Example 21 - PV of Interest Only Loan

This example applies to our online demo Time Value of Money Calculator. The C-Value! program for Windows works in a similar way and has a few more features. Note, our online demo TVM calculator is limited to calculations using interest rates between 4.0% and 5.99%

Note:This topic has not been proofed and images need to be added. However, we believe that the steps are complete and accurate.

Calculating the value of an existing fixed principal + interest or interest only loan requires you to use a special series.

1. Click the [New] button to clear any previous entries.
2. Set "Rounding" to "Ignore" by either:

• clicking on the "Rounding" button on the toolbar;
• clicking on the {Compute} menu choice and select {Rounding...};

1. This example illustrates the use of the Existing Fixed Special Series.
2. For greater detail about how values are entered into C-Value!, please see "Example 1 - conventional mortgage or loan".
3. For this example, we will assume that you are employed by an investment firm which purchases debt obligations. You need to value the debt of Some Expanding Firm held by Regional Commerce Bank. The facts of the loan are as follows: The loan is a six-year, $800,000 obligation with an origination date of June 1, 2004. Semiannual interest only payments start on December 1, 2004 and continue through June 1, 2005. Thereafter the debt is to be paid off in 10 fixed principal + interest payments beginning December 1, 2005. The nominal annual market rate is 8.25%.
4. The problem is, how to calculate the value of this loan as of September 30th, 2004 assuming a discount rate of 4.875%.
5. For this example, we are assuming semiannual compounding, a normal compute method and a 365 day year.
6. Computing the value of the cash flow will require two steps to calculate the two unknowns. First we'll compute the amount of the interest only payments and produce an schedule for later use. We'll compute the discounted value in the second step.
7. Step 1 - compute the amount of the interest only payments
8. 1) Open the C-Value! Setup Window. Press either [F6] or select {Settings}{Compute Setup} from the menu.
9. A) For the "Compute Method" select the "Normal" option.
10. B) Set the "Year Length" to 365.
11. C) Click on the [OK] button to close the window.
12. 2) Set compounding to "Semiannually".
13. 3) Enter 8.25% for the "Nominal Annual Rate".
14. 4) Create a "Loan" event in row one of the cash flow input area.
15. A) Set the "Date" to June 1, 2004 (06/01/2004)
16. B) Set the "Amount" to 800,000.00
17. C) Set the "# Periods" to 1.
18. 5) Move to the second row of the cash flow input area. Select "Payment" for the "Event" type.
19. A) Set the "Date" to December 1, 2004 (12/01/2004)
20. B) Set the "# Periods" to 2. The end date will display as 06/01/2005
21. C) "Frequency" should already be set to "Semiannually".
22. D) Click in the special series column on the second row to open the Special Series dialog or press [F2]
23. E) Select the Interest Only tab.
24. F) Click on the "Activate Interest Only series..." to select it. (A check will appear in the checkbox.)
25. G) Click [OK] to close the window.
26. H) The word "Interest Only" will appear in the amount column of the second row.
27. 3) Move to the third row of the cash flow input area. Select "Payment" for the "Event" type.
28. A) Set the "Date" to December 1, 2005 (12/01/2005)
29. B) Set the "# Periods" to 10. The end date will display as 06/01/2010
30. C) "Frequency" should already be set to "Semiannually".
31. D) Press [F2] to open the special series windows.
32. E) Select the Fixed Principal + Interest tab.
33. F) Click on "Activate Fixed Principal Plus Interest series..." to activate it.
34. G) Enter "Unknown" as the "Principal Payment"
35. H) Click [OK] to close the window.
36. 4) Calculate the unknown amount. The result will be $80,000 for the principal part of the regular payment. The amount of the regular payment will change each period due to the declining principal balance which causes the amount of interest due each period to decline. Thus, a smaller and smaller interest amount is being added to a constant principal amount of 80,000.
37. 5) Click on the Amortization tab. Print a copy of the schedule which will be referenced in step 2. Note that the two interest only payments are $33,000 each.
38. Step 2 - Compute the value of the debt assuming your selected discount rate.
39. 1) Click {File}{New}. If you are asked if you want to save the change, you may answer "No".
40. 2) Open the C-Value! Setup Window. Press either [F6] or select {Settings}{Compute Setup} from the menu.
41. A) For the "Compute Method" select the "Normal" option.
42. B) Set the "Year Length" to 365.
43. C) Click on the [OK] button to close the Window.
44. 3) Set compounding to "Semiannually".
45. 4) Enter 4.875% for the "Nominal Annual Rate". This is your discount rate.
46. 5) Create a "Loan" event in row one of the cash flow input area.
47. A) Set the "Date" to September 30th, 2004 (09/30/2004)
48. B) Set the "Amount" to "Unknown".
49. C) Set the "# Periods" to 1.
50. 6) Move to the second row of the cash flow input area. Select "Payment" for the "Event" type.
51. A) Set the "Date" to December 1, 2004 (12/01/2004)
52. B) Set the "# Periods" to 2.
53. C) "Frequency" should already be set to "Semiannually". The end date will display as 06/01/2005
54. D) Set the "Amount" to the amount of the interest only payment using the schedule calculated above. $33,000.00
55. 7) Move to the third row of the cash flow input area. Select "Payment" for the "Event" type.
56. A) Set the "Date" to December 1, 2005 (12/01/2005)
57. B) Set the "# Periods" to 10.
58. C) "Frequency" should already be set to "Semiannually". The end date will display as 06/01/2010
59. D) Press [F2] to open the special series windows.
60. E) Select the "Existing Fixed" tab.
61. F) Click on "Activate Existing Fixed series..." to activate it.
62. G) Enter $800,000 in the "Note balance" field. (Since only interest has been paid on the loan as of December 1, the note balance is equal to the original amount of the loan.)
63. H) Enter 8.25% for the "Rate for the note".
64. I) Enter $80,000 for the "Principal Payment".
65. J) Click [OK] to close the window.
66. 8) Calculate the unknown value. The result or fair value of the loan is $904,627.66 at your selected discount rate of 4.875%.
67. You may wonder why the value is greater than the amount of the loan. This actually makes perfect sense. The loan has a cash flow based on an 8.25% nominal annual rate. The discount rate is only 4.875%. Therefore, since the return is greater than your investment requirements, you should be willing to pay more than the balance of the outstanding debt. Had your discount rate been say 10.0%, then you would have needed to value the loan at less then the balance of the debt.
68. NOTE: You could also value a fixed principal + interest loan by entering each cash flow amount. But since the cash flow amounts are changing it can become somewhat tedious to enter say forty-eight payments or even ten payments. Using the Existing Fixed Special Series saves you this tedium.

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