I'm Larry Walter, this is principlesofaccounting.com Chapter 13.
And in this module, we would continue our consideration of long-term notes and
present value concepts.
Specifically looking at level payment loans.
This is very much an extension of the previous video,
where we talked about present value and future value considerations.
And so what I ask you to think about now is a typical loan that involves
level periodic payments that cover both principal and interest, or
the nature of that.
That is a stream of payments.
Each payment is the same over the life of the loan and
at the end of the loan the loan is paid off.
So we have an annuity and in point of fact the present
value of those payments is equal to the loan amount.
And so we can look at a formula rather than saying the present
value equal payments times an annuity present value factor.
We can say that the loan amount.
Are the payments times the annuity present value factor.
And we're now beginning to understand how we can calculate loan payments.
For example, if we borrow $100,000 on a 5-year loan with five annual payments.
And the interest rate is 6%, and we say to ourself, well what should our payment
be each year so at the end of the 5th year this thing is paid off?
It's a $100,000 loan equals the amount
of the payment times the present value of that stream of payments.
And I went to the book and gathered the present value factor, 4.212.
That's the present value of a 5-year annuity using a 6% interest rate.
You might want to stop the video for a moment and verify that.
But in any event, that's what we have.
And when we solve for
the unknown payment, that is, we'll find that the payment is 23,739.
23,739 times 4.21 equals a $100,000 amount.
So, very simply, we've calculated that mystical
amount of how much is the payment on this loan.
So here I have the loan amortization table.
I start out at the beginning of year one with a $100,000 loan.
It's a 6% loan so for the first year $6,000 of interest accumulates.
When I make my $23,739 payment that we calculated a moment ago.
The first $6,000 goes toward interest and
the other 17,739 serves as reduction of principal.
So that the $100,000 principal is reduced to $82,260.
Which is the beginning balance for the next year.
And that 82,260 earns interest at 6% or $4,935 for the second year.
As compared to the total payment gives me a principal reduction in the second year
of 18,804.
And leaving me a remaining balance of 63,000.
And so it would go for each of the next years.
Notice that the last payment in the last year will satisfy the interest of 1343 and
22,395 principal reduction leaving us a zero balance due at maturity.
So it's pretty nifty mathematics here.
But when we reduce this to journal entries, they become fairly simple.
We borrowed $100,000, we debit cash, and we credit notes payable.
The first year we make a $23,000 payment, 6000 being applied to interest expense,
and the difference being applied to reduce the note.
The next year we've got less interest.
Of the $23,000 payment, only 4900 is interest and
the difference is principle reduction.
And this process would continue each year.
And I'll just jump to the last year here and
note that the last payment of $23,000 satisfies the accrued interest of 1,343.
And reduces the balance by the 22,395, which wipes it out, says we're done and
it's paid off.
So let's close with a few additional comments.
And thinking about annuities, recognize that some scenarios may involve
beginning of period payments others may involve end of period payments.
In the supplements in the textbook, there are alternative present value and
future value tables reflecting these alternative timing patterns for payments.
And more said about this in Chapter 24,
for now we won't dwell on that any further.
But also consider that some payments may occur on other an annual basis,
we might have monthly or quarterly payments.
So if for example, we have a $10,000, 8% per annum or
annual interest rate loan, involving quarterly payments over two years.
What we really have is an innuity that involves
eight periods that is eight quarters.
Four quarters per year for two years, so we got eight periods, and
the interest rate per period is really 2% one-fourth of the annual amount.
And so, the present value factor would be 7.325.
That's eight periods at 2% per period.
So we can modify our calculations based on the number of periods
in the interest rate per period, it doesn't have to be tied to annual amounts.