Chapter 27
Banking Relationships
ANSWERS TO END-OF-CHAPTER QUESTIONS


27-1 a. Cash discounts are often used to encourage early payment and to attract customers by effectively lowering prices. Credit terms are usually stated in the following form: 2/10, net 30. This means a 2 percent discount will apply if the account is paid within 10 days, otherwise the account must be paid within 30 days.

b. Seasonal dating sets the invoice date, or date at which the credit and discount periods begin, to a time during the buyer’s own selling season, regardless of the actual sale date.

c. An aging schedule breaks down accounts receivable according to how long they have been outstanding. This gives the firm a more complete picture of the structure of accounts receivable than that provided by days sales outstanding. Days sales outstanding (DSO) is a measure of the average length of time it takes a firm's customers to pay off their credit purchases.

d. The payments pattern approach is a procedure which measures any changes that might occur in customers' payment behavior. The advantage of this approach is that it is not affected by changes in sales levels due to cyclical or seasonal factors. The uncollected balances schedule, which is an integral part of the payments pattern approach, helps a firm monitor its receivables better and also forecast future receivables balances.

e. The situation when interest is not compounded, that is, interest is not earned on interest, is simple interest. Discount interest is interest that is calculated on the face amount of a loan but is paid in advance. Add-on interest is interest that is calculated and added to funds received to determine the face amount of an installment loan.

27-2 The latest date for paying and taking discounts is May 10. The date by which the payment must be made is June 9.

27-3 False. An aging schedule will give more detail, especially as to what percentage of accounts are past due and what percentage of accounts are taking discounts.

27-4 No. Although B sustains slightly more losses due to uncollectible accounts, its credit manager may have a wise policy that is generating more sales revenues (and thus profits) than would be the case if he had a policy which cut those losses to zero.






27-5 A/R Sales Profit
a. The firm tightens its credit
standards. - - 0
b. The terms of trade are
changed from 2/10, net 30,
to 3/10, net 30. 0 + 0
c. The terms are changed from
2/10 net 30, to 3/10, net 40. 0 + 0
d. The credit manager gets tough
with past-due accounts. - - 0

Explanations:

a. When a firm “tightens” its credit standards, it sells on credit more selectively. It will likely sell less and certainly will make fewer credit sales. Profit may be affected in either direction.

b. The larger cash discount will probably induce more sales, but they will likely be from customers who pay bills quickly. Further, some of the current customers who do not take the 2 percent discount may be induced to start paying earlier. The effect of this would be to reduce accounts receivable, so accounts receivable and profits could go either way.

c. A less stringent credit policy in terms of the credit period should stimulate sales. The accounts receivable could go up or down depending upon whether customers take the new higher discount or delay payments for the 10 additional days, and depending upon the amount of new sales generated.


d. If the credit manager gets tough with past due accounts, sales will decline, as will accounts receivable.





SOLUTIONS TO END-OF-CHAPTER PROBLEMS
27-1 Analysis of change:
Projected Income Projected Income
Statement Effect of Statement
Under Current Credit Policy Under New
Credit Policy Change Credit Policy
Gross sales $1,600,000 +$ 25,000 $1,625,000
Less: Discounts 0 0 0
Net sales $1,600,000 +$ 25,000 $1,625,000
Variable costs 1,200,000 + 18,750 1,218,750
Profit before
credit costs
and taxes $ 400,000 +$ 6,250 $ 406,250
Credit-related costs:
Cost of carrying
receivables* 15,781 + 8,260 24,041
Collection expense 35,000 - 13,000 22,000
Bad debt losses 24,000 + 16,625 40,625
Profit before taxes $ 325,219 -$ 5,635 $ 319,584
Taxes (40%) 130,088 - 2,254 127,834
Net income $ 195,131 -$ 3,381 $ 191,750

*Cost of carrying receivables:

.

Current policy = (30) (0.75)(0.16) = $15,781.

New policy = (45) (0.75)(0.16) = $24,041.

Since the change in profitability is negative, the firm should not relax its collection efforts.



27-2 Analysis of change:
Projected Income Projected Income
Statement Effect of Statement
Under Current Credit Policy Under New
Credit Policy Change Credit Policy
Gross sales $2,500,000 -$125,000 $2,375,000
Less: Discounts 0 0 0
Net sales $2,500,000 -$125,000 $2,375,000
Variable costs 2,125,000 - 106,250 2,018,750
Profit before
credit costs
and taxes $ 375,000 -$ 18,750 $ 356,250
Credit-related costs:
Cost of carrying
receivables* 99,555 - 64,711 34,844
Bad debt losses 0 0 0
Profit before taxes $ 275,445 +$ 45,961 $ 321,406
Taxes (40%) 110,178 + 18,384 128,562
Net income $ 165,267 +$ 27,577 $ 192,844

*Cost of carrying receivables:

.

