When the goods are sold on hire purchase, the price so charged by the vendor is always higher than the cash price. The excess price i.e., the difference between the hire purchase price and the cash price, includes the interest charges and the compensation for risk. However, for accounting purposes, the difference between the two prices is treated as the payment for interest. Thus, the hire purchase price includes:

i) the cash price, which is a capital expenditure for purchase of an asset, and

ii) the interest, which is an item of revenue nature. Since the cash price is of capital nature and the interest payment is of revenue nature, both will be treated in a different manner in the books of account. It is, therefore, necessary to separate the hire purchase price into cash price and interest. However, it may be noted that the Cash Down Payment made immediately after signing the agreement will not include the element of interest. Another point to be kept in mind is that the interest element in each instalment is not same. It keeps on reducing with every instalment. This is so because the interest is charged on the balance of the principal amount due and not on the full amount. For proper allocation, therefore, we must know the cash price, the hire purchase price and the amount of interest.

**Ascertainment of Interest**

While calculating interest, we may be faced with any of the following two situations:

a) When rate of interest, total cash price and instalments are given

b) When total cash price and instalments are given but the rate of interest is not given.

In both the above mentioned cases, the interest has to be calculated. Let us now take them one by one.

**a) When Rate of Interest, Total Cash Price and Instalments are given**

In this situation, before calculating the element of interest included in each instalment, it will be helpful to ascertain the total amount of interest involved. This will be ascertained by subtracting the Total Cash Price from the hire purchase price. Then the following steps should be followed for calculating the amount of interest on each instalment.

i) Calculate the outstanding cash price at the time of first instalment by subtracting down payment from the total cash price.

ii) Calculate interest on the first instalment. This is to be calculated on the outstanding cash price at the time of first instalment by applying the given rate of interest. In this connection, you should keep in view the mode of instalments i.e., whether the instalment is annual, half-yearly or quarterly. Usually, in case of purchases for heavy equipment,the instalment is annual.

iii) Calculate the amount of cash price included in the first instalment by subtracting the amount of interest as calculated in step (ii) from the amount of the first instalment.

iv) Calculate the outstanding cash price at the time of second instalment by subtracting the amount of cash price of the first instalment from the outstanding cash price at the time of first instalment i.e., (i) —(iii).

v) Calculate, interest on the second instalment by applying the rate of interest to the outstanding cash price at the time of second instalment.

The amount of the subsequent instalments can be worked out in the same manner i.e., by first calculating the outstanding cash price at the time of the instalment due and then applying the rate of interest to this amount. However, the amount of interest on the last instalment is worked out differently. This can be done by simply subtracting the outstanding cash price at the time of last instalment from the amount of the last instalment. Alternatively, you can work it out by subtracting the sum of interests of all previous instalments from the total amount of interest included in the hire purchase price. The amount of interest so calculated can also be verified by applying the rate of interest to the outstanding cash price at the time of last instalment. Of course, there may be a small difference due to the fact that the hire purchase price is not fixed by inclusion of the exact amount of interest. It is usually fixed as a round figure. However, if the difference happens to be a large amount, you should check all calculations of interest and outstanding cash price at the time of each instalment.

**b) When Total Cash Price and Instalments are given, but rate of interest is not given:**

When the total cash price, down payment and the amount of each instalment is given, but the rate of interest is not given, the interest will be calculated by procedure mentioned below.

i) Calculate the total interest by subtracting the total cash price from the total hire purchase price

ii) Calculate the amounts of hire purchase outstanding at the beginning of each year after subtracting the down payment

iii) Find out the ratio of outstanding amounts calculated in step (ii). If the amount of each instalment is equal, the ascertainment of ratio is simple.

For example, if there are four instalments of equal amounts, the ratio will be 4 : 3 : 2 : 1 and if there are three instalments of equal amounts, it will be 3 : 2 :1.

iv) Apply this ratio to the total interest and calculate the interest on each instalment.

**Ascertainment of Total Cash Price**

Sometimes, the total cash price is not given. In such a situation, we cannot proceed with the accounting for hire purchase transaction because in the books of the buyer, the amount to be capitalised cannot be more than the cash price. The different methods of calculation of cash price are as below:

i) Without the help of annuity table

ii) With the help of annuity table

**Let us now discuss both the methods**

**i) Without the Help of Annuity Table**

Under this method, interest is calculated starting with the last instalment. Suppose there are three instalments, the interest will be calculated first on the third instalment, then on the second and lastly on the first instalment. No interest is calculated on down payment as it doesnot involve any element of interest.

You know that the interest is to be calculated on the outstanding amount of cash price. But since it is not known, it will have to be calculated with the help of total amount due on hire purchase price. For this purpose, we will have to use the following formula for calculating first the interest involved in each instalment and then subtract this amount of interest from the total amount due, so as to work out the outstanding amount of cash price.

**Interest =Total amount due at the time of instalment X rate of interest/100 + rate of interest**

Let us now see what steps are followed for the calculation of Cash Price due at the time of each instalment assuming there are three yearly instalments.

a) Calculate the interest on the instalment of the third year, deduct interest from this instalment. The resultant figure is the outstanding cash price at the time of third (last) instalment.

b) Add the cash price calculated under (a) above to the instalment amount of the second year. Calculate the interest on the sum so obtained and subtract it from the total amount due at the end of the second year to get the outstanding cash price at the time of second instalment.

c) Add the cash price calculated under (b) above to the instalment amount of the first year and calculate the interest on the sum so obtained. Deduct this amount of interest from the total amount due at the end of the first year. The resultant figure is the cash price due at the time of the first instalment.

d) Add the cash price calculated under (c) above to the down payment, if any. The sum so obtained will be the total cash price.

**ii) With the Help of an Annuity Table **

If the annuity table is available, calculation of interest involved in each instalment is simplified. In the annuity table, the rate of interest is given in the rows and the years in the columns. With reference to the table, the present value of each instalment can be calculated. The sum of these present values as calculated, if added to the cash down payment gives us the cash price. The procedure is as follows:

a) See the given rate of interest in the row and the year in the column and find out the corresponding figure in the table.

b) This figure is the present value of Re. 1

c) Multiply the present value of Re. 1 with the amount of the instalment.

d) The resulting figure is the present value of the instalment. This is nothing but the amount of cash price included in the instalment.

e) Calculate the present values of all the instalments in same manner.

f) Add the present values of all the instalments to the down payment if any. The resultant figure will be the total cash price.