DISCOUNTING AND FACTORING TECHNIQUES

DISCOUNT Discount is defined as the reduction made from the amount of a bill in lieu of its immediate cash payment or alternatively, in lieu of bulk purchase by a trader. Discount enjoyed by a person paying cash against his purchases is termed as cash discount.

Definitions The Present Worth or Present Value of a sum of money, due at the end of a given period is that sum which, with its interest for the given time at the given rate per cent, amount to the sum due. Some times the Sum Due (S.D.) is also called Amount or Amount Due.

The True Discount is the difference between the sum due (or amount) and its present worth (P.W.) i.e., true discount is the interest on the present worth. It is also called Theoretical Discount (T.D.). We take P.W. as principal; T.D. as interest on P.W. and sum due as Amount. In other words, discount is always on the amount and interest on the principal.

In case of simple interest we can make the use of the following formulae i.e. P.W. = Sum x R x T And 100+ (R x T) T.D. = Sum x R x T 100+ (R x T)

If the interest is compounded P.W. = Sum (1+ r/100 And T.D. = S.D.-P.W. = Sum- Sum (1+r/100

To calculate interest we can use the following formulae : (i) For simple interest S.I.= P x r x t 100 (ii) For compound interest C.I. = P(1= r/100 – P Where P is principal; r the rate of interest and t is the time.

QUESTIONS: 1. The TD on the bill for Rs. 540 is Rs.90. Find the Banker’s Discount and Banker’s Gain. Solution- Sum Due (S.D.) = Rs. 540 TD = Rs.90 PW = = Rs. 450 Interest on Rs. 450 = Rs. 90 Therefore, interest on Re. 1= 90/450 Interest on Rs. 540= 90/450 x 540 = Rs. 108 BD= Rs.108 BG= BD-TD= = Rs.18

2. A bill for Rs at 90 days sight was presented for acceptance on 6 January 2004 and discounted on 16 March 2004.How much was received for it, if the rate of discount being 6% per annum. Solution- Bill value = Rs Time= 90 days Rate= 6% Drawn date= 6 January 2004 Time= 90 days Nominal date= 6 April 2004 Nominal due date= 9 April 2004 (3 grace days) Discounted date= 16 March 2004

Time= between discounted date and nominal due date Days, March = 16 April = 8 = 24 T = 24/365 years BD= x 24/365 x 1/100 x 6 = 432/5 = Rs Money paid by bank = = Rs

DISCOUNTING THE BILL OF EXCHANGE Bill of exchange: Bill of exchange is a written document to pay the required amount at the end of certain period of time. There are three parties involved in a bill of exchange. 1.The Drawer who rights Bill. 2.The Drawee who pays the Bill. 3.The payee who receives the Money. The bill of exchange is prepared by the drawer and sent to drawee for acceptance. The drawee then gives his consent by writing ‘accepted'. After this it become legally valid and is called acceptance. The unaccepted bill has no value.

There are two types of bills of exchange. (i) Bill of exchange after due date is known as the bill in which date of maturity is counted from the date of drawing the bill (ii) Bill of exchange after sight is the bill in which date of maturity is counted from the date of acceptance. Banker’s Discount: If the money is withdrawn from the bank before the due date, then the Bank deduct some amount from the face value of the bill. It is called Bank’s discount. Thus the money deducted by the banker is called Banker’s discount and it is the interest on the face value of the bill.

When the drawer of the bill needs money before due date, he can go to his banker or bill-broker to get the cash. It is known as discounting of bill. While discounting the bill, the bank or the bill- broker does not pay the face value of the bill to the drawer (holder) of the bill. He deducts the some amount from the face value of the bill and pays some amount lesser then the face value. The amount, which the banker/bill-broker deducts from the face value is called Banker’s Discount (or commercial discount or Mercantile discount). The net amount received by the holder (or drawer) of the bill is called discounted value (D.V.) or cash value.

Bankers Discount (B.D) Vs. True Discount (T.D.) While discounting a bill, the banker or bill-broker should deduct the interest on the present worth of the bill (P.W.) i.e. True Discount, from value (amount) of the Bill. This helps the holder to receive the True present worth of the bill at the time of discounting from the banker/bill-broker. But in practice, the banker/broker does not pay this amount to the holder or drawer of bill. The reason is by this, the banker or broker gains nothing except actual interest on present worth. Hence they (Banker/broker) deduct the interest on the bill value for the discounted period, so that they get something extra over and above the actual interest on present worth. Therefore, the amount of banker’s discount is always higher than the true discount, if the bill value and discounted period remain same.

FORMULAE 1.Bill value (B.V.)= face value of bill= sum 2.Banker’s discount (B.D.)= simple interest on B.V.= BV x R x T Discounted period (D.P.)= legal due date- date of discounting 4.Discounted value (D.V.)= R.V.- B.D. 5.True discount (T.D.)= simple interest on P.W.= P.W. x R x T 100

6. Banker’s gain (BG) = BD-TD = Interest on TD= TD x R x T Bill value (sum)= SD x TD = BD x TD = DV+TD BD-TD BG =TD x (100+RT) = PV(100+RT) RT True discount (T.D.)= PW x R x T Present worth/value (PW)= BV-TD= BV I+RT

QUESTIONS: 1.Calculate TD, BD and BG on a bill of Rs. 800 due 3 months, at 8% per annum. Solution- Amt. of bill= Rs. 800; Time= 3 months; Rate= 8% BD = 800 x 3 x 8 = Rs x 100 TD = 800 x 3/12 x 8 = 800 x 3 x 8 = Rs (8 x 3/12) 12 x 104 BG = = Re.0.32

2. Vinod has a two months bill for Rs which he discounts at 6% per annum. At what rate should he earn the interest so that he may not suffer the loss? Solution- BD = Int. on Rs for 2 months at 6% p.a. = 1000 x 2 x 6 = Rs x 12 After discounting the bill, the merchant gets Rs Rs.10 = Rs. 990 Now the merchant must earn Rs. 10on 990 in 2 months so that he may not suffer loss. Therefore, Rate = 10 x 100 = 6.06% 900 x 2/12

FACTORING TECHNIQUES Business is manifested with a variety of problems and an astute businessman has to encounter them all. He marches ahead inch, starting from the purchase of raw-material, arrangement of the finances and giving a marketable shape to the products and finally monopolizing the gains out of it. The principle of discounting, which refers to the difference between the present worth and the final amount which is paid after a certain period of time, serves as a spinal cord to the total business activity that the business house wants to undertake. The factoring techniques, to reduce the total into tiny parts, serve as a useful tool to segregate the share that should go to different factors of production.

Not only this, the proportional increase or decrease of the share can also be determine as per the requirements or challenges that the business enterprises deem fit from time to time, with the help of factorization. So factoring techniques help to promote the cause of easy study and comprehension of the problem of discounting.

(a+b = + + 2ab (a-b = + - 2ab (a+b) (a-b)= -

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