Current policy = (95) (0.85)(0.18) = $99,555.

New policy = (35) (0.85)(0.18) = $34,844.

The firm should change its credit terms since the change in profitability is positive.


27-3 a. March receivables = $120,000(0.8) + $100,000(0.5) = $146,000.
June receivables = $160,000(0.8) + $140,000(0.5) = $198,000.

b. 1st Quarter: ADS = ($50,000 + $100,000 + $120,000)/90 = $3,000.
DSO = $146,000/$3,000 = 48.7 days.

2nd Quarter: ADS = ($105,000 + $140,000 + $160,000)/90 = $4,500.
DSO = $198,000/$4,500 = 44.0 days.


Cumulative: ADS = ($50,000 + $100,000 + $120,000
+ $105,000 + $140,000 + $160,000)/180 = $3,750,

or ADS = ($3,000 + $4,500)/2 = $3,750.
DSO = $198,000/$3,750 = 52.8 days.

c. Age of Accounts Dollar Value Percent of Total
0 - 30 days $128,000 65%
31 - 60 70,000 35
61 - 90 0 0
$198,000 100%

d. Month Sales Receivables Receivables/Sales
April $105,000 $ 0 0%
May 140,000 70,000 50
June 160,000 128,000 80
$198,000 130%

27-4 $25,000 interest-only loan, 11% nominal rate. Interest calculated as simple interest based on 365-day year. Interest for 1st month = ?

Interest rate per day = 0.11/365 = 0.000301.

Interest charge for period = (31)(0.11/365)($25,000)
= $233.56.

















27-5 $15,000 installment loan, 11% nominal rate.
Effective annual rate, assuming a 365-day year = ?

Add-on interest = 0.11($15,000) = $1,650.

Monthly Payment = = $1,387.50.

0 1 2 11 12
| | | · · · | |
15,000 -1,387.50 -1,387.50 -1,387.50 -1,387.50

With a financial calculator, enter N = 12, PV = 15000, PMT = -1387.50,
FV = 0, and then press I to obtain 1.6432%. However, this is a monthly rate.


Effective annual rateAdd-on = (1 + rd)n - 1.0
= (1.016432)12 - 1.0
= 1.2160 - 1.0 = 0.2160 = 21.60%.


27-6 a. Effective rate = 12%.

b. 0 1
| |
50,000 -50,000
- 4,500
-10,000 (compensating balance) 10,000
40,000 -44,500

With a financial calculator, enter N = 1, PV = 40000, PMT = 0, and
FV = -44500 to solve for I = 11.25%.

Note that, if Hawley actually needs $50,000 of funds, he will have to borrow = $62,500. The effective interest rate will still be 11.25%.














c. 0 1
| |
50,000 -50,000
- 4,375 (discount interest) 7,500
- 7,500 (compensating balance) -42,500
38,125

With a financial calculator, enter N = 1, PV = 38125, PMT = 0, and
FV = -42500 to solve for I = 11.4754% ? 11.48%.

Note that, if Hawley actually needs $50,000 of funds, he will have to borrow = $65,573.77. The effective interest rate will still be 11.48%.

d. Approximate annual rate = = = 16%.
Precise effective rate:

$50,000 =

rd, the monthly interest rate, is 1.1326%, found with a financial calculator. Input N = 12; PV = 50000; PMT = -4166.67; FV = -4000; and I = ?. The precise effective annual rate is (1.011326)12 - 1.0 = 14.47%.

Alternative b has the lowest effective interest rate.


27-7 Accounts payable:

Nominal cost = = (0.0204(7.2) = 14.69%.

EAR cost = (1.03093)4.5 - 1.0 = 14.69%.

Bank loan:

0 1
| |
500,000 -500,000
-60,000 (discount interest)
440,000

With a financial calculator, enter N = 1, PV = 440000, PMT = 0, and FV = -500000 to solve for I = 13.636% ? 13.64%.

Note that, if Masson actually needs $500,000 of funds, he will have to borrow = $568,181.82. The effective interest rate will still be 13.64%.

The bank loan is the lowest cost source of capital available to D.J. Masson at 13.64%.



27-8 a. Simple interest: 12%.

b. 3-months: (1 + 0.115/4)4 - 1 = 12.0055%, or use the interest conversion feature of your calculator as follows:

NOM% = 11.5; P/YR = 4; EFF% = ? EFF% = 12.0055%.

c. Add-on: Interest = Funds needed(rd).

Loan = Funds needed(1 + rd).
PMT = Loan/12.

Assume you borrowed $100. Then, Loan = $100(1.06) = $106.
PMT = $106/12 = $8.8333.

$100 = .

