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problem 10: cross drugs currently fills mail orders from all over the u.s., and receipts come in to a head office in little rock, arkansas. the firm's average accounts receivable (a/r) is $2.5 million and is financed by a bank loan with 11 percent annual interest. cross is considering a regional lockbox system to speed up collections which it believes will reduce a/r by 20 percent. the annual cost of the system is $15,000. what is the estimated net annual savings to the firm from implementing the lockbox system? (hint: the company borrows cash to cover its a/r until it collects payment for the sale. but, with a continuing a/r balance, it must continue to borrow. however, if it can lower its a/r balance, it can reduce the carrying cost, or the interest it pays on the loan. if the regional lockbox system reduces the company's a/r balance, it can lower its annual carrying cost. what is the annual reduction in interest expense net of the cost of the lockbock system?)

Sagot :

The estimated net annual savings to the firm from implementing the lockbox system, using an exponential function, is of $40,000.

What is an exponential function?

Problems involving interest rates are solved with exponential functions, as the amounts are multiplied by a constant each period.

The general format of the equation is given as follows:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which the parameters of the equation are listed as follows:

  • A(0) is the money subjected to interest.
  • r is the interest rate.

For the standard system, the values of these parameters are given as follows:

A(0) = 2500000, r = 0.11.

Hence the yearly cost is of:

A(1) = 2,500,000 x 1.11 = $2,775,000.

The interest with a reduction of 20% would be of:

r = 0.8 x 0.11 = 0.088.

Hence the new yearly cost, considering the $15,000 expenses, would be of:

A(1) = 2,500,000 x 1.088 + 15,000 = $2,735,000.

Hence the annual savings would be of:

2,775,000 - 2,735,000 = $40,000.

More can be learned about exponential functions at https://brainly.com/question/25537936

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