Set Schedule Type to “Loan”.
   • Or click the New button to clear any previous entries.
2. Set Rounding to “Adjust last amount to reach “0” balance”.
   Click Settings, then select > Rounding Options.
3. Set 365 Days Per Year.
   Click Settings, then select > 360 / 365 Days.
4. In the header section, apply the following settings:
   1. Set Calculation Method to “Normal”.
   2. Set Initial Compounding to “Semiannually”.
   3. Enter 8.25 for Initial Interest Rate.

5. In row one of the cash flow input area, create a “Loan” series:
   1. Set the Date to June 1, 2024.
   2. Set the Amount to 800,000.00.
   3. Set # Periods to 1.
      • Note: Since the number of periods is 1, you will not be able to set a frequency. If a frequency is set, it will be cleared when you leave the row.
6. In row two, create a “Payment” series:
   1. Set the Date to December 1, 2024.
   2. Set # Periods to 2.
   3. Set Frequency to “Semiannually”.
   4. Click on the second row's Cash Flow Options and activate an “Interest-Only” series.
      • Related interest-only payment tutorial.
      • # Periods must be greater than 1 to access the Cash Flow Options link.
7. In row three, create a “Fixed Principal + Interest” Payment series.

• 1. Set the Date to December 1, 2025.
  2. Set the Amount to “Unknown”.
  3. Set # Periods to 10.
  4. Set Frequency to “Semiannually”.
  5. Click on Cash Flow Options and activate a “Fixed Principal + Interest” series.
     • # Periods must be greater than 1 to access the Cash Flow Options link.

• Before calculating, your screen will look like this:

8. Calculate the unknown. The result is $80,000.00.
   • In this case, the amount is the fixed principal value. No interest is included.
   • View the schedule to see the declining payment amounts, each including interest.

• Up until this point, we've been using the calculator to create a moderately complex fixed principal loan schedule. But if you are an investor evaluating a loan purchase, you need to know the present value of this cash flow as of your investment date. As mentioned, this is easy to calculate. Start by entering your discount rate (the rate of return you expect to earn on your investment).

9. Click Settings, then select > Analytics.
   1. Set Discount Rate to 6.5.
   2. Set As of Date to September 30, 2024.
   3. Select “Include present value (PV) on schedule...”.
   4. Click Save Changes to close.

10. Click the Schedule button.
    • As of September 30, 2024, assuming a 6.5% return, the present value is $863,159.06.

If an investor purchases the loan on September 30, 2024 for a price of $863,159.00 and holds the loan until all payments are made on time, they will earn an annual return of 6.5% on the investment. The total payments received will equal $1,047,500.00.

Back to the Ultimate Financial Calculator.