Enter N = 12, PV = 100, PMT = -8.8333, FV = 0, and press I to get
I = 0.908032% = rd. This is a monthly periodic rate, so the effective annual rate = (1.00908032)12 - 1 = 0.1146 = 11.46%.

d. Trade credit: 1/99 = 1.01% on discount if pay in 15 days, otherwise pay 45 days later. So, get 60 - 15 = 45 days of credit at a cost of 1/99 = 1.01%. There are 360/45 = 8 periods, so the effective cost rate is:

(1 + 1/99)8 - 1 = (1.0101)8 - 1 = 8.3723%.

Thus, the least expensive type of credit for Yonge is trade credit with an effective cost of 8.3723 percent.











27-9 a. The quarterly interest rate is equal to 11.25%/4 = 2.8125%.

Effective annual rate = (1 + 0.028125)4 - 1
= 1.117336 - 1 = 0.117336 = 11.73%.

b. 0 1
| |
1,500,000 -1,500,000
-33,750 (discount interest) 300,000
-300,000 (compensating balance) -1,200,000
1,166,250

With a financial calculator, enter N = 1, PV = 1166250, PMT = 0, and
FV = -1200000 to solve for I = 2.89389% ? 2.89%. However, this is a periodic rate.

Effective annual rate = (1 + 0.0289389)4 - 1 = 12.088% ? 12.09%.


Note that, if Gifts Galore actually needs $1,500,000 of funds, it will have to borrow = = $1,929,260.45. The effective interest rate will still be 12.088% ? 12.09%.

c. Installment loan:

PMT = ($1,500,000 + $33,750)/3 = $511,250.
INPUT N = 3, PV = 1500000, PMT = -511250, FV = 0.
OUTPUT = I = 1.121% per month. Nominal annual rate = 12(1.121%) = 13.45%.


27-10 a. Malone’s current accounts payable balance represents 60 days purchases. Daily purchases can be calculated as = $8.33.
If Malone takes discounts then the accounts payable balance would include only 10 days purchases, so the A/P balance would be $8.33 ? 10 = $83.33.

If Malone doesn’t take discounts but pays in 30 days, its A/P balance would be $8.33 ? 30 = $250.













b. Takes Discounts:
If Malone takes discounts its A/P balance would be $83.33. The cash it would need to be loaned is $500 - $83.33 = $416.67.

Since the loan is a discount loan with compensating balances, Malone would require more than a $416.67 loan.

Face amount of loan = = $641.03.

Doesn’t Take Discounts:
If Malone doesn’t take discounts, its A/P balance would be $250. The cash needed from the bank is $500 - $250 = $250.

Face amount of loan = = $384.62.

c. Nonfree Trade Credit:
Nominal annual cost:
= = 18.18%.

Effective cost:


Bank Loan: 15% Discount Loan with 20% compensating balance.
Assume the firm doesn’t take discounts so it needs $250 and borrows $384.62. (The cost will be the same regardless of how much the firm borrows.)

0 1
| |
384.62 -384.62
-57.69 Discount interest +76.92
-76.92 Compensating balance -307.70
250.00

With a financial calculator, input the following data, N = 1, PV = 250, PMT = 0, FV = -307.70, and then solve for I = 23.08%.

Just to show you that it doesn’t matter how much the firm borrows, assume the firm takes discounts and it reduces A/P to $83.33 so it needs $416.67 cash and borrows $641.03.

0 1
| |
641.03 -641.03
-96.15 Discount interest +128.21
-128.21 Compensating balance -512.82
416.67

With a financial calculator, input the following data, N = 1, PV = 416.67, PMT = 0, FV = -512.82, and then solve for I = 23.08%.

Because the cost of nonfree trade credit is less than the cost of the bank loan, Malone should forge discounts and reduce its payables only to $250,000.

d. Pro Forma Balance Sheet (Thousands of Dollars):

Casha $ 126.9 Accounts payable $ 250.0
Accounts receivable 450.0 Notes payableb 434.6
Inventory 750.0 Accruals 50.0
Prepaid interest 57.7
Total current Total current
assets $1,384.6 liabilities $ 734.6
Fixed assets 750.0 Long-term debt 150.0
Common equity 1,250.0
Total assets $2,134.6 Total claims $2,134.6

a $384,615(0.2) = $76,923 = Compensating balance.
Cash = $50 + $76.923 = $126.9.
b Notes payable = $50 + $384.6 = $434.6.


e. To reduce the accounts payable by $250,000, which reflects the 1% discount, Malone must pay the full cost of the payables, which is $250,000/0.99 = $252,525.25. The lost discount is the difference between the full cost of the payables and the amount that is reported net of discount: Lost discount = $252,525.25 - $250,000.00 = $2,525.25. The after-tax cost of the lost discount is $2,525.25(1-0.40) = $1,515.15. Notice that this provides a tax shield in the amount of $2,525.25(0.40) = $1,010.10. The total amount of cash that Malone needs to pay down $250,000 of accounts payable is the gross amount minus the tax shield: $252,525.25 - $1,010.10 = $251,515.15.

