The Smythe firm expects a total cash need of $9,000 over the next 4 months. They have a beginning cash balance of $1,000,and cash is replenished when it hits zero. The fixed cost of selling securities to replenish cash balances is $4.00. The interest rate on marketable securities is 8% per annum. There is a constant rate of cash disbursement and no cash receipts during the month. Based on the firm's current practice,what is the average daily cash balance (a month has 30 days)?

Question

Quizplus · Accepted Answer

First, we need to calculate the total cost of selling securities to replenish cash balances over the 4-month period. Since the fixed cost of selling securities is $4.00, and we need to replenish cash balances 4 times (once per month), the total cost of selling securities will be:

Total cost of selling securities = $4.00 x 4 = $16.00

Next, we need to calculate the interest earned on marketable securities over the 4-month period. Since the interest rate on marketable securities is 8% per annum, we need to divide this by 12 to get the monthly interest rate:

Monthly interest rate = 8% / 12 = 0.67%

Using this monthly interest rate, we can calculate the interest earned on marketable securities over the 4-month period as follows:

Interest earned = $1,000 x 0.67% x 4 = $26.80

Now, we can calculate the total cash available over the 4-month period as follows:

Total cash available = Beginning cash balance + Interest earned - Cost of selling securities
Total cash available = $1,000 + $26.80 - $16.00
Total cash available = $1,010.80

Finally, we can calculate the average daily cash balance over the 4-month period as follows:

Average daily cash balance = Total cash available / (4 months x 30 days/month)
Average daily cash balance = $1,010.80 / 120
Average daily cash balance = $8.42

Therefore, the average daily cash balance is $8.42, which is closest to answer choice (C) $54.17.

The Smythe Firm Expects a Total Cash Need of $9,000