P14-9 Accounts receivable changes with bad debts.
A firm is evaluating an accounts
receivable change that would increase bad debts from 2% to 4% of sales. Sales are
currently 50,000 units, the selling price is $20 per unit, and the variable cost per
unit is $15. As a result of the proposed change, sales are forecast to increase
to 60,000 units.
a. What are bad debts in dollars currently and under the proposed change?
Current bad debts
Sales (50,000 x $20) 1,000,000
Bad debts (2% of sales) 20,000
Proposed change
Sales (60,000 x 20) 1,200,000
Bad debts (4% of sales) 48,000
b. Calculate the cost of the marginal bad debts to the firm.
The cost of marginal bad debts = change in bad debts = 48,000 - 20,000 = $28,000
c. Ignoring the additional profit contribution from increased sales, if the proposed
change saves $3,500 and causes no change in the average investment
in accounts receivable, would you recommend it? Explain.
In this case, there would be a savings of $3,500 and a loss of $28,000 due to increase in
bad debts, if you ignore additional profit. The proposed change is not recommended as
the loss is higher than the savings.
d. Considering all changes in costs and benefits, would you recommend the
proposed change? Explain.
Now, we consider the incremental profit from higher sales. The variable cost per unit is
$15, so the per unit profit is $5 since the fixed cost will not change. Units sold will
increase by 10,000.
Incremental profit (10,000 x 5) 50,000
Savings 3,500
Increase in bad debts (28,000)
Net benefit 25,500
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Yes, the proposed plan is recommended as there is a positive net benefit.
e. Compare and discuss your answers in parts c and d.
In part c, we did not take into account the incremental profit from the increase in sales
and so the proposed change was rejected. In part d, when the incremental profits are
considered, the total benefit is higher than the increase in bad debt expense and so the
plan is accepted.
P14-16 Zero-balance account Union Company is considering establishment of a zero
balance account. The firm currently maintains an average balance of $420,000 in its
disbursement account. As compensation to the bank for maintaining the zero-balance
account, the firm will have to pay a monthly fee of $1,000 and maintain a $300,000 non–
interest-earning deposit in the bank. The firm currently has no other deposits in the bank.
Evaluate the proposed zero-balance account, and make a recommendation to the firm,
assuming that it has a 12% opportunity cost.
Current average balance in disbursement account $420,000
Opportunity cost (12%) × 0.12
Current opportunity cost $ 50,400
Zero-Balance Account
Compensating balance $300,000
Opportunity cost (12%) × 0.12
Opportunity cost $36,000
Add: Monthly fee ($1,000 × 12 months) $12,000
Total cost $48,000
The opportunity cost of the zero-balance account proposal ($48,000) is less than
the current account opportunity cost ($50,000). Therefore, Union Company
should accept the zero-balance proposal.
15-9 Cost of bank loan Data Back-Up Systems has obtained a $10,000, 90-day bank loan
at an annual interest rate of 15%, payable at maturity. (Note: Assume a 365-day year.) a)
How much interest (in dollars) will the firm pay on the 90-day loan? b) Find the effective
90-day rate on the loan. c) Annualize your result in part b to find the effective annual rate
for this loan, assuming that it is rolled over every 90 days throughout the year under the
same terms and circumstances.
a) Interest Paid = Loan amount x Interest rate x Number of days/365 = 10,000 x 15% x
90/365 = $369.86
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b) Effective 90 day rate on loan (rq) = Interest paid / Loan Amount = 369.86 /10, 000 =
3.699%
c) Annualized rate = ((1 + rq)^(365 / # of days) -1) = (1 + 0.03699^(365/90)) - 1 =
15.87%
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