Face amount of loan = = $386,946.38.


Pro Forma Balance Sheet (Thousands of Dollars):

Casha $ 127.4 Accounts payable $ 250.0
Accounts receivable 450.0 Notes payableb 436.9
Inventory 750.0 Accruals 50.0
Prepaid interest 58.0
Total current Total current
assets $1,385.4 liabilities $ 736.9
Fixed assets 750.0 Long-term debt 150.0
Common equityc 1,248.5
Total assets $2,135.4 Total claims $2,135.4

a $386,946.38(0.2) = $77,389.27 = Compensating balance.
Cash = $50 + $77.4 = $127.4.
b Notes payable = $50 + $386.9 = $436.9.
c Common equity = Previous common equity – after-tax lost discount
= $1,250 - $1.5 = $1,248.5




















27-11 a. 1. Line of credit:
Commitment fee = (0.005)($2,000,000)(11/12) = $ 9,167
Interest = (0.11)(1/12)($2,000,000) = 18,333
Total $27,500

2. Trade discount:
a. = = 24.49 ? 24.5%.

Total cost = 0.245($2,000,000)/12 = $40,833.

b. Effective cost = (1 + 2/98)360/30 - 1 = 0.2743 = 27.43%.

Total cost = 0.2743($2,000,000)/12 = $45,717.

3. 30-day commercial paper:
Interest = (0.095)($2,000,000)(1/12) = $15,833
Transaction fee = (0.005)($2,000,000) = 10,000
$25,833

4. 60-day commercial paper:
Interest = (0.09)($2,000,000)(2/12) = $30,000
Transaction fee = (0.005)($2,000,000) = 10,000
$40,000

Marketable securities interest received
= (0.094)($2,000,000)(1/12) = -15,667

Transactions cost, marketable securities
= (0.004)($2,000,000) = +8,000
$32,333

The 30-day commercial paper has the lowest cost.

b. The lowest cost of financing is not necessarily the best. The use of 30-day commercial paper is the cheapest; however, sometimes the commercial paper market is tight and funds are not available. This market also is impersonal. A banking arrangement may provide financial counseling and a long-run relationship in which the bank performs almost as a "partner and counselor" to the firm. Note also that while the use of 60-day commercial paper is more expensive than the use of 30-day paper, it provides more flexibility in the event the money is needed for more than 30 days. However, the line of credit provides even more flexibility than the 60-day commercial paper and at a lower cost.


SOLUTION TO SPREADSHEET PROBLEMS



27-12 The detailed solution for the problem is available both on the instructor’s resource CD-ROM (in the file Solution to FM11 Ch 27-12 Build a Model.xls) and on the instructor’s side of the web site, http://brigham.swcollege.com.

MINI CASE



Rich Jackson, a recent finance graduate, is planning to go into the wholesale building supply business with his brother, Jim, who majored in building construction. The firm would sell primarily to general contractors, and it would start operating next January. Sales would be slow during the cold months, rise during the spring, and then fall off again in the summer, when new construction in the area slows. Sales estimates for the first 6 months are as follows (in thousands of dollars):

Jan $100
Feb 200
Mar 300
Apr 300
May 200
Jun 100

The terms of sale are net 30, but because of special incentives, the brothers expect 30 percent of the customers (by dollar value) to pay on the 10th day following the sale, 50 percent to pay on the 40th day, and the remaining 20 percent to pay on the 70th day. No bad debt losses are expected, because Jim, the building construction expert, knows which contractors are having financial problems.

a. Discuss, in general, what it means for the brothers to set a credit and collections policy.

Answer: When a firm sets its credit and collections policy it determines four things:
1. The credit period, which is the length of time buyers are given to pay for their purchases
2. The discounts that are given for early payment.
3. The credit standards, which are the financial strength requirements for customers to purchase on credit from the firm.
4. The collection policy, which is how hard the company will work to collect slow-paying accounts.

These policies determine the level of sales and also the level of accounts receivable. Note that although sales contribute to profitability, additional accounts receivable require the investment of funds, so a firm must take both the profits from additional sales and the additional capital required to fund accounts receivable when it determines a credit policy.

b. Assume that, on average, the brothers expect annual sales of 18,000 items at an average price of $100 per item. (use a 365-day year.)

1. What is the firm’s expected days sales outstanding (DSO)?

Answer: Days sales outstanding = DSO = 0.3(10) + 0.5(40) + 0.2(70) = 37 days, vs. 30-day credit period. One would expect some customers to pay somewhat slowly, so a 37-day DSO is probably not too bad.


b. 2. What is its expected average daily sales (ADS)?

