Let's illustrate how the calculation of the present value of an annuity is used in recording an accounting transaction.
Exercise #11. On December 31, 2005, FreshStart provides a service for its customer DownCo in exchange for a promissory note requiring five annual payments of $1,000 each. The payments are to occur on December 31 of each year beginning on December 31, 2006. The note does not specify any interest, and there is no market for the note. The value of the service performed by FreshStart is very unique and no market value is available. Based on the credit worthiness of DownCo and the length of the note, it is estimated that DownCo would have to pay 10% interest if it borrowed a similar amount from a bank. As FreshStart's accountant, how would you record the transaction on December 31, 2005?
Both the
cost principle and the
revenue recognition principle prohibit you from recording the $5,000 as December 2005 revenue, since a portion of the $5,000 is interest that will be earned in years 2006-10. Since there is no fair market value (or cash equivalent amount) known for the note or for the service provided, you realize that the present value (or cash equivalent amount) of the note must be computed.
Your first step is to prepare a time line that displays the relevant facts:
| PVOA= |
?? |
|
|
|
|
|
|
$1,000 |
$1,000 |
$1,000 |
$1,000 |
$1,000 |
|
|
|
|
|
|
|
|
|
← 1 year → |
← 1 year → |
← 1 year → |
← 1 year → |
← 1 year → |
|
| 12/31/05 |
12/31/06 |
12/31/07 |
12/31/08 |
12/31/09 |
12/31/10 |
|
| 0 |
1 |
2 |
3 |
4 |
5 |
|
|
| n = 5 years; i = 10% per year |
Calculation of Exercise #11 using the PVOA Table
Using the information on the time line, you insert the known figures into the PVOA equation:
PVOA = PMT times [ PVOA factor for n = 5; i = 10% ]
PVOA = $1,000 times [ 3.791 ] ← PVOA factor from PVOA Table
PVOA = $3,791
This calculation tells you that receiving $1,000 at the end of each of the next 5 years is the equivalent of $3,791 at the present time if the time value of money is 10% per year. The difference between $3,791 and the future amounts aggregating $5,000 (5 payments at $1,000 each) is $1,209. This $1,209 is
interest that will be earned by FreshStart over the next five years. Expressed another way, FreshStart earned only $3,791 in
service revenues from DownCo in December 31, 2005.
A proof of this calculation is shown below:
Loan Amortization Schedule
(For $3,791 at 10% per year with 5 annual payments.)
| Date |
Total Payment |
Interest Payment* |
Principal Payment** |
Principal Balance |
| Dec. 31, 2005 |
|
|
|
$ 3,791.00 |
| Dec. 31, 2006 |
$ 1,000.00 |
$ 379.10 |
$ 620.90 |
3,170.10 |
| Dec. 31, 2007 |
1,000.00 |
317.01 |
682.99 |
2,487.11 |
| Dec. 31, 2008 |
1,000.00 |
248.71 |
751.29 |
1,735.82 |
| Dec. 31, 2009 |
1,000.00 |
173.58 |
826.42 |
909.40 |
| Dec. 31, 2010 |
1,000.00 |
90.60 (R) |
909.40 |
0.00 |
|
|
$ 1,209.00 |
|
|
* Interest payment equals 10% of the previous principal balance.
** Principal payment equals $1,000 minus interest payment.
(R) Rounded
FreshStart's journal entry to record this transaction on December 31, 2005 is:
| Date | Account Name |
Debit | Credit |
The $1,209 in
Discount on Notes Receivable is to be
amortized from this balance sheet account to the income statement account
Interest Revenues over the life of the note.
If the discount and resulting interest revenue is
immaterial in light of FreshStart's income statement, the discount can be amortized by using the straight-line method. Under the straight-line method, $241.80 ($1,209 divided by 5 years) will be recorded in each of the years 2006–2010, as shown in the following entry:
If the discount and resulting interest revenue is material in light of FreshStart's income statement, generally accepted accounting principles requires that the discount be amortized by the
effective interest rate method. The amounts for the effective interest rate method appear in the Interest Payment column of
$3,791 amortization schedule and are used in the following journal entries:
| Date | Account Name |
Debit | Credit |
After posting these journal entries, the book value (or carrying value) of this note receivable can be determined from the balances in the following T-accounts:
| Notes Receivable |
|
Discount on Notes Receivable |
| 12–31–05 entry |
5,000 |
|
|
|
|
|
1,209 |
12–31–05 entry |
|
|
1,000 |
12–31–06 entry |
|
12–31–06 entry |
379 |
|
|
| bal. 12–31–06 |
4,000 |
|
|
|
|
|
830 |
bal. 12–31–06 |
|
|
1,000 |
12–31–07 entry |
|
12–31–07 entry |
317 |
|
|
| bal. 12–31–07 |
3,000 |
|
|
|
|
|
513 |
bal. 12–31–07 |
|
|
1,000 |
12–31–08 entry |
|
12–31–08 entry |
249 |
|
|
| bal. 12–31–08 |
2,000 |
|
|
|
|
|
264 |
bal. 12–31–08 |
|
|
1,000 |
12–31–09 entry |
|
12–31–09 entry |
174 |
|
|
| bal. 12–31–09 |
1,000 |
|
|
|
|
|
90 |
bal. 12–31–09 |
|
|
1,000 |
12–31–10 entry |
|
12–31–10 entry |
90 |
|
|
| bal. 12–31–10 |
–0– |
|
|
|
|
|
–0– |
bal. 12–31–10 |
The book value (or carrying value) of the note receivable is calculated as shown here:
| Date |
Notes Receivable |
Less:
Discount on Notes Receivable |
Book Value of Notes Receivable |
| 12–31–05 |
$ 5,000 |
$ 1,209 |
$ 3,791 |
| 12–31–06 |
4,000 |
830 |
3,170 |
| 12–31–07 |
3,000 |
513 |
2,487 |
| 12–31–08 |
2,000 |
264 |
1,736 |
| 12–31–09 |
1,000 |
90 |
910 |
| 12–31–10 |
– |
– |
– |
Note that the
book value amounts in the above exhibit are the same as the
principal balance amounts in
$3,791 amortization schedule. If the note receivable was written for $3,791 with a stated interest of 10% and annual payments of $1,000, the journal entries would have been:
| Date | Account Name |
Debit | Credit |
Because the material covered here is considered an introduction to the topic of present value of an ordinary annuity, there are many complexities not presented. You should always consult with an accounting professional for assistance with your own specific circumstances.
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