Question

05. a) Alpha Itd, a large fertilizer distributor based in Dehradun is planning to use a lockbox system to speed up collections from its customers based in nearby towns. A prominent bank based in Dehradun has proposed to provide this service for an annual fee of Rs.15000 plus 10 paisa per transaction. The estimated reduction in collection is one day. If the average customer payment in this region is Rs.4800, how many customers are needed on an average, each day to make this system profitable for Alpha Ltd. Treasury bills are currently yielding 5 percent per year. Assume 360 days in a year. (4 Marks)

Answer 1

The annual fee charged by the bank is 15000 + 10 paisa per transaction The reduction in collecion day is 1 we first have to calculate the daily interest rate annual interest rate = (1+daily interest rate)^360 -1 0.05 = (1+ daily interest rate)^360-1 1+ daily interest rate = (1+0.05)^(1/360) 1.000136 daily interest rate = (1.000136-1) 0.000136 0.0136% Now, the minimum number of customer for the cost to be justifiable would be (average payment Collection period * No. of customer) - (Transaction fee* No.of customer)/dailyinterest rate - annual fee/annual interest rate = 0 (4800*1*N)-(0.10*N)/0.000136 - 15000/0.000136 = 0 (4800*1*N)-(0.10*N)/0.000136 = 300,000.00 0.000136"(4800*1*N) - (0.10*N) = 300000*0.000136 0.6528 N -0.10N = 40.8 40.8/(0.6528-0.1) 73.81 So approximately 74 customer