Answer: Average daily sales = ADS = = $4,931 per day.

b. 3. What is its expected average accounts receivable level?

Answer: Accounts receivable (A/R) = (DSO)(ADS) = 37($4,931) = $182,466. Thus, $182,466 of receivables are outstanding, and the firm must raise capital to carry receivables. If collections could be speeded up, and DSO reduced, then A/R, and hence the required financing, would be reduced.


b. 4. Assume that the firm’s profit margin is 25 percent. How much of the receivables balance must be financed? What would the firm’s balance sheet figures for accounts receivable, notes payable, and retained earnings be at the end of one year if notes payable are used to finance the investment in receivables? Assume that the cost of carrying receivables had been deducted when the 25 percent profit margin was calculated.

Answer: Although the firm has $182,466 in receivables, the entire amount does not have to be financed, since 25 percent of the sales price is profit. This means that 75 percent of the price represents costs of materials, labor, rent, utilities, insurance, and so on. Thus, the firm must finance only 0.75($182,466) = $136,849 of the receivables balance. Disregarding other assets and liabilities, its balance sheet would look like this if notes payable are used to finance receivables:

Accounts receivable $182,466 Notes payable $136,849
Retained earnings 45,616
$182,466


b. 5. If bank loans have a cost of 12 percent, what is the annual dollar cost of carrying the receivables?

Answer: Cost of carrying receivables = 0.12($136,849) = $16,422. In addition, there is an opportunity cost associated with not having the use of the profit component of the receivables.

c. What are some factors that influence (1) a firm's receivables level
and (2) the dollar cost of carrying receivables?

Answer: 1. As shown in question B.3. Above, receivables are a function of the average daily sales and the days sales outstanding. Exogenous economic factors such as the state of the economy and competition within the industry affect average daily sales, but so does the firm's credit policy. The days sales outstanding depends mainly on credit policy, although poor economic conditions can lead to a reduction in customers' ability to make payments.

2. For a given level of receivables, the lower the profit margin, the higher the cost of carrying receivables, because the greater the portion of each sales dollar that must actually be financed. Similarly, the higher the cost of the financing, the higher the dollar cost of carrying the receivables.
d. Assuming that the monthly sales forecasts given previously are accurate, and that customers pay exactly as was predicted, what would the receivables level be at the end of each month? To reduce calculations, assume that 30 percent of the firm's customers pay in the month of sale, 50 percent pay in the month following the sale, and the remaining 20 percent pay in the second month following the sale. Note that this is a different assumption than was made earlier. Use the following format to answer parts c and d:

E.O.M. Quarterly DSO =
Month Sales A/R Sales ADS (A/R)/(ADS)
Jan $100 $ 70
Feb 200 160
Mar 300 250 $600 $6.59 37.9

Apr 300
May 200
Jun 100

Answer: (Note: from this point on, the solutions are expressed in thousands of dollars. Also, the table given below is developed in the solutions to parts D and E.)
At the end of January, 30 percent of the $100 in sales will have been collected, so (1 - 0.3)($100) = 0.7($100) = $70 will remain outstanding, that is, in the receivables account. At the end of February, 30% + 50% = 80% of January's sales will have been collected, so receivables associated with January sales will be (1 - 0.3 - 0.5)($100) = 0.2($100) = $20. Of February's $200 in sales, 30 percent will have been collected, so 0.7($200) = $140 will remain outstanding. Thus, the receivables balance at the end of February will be $20 from January's sales plus $140 from February's sales, for a total of $160.











By the end of march, all of January's sales will have been collected, but 20 percent of February's sales and 70 percent of march's sales will still be outstanding, so receivables will equal 0.2($200) + 0.7($300) = $250. Following this logic, the receivables balance at the end of any month can be estimated as follows:

A/R = 0.7(sales in that month) + 0.2(sales in previous month).

E.O.M. Quarterly DSO =
Month Sales A/R Sales ADS (A/R)/(ADS)
Jan $100 $ 70
Feb 200 160
Mar 300 250 $600 $6.59 37.9

Apr $300 $270
May 200 200
Jun 100 110 $600 $6.59 16.7


e. What is the firm's forecasted average daily sales for the first 3 months? For the entire half-year? The days sales outstanding is commonly used to measure receivables performance. What DSO is expected at the end of March? At the end of June? What does the DSO indicate about customers' payments? Is DSO a good management tool in this situation? If not, why not?

Answer: For the first quarter, sales totaled $100 + $200 + $300 = $600, so ads = $600/91 = $6.59. Although the sales pattern is different, ads for the second quarter, and hence for the full half-year, is also $6.59. Note that we can rearrange the formula for receivables as follows:

A/R = (DSO)(ADS)
DSO = .

March: DSO = = 37.9 days; June: DSO = = 16.7 days.

Thus, at the end of March, DSO = 37.9 days, while at the end of June, DSO = 16.7 days.

