LOAN REPAYMENT METHODS

        When money is lent, is is done in two ways.

Equal Interest Method

1. The principal is expected to be repaid at the end of the loam term. Regular equal interest payments are done at a specified interest. This done in loans like some collateralised loans (eg: gold loan), company loans like bonds etc. Loans can be made with or without a discount/premium.

WITHOUT DISCOUNT/PREMIUM

for eg: suppose a loan is given for an amount of $50000, for 5 yrs with an interest of 10%

jan 1 19x1

notes receivable          50000

cash                                                        50000

dec 31

cash                                10000

interest receivable                             10000

dec 31 19x5

cash                                10000

interest receivable                             10000

cash                                50000

notes receivable                                 50000

WITH DISCOUNT

Consider a bond issued at a rated interest of 4%. Since the market rate prevailing is 5%, the 1% difference has to be compensated to the lender by issuing the bond at a discount in order to compensate the 1% difference. This is illustrated in the following example..

The bond of $100000 par is issued at a rated interest of 4%, with a maturity period of 8 periods and the market rate is 5%. The interest payment of $4000 has to be paid to the lender, because that is what is mentioned in the bond. But in order to compensate the 1%, the bond is issued at a discount

We find the present value of the principal by finding the present value of the principal and the payments at the actual interest rate which is the market rate ie at 5% for 8 periods..

Present value of $100000 @ 5% int for 8 years+ the present value of all the $4000 payments (8 payments)

= $93552.

This means that when we finally pay the $100000 and the 8 payments of $4000  after 8 years has only a real value for the lender of $93552. But he needs to get his $100000 at the end of the period. The interest payment of $4000 is only to maintain the value of his $10000 at the end of the period. In order to compensate for the deficit of $6448, the lender is allowed to lend only $93552 in the beginning and is assured to be paid with $100000 at the end of the term.

So at the date of receipt of cash, the entry is

cash                                93552

discount                            6448

bond payable                                        100000

At this point the amount liable to the lender is only $93552. (whatever he has paid if there is no prepayment charge)

Now when the first interest which has to be paid in cash according to the bond conditions, payed at 4% after 1 year, the entry is

interest expense              4000

cash                                                        4000

But we have to pay 5% ie at the market rate of $93552 ( this was the actual amount liable at the beginning of the year ). This will amount to $4678. But since $4000 has already been paid, the amount to be paid is only $678. This $678 is added to the amount to be paid ie $93552 instead of paying in cash and the actual amount to be paid at the end of the period is calculated as $ 94230.  The entry is

interest expense               $678

discount                                                  $678

Now the amount payable at the end of the year to the lender is increased to $100000-$5770=$94230. The balance of the various accounts at the end of the year is

Bond payable                                 $100000

minus discount                                ( $5770 )

Net liability in the balance sheet       $94230

At this point if the loan is closed, then the cash given is only $94230 ( if there is no loan pre payment charge)

Bond payable                   $100000

discount                                                  $5770

cash                                                       $94230

The complete table of payments is given below

Interest Period	Interest Paid (4% of Par)	Interest Expense (5% of Book Value)	Amortisation	Discount Balance	Book Value
Issue date	$4000	-------------------	-------------------	6448	93552
1	4000	4678	678	5770	94230
2	4000	4712	712	5058	94942
3	4000	4747	747	4311	95689
4	4000	4784	784	3527	96473
5	4000	4824	824	2703	97297
6	4000	4865	865	1838	98162
7	4000	4908	908	930	99070
8	4000	4930	930	0	100000

                  

Here the discount is also AMORTIZED over the period.

WITH PREMIUM

If bond of $100000 is issued @4% for 8 years and the market rate is only 3%, then we are over compensating the lender by 1%. In order to compensate for this extra interest payment to the lender, we issue the bonds at the premium.

By applying the same logic in a discount situation, the present value of $100000 and and $4000 interest at the actual rate of 5%= $106980. This additional $6980 is a premium we demand from the lender to compensate for the additional 1% interest we give him.

cash                             106980

premium                                              6980

bond payable                                   100000

At this point the amount liable to the lender is $106980 ( if there is no prepayment charge)

Now when the first interest which has to be paid in cash according to the bond conditions, payed at 4% after 1 year, the entry is

interest expense              4000

cash                                                        4000

But we have to pay only 3% ie at the market rate of $106980 ( this was the actual amount liable at the beginning of the year ). This will amount to $3209. But since $4000 has already been paid, the amount to be retrieved bakc is $791. This $791 is subtracted to the amount to be paid ie $106980, instead of paying in cash and the actual amount to be paid at the end of the period is calculated as $ 106189.  The entry is

premium               $791

interest expense                                                  $791

Now the amount payable at the end of the year to the lender is decreased to $100000+$6189=$106189. The balance of the various accounts at the end of the year is

