Calculating the Present Value of a Fixed Principal Loan

Also applies to interest-only loans.

A Step-by-Step Tutorial
Tutorial 21

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

With normal loans, the amount of each payment applied to principal increases as the interest decreases due to the balance decreasing. With fixed principal loans, the amount applied to principal does not vary (fixed principal amount). But because the balance is declining as payments are made, the interest due with each payment is declining. Thus, the fixed principal plus the declining interest amount results in a declining periodic payment.

Therefore, finding the present value of a fixed principal loan is normally tedious, given the ever changing payment amount. What one would usually have to do is enter each payment amount into a calculator. With the Ultimate Financial Calculator, entering individual payments is not necessary. This tutorial illustrates how to use the 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" by clicking on the {Settings} {Rounding Options}
  3. Set to "365 Days Per Year" by clicking on the {Settings} {360 / 365 Days}
  4. In the header section, make the following settings:
    1. For "Calculate Method" select "Normal".
    2. Set "Initial Compounding" to "Semiannually".
    3. Enter 8.25 for the "Initial Interest Rate".
  1. 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 the "# 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
  2. In row two, create a "Payment" series
    1. Set the "Date" to "December 1, 2024"
    2. Set the "# Periods" to 2
    3. Set the "Frequency" to "Semiannually"
    4. Click on the second row's "Cash Flow Options" and activate an "Interest-Only" series
  3. In row three, create a "Fixed Principal + Interest" "Payment" series
Activate a fixed principal series
Fig. 1 - Activate a fixed principal series
    1. Set the "Date" to "December 1, 2025"
    2. Set the "Amount" to "Unknown"
    3. Set the "# Periods" to 10
    4. Set the "Frequency" to "Semiannually"
    5. Click on "Cash Flow Options" and activate a "Fixed Principal + Interest" series
      • "# Periods" must be greater than "1" to see the "Cash Flow Options" link
  • Before calculating, your screen will look like this:
Interest-only followed by fixed principal setup
Fig. 2 - Discounting an interest-only followed by fixed principal loan - initial setup
  1. Calculate the unknown. The result is $80,000
    • In this case, the amount is the fixed principal amount. No interest is included.
    • View the schedule to see the declining payment with interest
Interest-only followed by fixed principal result
Fig. 3 - Calculated fixed principal amount
  • 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 investing in loans you need to know the present value of this cash flow as of your investment date. As mentioned, it is very easy. We start by entering your discount rate (the rate of return you want to earn on your investments).
Fig. 4 - Analytics
  1. Select {Settings} {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
Present value option
Fig. 5 - Present value options
  1. Click on [Schedule]
    • As of September 30, 2024 assuming 6.5% return, the present value is $863,159.06
Fixed principal discount schedule
Fig. 6 - Fixed principal amortization table with present value calculation at user selected discount rate

If an investor purchases the loan on September 30, 2024 for a price of $863,159 and holds the loan until the last payment is paid and the payments are paid on time, they will earn 6.5% per annum on the investment amount. The payments they receive will total $1,047,500.