Looking at the DSO, it appears that customers are paying significantly faster in the second quarter than in the first. However, the receivables balances were created assuming a constant payment pattern, so the DSO is giving a false measure of customers' payment performance. The underlying cause of the problem with the DSO is the seasonal variability in sales. If there were no seasonal pattern, and hence sales were a constant $200 each month, then the DSO would be 27 days in both March and June, indicating that customers' payment patterns had remained steady.


f. Construct aging schedules for the end of March and the end of June (use the format given below). Do these schedules properly measure customers’ payment patterns? If not, why not?

Age of account March June
(days) A/R % A/R %
0 – 30 $210 84%
31 – 60 40 16
61 – 90 0 0
$250 100%


Answer: Aging schedule:

Age of account March June
(days) A/R % A/R %
0 – 30 $210 Mar 84% $ 70 Jun 64%
31 – 60 40 Feb 16 40 May 36
61 – 90 0 Jan 0 Apr 0
$250 100% $110 100

To see how these aging schedules were constructed, consider first the end-of-March schedule. At that time, 30 percent of March's sales had been collected, so 70 percent remained uncollected: 0.7($300) = $210. February's contribution to receivables is 0.2($200) = $40. Finally, by the end of March, all of January's sales had been collected, so none of January's sales remained outstanding. Thus, the receivables account totals $250 at the end of March, which is consistent with the answer to part C.
Note that the end-of-June aging schedule suggests that customers are paying more slowly than in the earlier quarter. However, we know that the payment pattern has remained constant, so the firm's customers' payment performance has not changed. Again, a seasonally fluctuating sales level is the cause of the problem: aging schedules give incorrect signals if sales are trending up or down. If sales were a constant $200 in each month, then both aging schedules would indicate that 78 percent of receivables were 0 – 30 days old and 22 percent were 31 - 60 days old.








g. Construct the uncollected balances schedules for the end of March and the end of June. Use the format given below. Do these schedules properly measure customers' payment patterns?

March June
contribution A/R-to- contribution A/R-to-
Month Sales to A/R sales ratio month sales to A/R sales ratio
Jan $100 $ 0 0% Apr
Feb 200 40 20 May
Mar 300 210 70 Jun


Answer: Uncollected balances schedules:

Contribution to Ratio of month's
Month Sales end-of-period A/R A/R to month’s sales
(1) (2) (3) (4)
Jan $100 $ 0 0%
Feb 200 40 20
Mar 300 210 70
End of quarter A/R $250 90%

Apr $300 $ 0 0%
May 200 40 20
Jun 100 70 70
end of quarter A/R $110 90%

In column 3 above, the contribution of each month's sales to the firm's receivables balance is identified. To illustrate, at the end of March, all of January's sales had been collected, but only 80 percent of February's sales had been collected, so $40 remained outstanding. Similarly, 70 percent of March's sales were still outstanding, so March's contribution to receivables was 0.7($300) = $210.
The focal point of the uncollected balances schedule is column 4, the receivables-to-sales ratio. When we compare March and June, we see no difference, which is what we should see, given that there has been no change in the payment pattern. Thus, the uncollected balances schedule gives a true picture of customers' payment patterns, even when sales fluctuate. Note also (1) that any increase in column 4 from a month in one quarter to the corresponding month in the next quarter is "bad" in the sense that it indicates a slowdown in payments, and (2) that the bottom line gives a summary of the changes in payment patterns.



h. Assume that it is now July of year 1, and the brothers are developing pro forma financial statements for the following year. Further, assume that sales and collections in the first half-year matched the predicted levels. Using the year 2 sales forecasts as shown next, what are next year's pro forma receivables levels for the end of March and for the end of June?

Predicted Predicted Predicted contribution
Month sales A/R-to-sales ratio to receivables
Jan $150 0% $ 0
Feb 300 20 60
Mar 500 70 350
projected March 31 A/R balance = $410

Apr $400
May 300
Jun 200
Projected June 30 A/R balance =


Answer: The uncollected balances schedule can be used to forecast the pro forma receivables balance. For forecasting, the historical receivables-to-sales ratios are generally assumed to be good predictors of future payment patterns, and hence are applied to the sales forecasts to develop the expected receivables:

Predicted Predicted Predicted contribution
Month sales A/R-to-sales ratio to receivables
Jan $150 0% $ 0
Feb 300 20 60
Mar 500 70 350
projected March 31 A/R balance = $410

