Question

A retail company receives most of its revenue from credit or debit card transactions or payments by check. Funds received from credit and debit card transactions automatically deposit in interest bearing accounts. However, the company does receive some cash payments from customers each day. These cash receipts total $7,250,000 annually. The company makes no cash payments to its suppliers or creditors. Money held in the cash account earns no interest. The company estimates that the transaction cost of moving funds from the cash account into investments that earn interest are $30.00 regardless of the amount transferred. The company earns on average 1.65% interest on funds held in interest bearing accounts and investments. 1. How much cash should the company allow to accumulate before making a deposit if it wants to minimize the total cost associated with carrying and converting cash? 2. If the company follows the optimal strategy identified in question 1, how frequently (on average) will the company move cash from the cash account into interest bearing investments? 3. If the company transfers funds as frequently as indicated in question 2: a. what will the total annual costs to transfer funds be? b. what will the average balance in the company’s cash account be? c. how much interest will the company forego annually by keeping funds in the cash account? d. what is the total cost to maintain a cash account? 4a. Determine the total cost associated with the cash account if the company transfers funds to interest bearing investments weekly rather than as often as indicated in question 2.

Answer 1

answer1

annual cash receipts= 7250000

conversion cost per lot= 30

annual interest rate= 1.65%= 0.0165

According to Baumol model optimal conversion lot(amount of cash to be converted into securities in one lot) can be found out by using the formula

=

= $162369

company should allow $162369 to accumulate and then deposit

2. Number of times cash needs to be converted to securities= 7250000/162369= 45 conversions

company will move cash from cash accounts into interest bearing investments about 45 times on an average

3.

( a) annual cost to transfer funds= 45 transaction * $30 per transaction = $1350

( b) average balance in the company's cash account will bre 162369/2= $81185

( c ) interest foregone= 81185 * 1.65%= 1340

( d ) total cost associated with the cash account= conversion cost + interest cost

= 1350+ 1340=$2690

answer4

if comp[any transfers weekly then number of transactions/conversions will be 52 (that is 52 weeks

conversion cost = 52 * $30= $1560

amount of cash converted in one lot will be= 7250000/52=$139423

average balance in cash account= 139423/2= $69712

intwerest cost= 69712 * 1.65%=$1150

TOTAL COST associateds with cash account= 1560 +1150= $2710