Bond payable                                 $100000

plus premium                                    $6189

Net liability in the balance sheet       $106189

At this point if the loan is closed, then the cash given is only $106189 ( if there is no loan pre payment charge)

Bond payable                   $100000

premium                                $6189

cash                                                       $106189

The complete table of payments is given below

Interest Period	Interest Paid (4% of Par)	Interest Expense (5% of Book Value)	Amortisation	Discount Balance	Book Value
Issue date	$4000	-------------------	-------------------	6980	106980
1	4000	$3209	791	6189	106189
2	4000	3186	814	5375	105375
3	4000	3161	839	4536	104536
4	4000	3136	864	3672	103672
5	4000	3110	890	2782	102782
6	4000	3083	917	1865	101865
7	4000	3056	944	921	100921
8	4000	3079	921	0	100000

Here the premium is amortised over the period.

Equated Periodic Installments or Diminishing Interest Method.

WITHOUT DISCOUNT

2. The principal is expected to be received in installments along with the interest. This is normally done in loans like personal loans, vehicle and home loans etc

eg:  a loan is made for an amount of  $25000 for 3 years, the interest is 10% and the principal and the interest is expected to be paid in equated yearly installments with first installment to be paid initially.

This is an annuity due situation. To find the annuity payments, we divide the principal $25000 by the annuity due for $1.

25000/2.73554= 9139

for loan

notes receivable          25000

cash                                                          25000

for the first payment received at the beginning of the first year,

cash                                   9139

notes receivable                                          9139

by the end of the year, an interest is accrued on the remaining notes receivable, which is recorded as an interest revenue as

notes receivable                1586    

Interest revenue                                          1586

This process is repeated every year until the note is completely received. The interest revenue account gets accumulated with all the interest revenues of each year.

The full table of transactions in each accounts is given below

Date	Payment	Interest	Change in Receivable	Balance of Receivable
Yr 1 Beginning	-----------------------	----------------------	----------------------	$25000
Yr 1 Beginning	$9138.96	----------------------	$(9138.96)	15861.04
Yr 1 end	-----------------------	$1586.10	1586.1	17447.14
Yr 2 beginning	9138.96	------------------------	(9138.96)	8308.18
Yr 2 end	-----------------------	830.82	830.82	9139.00
Yr 3 beginning	9138.96	-----------------------	(9138.96)	-0-(rounded)

Here a few points may be noted

1. In the Equal Interest Method, the interest payments are all equal in amount and the principal outstanding always stands the same.

2. In the Equated Periodic Installment method, the payment amount always is the same every period.

3. The component which goes to the principal always increases when the payments progress, while the interest component always decreases. This is evident from the table of payments in the example.

WITH DISCOUNT

A bond like discount is never given in cases of equated periodic installments. This is because, only bonds are issued at a discount or premium to the par value, in order to compensate or get compensated for the difference in interest rate from the market rate.

There are situations where the loan incurred will be with a discount in a equated periodic installment situation.

For example

Suppose a machine is bought from a dealer for an amount of $10000, and the dealer agrees to get paid in 5 equal installments, then a discount situation arises. On the face of it, this is a transaction in which the dealer does not charge interest on the delayed payments in installment and we might be surprised why he forfeits a portion of his profits in the decaying value of his payment. But he should have more than made up for it in marking up the price of the machine at the time of sale.

In order to estimate how much he might have possibly marked up in order to make up for the apparently forfeited interest, we find the present value of the payments with the imputed rate.

If the rate we use is 10%, present value of $2000 for 5 periods is $7582

Now we can see that there is a $2418 loss for the dealer in interest had he not marked up the price of the machine by the same amount. So we make belief that has has done so and believe that he compensates the loss in the interest by amortizing the discount as seen below

The entry when the machine is delivered is

machine                   7582
discount                   2418
notes payable                           10000

At this point if the machine is returned the dealer will have to give only $7582 at the maximum

At the end of the year, for the installment payment

notes payable           2000
cash                                          2000

At the end of the year to compensate the dealer, we add the interest onto the amount we owe him ($7582) which is a non cash payment.

interest exp                 758
discount                                      758

Now the amount we owe him increases to   $8430. The amortization table is given below

Date	Payment	Change in net payable (payable-discount)	Balance of net payable	Interest on the net payable in one year	Change in net Payable (payable-discount)	Balance of net payable
Yr 1 Beginning	-------------	-------------	-------------	--------------	$(2418)	$7582
Yr 1 end	$2000	$(2000)	$5582	$758.2	$758.2	6340.2
Yr 2 end	2000	(2000)	4340.2	634.02	634.02	4974.2
Yr 3 end	2000	(2000)	2974.2	497.4	497.4	3471.6
Yr 4 end	2000	(2000)	1471.6	347.2	347.2	1818.8
Yr 5 end	2000	(2000)	(182)	182	182	-0-