Apr $400 0% $ 0
May 300 20 60
Jun 200 70 140
projected June 30 A/R balance = $200



i. Assume now that it is several years later. The brothers are concerned about the firm's current credit terms, which are now net 30, which means that contractors buying building products from the firm are not offered a discount, and they are supposed to pay the full amount in 30 days. Gross sales are now running $1,000,000 a year, and 80 percent (by dollar volume) of the firm's paying customers generally pay the full amount on day 30, while the other 20 percent pay, on average, on day 40. Two percent of the firm's gross sales end up as bad debt losses.
The brothers are now considering a change in the firm's credit policy. The change would entail (1) changing the credit terms to 2/10, net 20, (2) employing stricter credit standards before granting credit, and (3) enforcing collections with greater vigor than in the past. Thus, cash customers and those paying within 10 days would receive a 2 percent discount, but all others would have to pay the full amount after only 20 days. The brothers believe that the discount would both attract additional customers and encourage some existing customers to purchase more from the firm--after all, the discount amounts to a price reduction. Of course, these customers would take the discount and, hence, would pay in only 10 days.
The net expected result is for sales to increase to $1,100,000; for 60 percent of the paying customers to take the discount and pay on the 10th day; for 30 percent to pay the full amount on day 20; for 10 percent to pay late on day 30; and for bad debt losses to fall from 2 percent to 1 percent of gross sales. The firm's operating cost ratio will remain unchanged at 75 percent, and its cost of carrying receivables will remain unchanged at 12 percent.
To begin the analysis, describe the four variables that make up a firm's credit policy, and explain how each of them affects sales and collections. Then use the information given in part H to answer parts I through N.


Answer: The four variables which make up a firm's credit policy are (1) the discount offered, including the amount and period; (2) the credit period; (3) the credit standards used when determining who shall receive credit, and how much credit; and (4) the collection policy.
Cash discounts generally produce two benefits: (1) they attract both new customers and expanded sales from current customers, because people view discounts as a price reduction, and (2) discounts cause a reduction in the days sales outstanding, since both new customers and some established customers will pay more promptly in order to get the discount. Of course, these benefits are offset to some degree by the dollar cost of the discounts themselves.
The credit period is the length of time allowed to all "qualified" customers to pay for their purchases. In order to qualify for credit in the first place, customers must meet the firm's credit standards. These dictate the minimum acceptable financial position required of customers to receive credit. Also, a firm may impose differing credit limits depending on the customer's financial strength as judged by the credit department.
Finally, collection policy refers to the procedures that the firm follows to collect past-due accounts. These can range from a simple letter or phone call to turning the account over to a collection agency.
How the firm handles each element of credit policy will have an influence on sales, speed of collections, and bad debt losses. The object is to be tough enough to get timely payments and to minimize bad debt losses, yet not to create ill will and thus lose customers.


j. Under the current credit policy, what is the firm's days sales outstanding (DSO)? What would the expected DSO be if the credit policy change were made?

Answer: Old (current) situation: DSO0 = 0.8(30) + 0.2(40) = 32 days. New situation: DSOn = 0.6(10) + 0.3(20) + 0.1(30) = 15 days. Thus, the new credit policy is expected to cut the DSO in half.







k. What is the dollar amount of the firm's current bad debt losses? What losses would be expected under the new policy?

Answer: Old (current) situation: BDLo = 0.02($1,000,000) = $20,000. New situation: BDLn = 0.01($1,100,000) = $11,000. Thus, the new policy is expected to cut bad debt losses sharply.


l. What would be the firm's expected dollar cost of granting discounts under the new policy?

Answer: Current situation: under the current, no discount policy, the cost of discounts is $0.
New situation: of the $1,100,000 gross sales expected under the new policy, 1 percent is lost to bad debts, so good sales = 0.99($1,100,000) = $1,089,000. Since 60 percent of the good sales are discount sales, discount sales = 0.6($1,089,000) = $653,400. Finally, the discount is 2 percent, so the cost of discounts is expected to be 0.02($653,400) = $13,068.


m. What is the firm's current dollar cost of carrying receivables? What would it be after the proposed change?

Answer: Current situation: the firm's average daily sales currently amount to $1,000,000/365 = $2,739.73. The DSO is 32 days, so accounts receivable amount to 32($2,739.73) = $87,671. However, only 75 percent of this total represents cash costs--the remainder is profit--so the investment in receivables (the actual amount that must be financed) is 0.75($87,671) = $65,753. At a cost of 12 percent, the annual cost of carrying the receivables is 0.12($65,753) = $7,890.
New situation: the cost of carrying the receivables balance under the new policy would be $4,068:

($1,100,000/365)(15)(0.75)(0.12) = $4,068.



n. What is the incremental after-tax profit associated with the change in credit terms? Should the company make the change? (assume a tax rate of 40 percent.)

New Old Difference
Gross sales $1,000,000
Less discounts 0
Net sales $1,000,000
Production costs 750,000
Profit before credit
Costs and taxes $ 250,000
Credit-related costs:
Carrying costs 7,890
Bad debt losses 20,000
Profit before taxes $ 222,110
Taxes (40%) 88,844
Net income $ 133,266


Answer: The income statements and differentials under the two credit policies are shown below:

New Old Difference
Gross sales $1,100,000 $1,000,000 $100,000
Less discounts 13,068 0 13,068
Net sales $1,086,932 $1,000,000 $ 86,932
Production costs 825,000 750,000 75,000
Profit before credit
Costs and taxes $ 261,932 $ 250,000 $ 11,932
Credit-related costs:
Carrying costs 4,068 7,890 (3,822)
Bad debt losses 11,000 20,000 (9,000)
Profit before taxes $ 246,846 $ 222,110 $ 24,754
Taxes (40%) 98,745 88,844 9,902
Net income $ 148,118 $ 133,266 $ 14,852

Thus, if expectations are met, the credit policy change would increase the firm's annual after-tax profit by $14,884. Since there are no non-cash expenses involved here, the $14,884 is also the incremental cash flow expected under the new policy.
However, the new policy is not riskless. If the firm's customers do not react as predicted, then the firm's profits could actually decrease as a result of the change. The amount of risk involved in the decision depends on the uncertainty inherent in the estimates, especially the sales estimate. Typically, it is very difficult to predict customers' responses to credit policy changes. Further, a credit policy change may prompt the company's competitors to change their own credit terms, and this could offset the expected increase in sales. Thus, the final decision is judgmental. If the prospect of an annual $14,884 increase in net income is sufficient to compensate for the risks involved, then the change should be made. (note: large, national companies often make credit policy changes in a given region in an effort to determine how customers and competitors will react, and then use the information gained when setting national policy. Note also that credit policy changes may not be announced in a "broadcast" sense so as to slow down competitors' reactions.)


o. Suppose the firm makes the change, but its competitors react by making similar changes to their own credit terms, with the net result being that gross sales remain at the current $1,000,000 level. What would the impact be on the firm's post-tax profitability?

Answer: If sales remain at $1,000,000 after the change is made, then the following situation would exist:

Gross sales $1,000,000
Less discounts 11,880
Net sales $ 988,120
Production costs 750,000
Profit before credit
Costs and taxes $ 238,120
Credit costs:
Carrying costs 3,699
Bad debt losses 10,000
Profit before taxes $ 224,421
Taxes (40%) 89,769
Net income $ 134,653

Under the old terms the net income was $133,266, so the policy change would result in a slight incremental gain of $134,653 - $133,266 = $1,387.

p. The brothers are considering taking out a 1-year bank loan for $100,000 to finance part of their working capital needs and have been quoted a rate of 8 percent. What is the effective annual cost rate assuming (1) simple interest, (2) discount interest, (3) discount interest with a 10 percent compensating balance, and (4) add-on interest on a 12-month installment loan? For the first 3 of these assumptions, would it matter of the loan were for 90 days, but renewable, rather than for a year?

Answer: 1. With a simple interest loan, they gets the full use of the $100,000 for a year, and then pay 0.08($100,000) = $8,000 in interest at the end of the term, along with the $100,000 principal repayment. For a 1-year simple interest loan, the nominal rate, 8 percent, is also the effective annual rate.

2. On a discount interest loan, the bank deducts the interest from the face amount of the loan in advance; that is, the bank "discounts" the loan. If the loan had a $100,000 face amount, then the 0.08($100,000) = $8,000 would be deducted up front, so the borrower would have the use of only $100,000 - $8,000 = $92,000. At the end of the year, the borrower must repay the $100,000 face amount. Thus, the effective annual rate is 8.7 percent:

Effective rate = = 0.087 = 8.7%.

Note that a timeline can also be used to calculate the effective annual rate of the 1-year discount loan:

0 1
| |
100,000 -100,000
-8,000 (discount interest)
92,000

With a financial calculator, enter n = 1, PV = 92000, pmt = 0, and FV = -100000 to solve for i = 8.6957% ? 8.7%.

3. If the loan is a discount loan, and a compensating balance is also required, then the effective rate is calculated as follows:

Amount borrowed = = $121,951.22.

0 1
| |
121,951.22 -121,951.22
- 9,756.10 (discount interest) 12,195.12
-12,195.12 (compensating balance) -109,756.10
100,000.00

With a financial calculator, enter n = 1, PV = 100000, pmt = 0, and FV = -109756.10 to solve for i = 9.7561% . 9.76%.

4. In an installment (add-on) loan, the interest is calculated and added on to the required cash amount, and then this sum is the face amount of loan, and it is amortized by equal payments over the stated life. Thus, the interest would be $100,000 ? 0.08 = $8,000, the face amount would be $108,000, and each monthly payment would be $9,000: $108,000/12 = $9,000.
However, the firm would receive only $100,000, and it must begin to repay the principal after only one month. Thus, it would get the use of $100,000 in the first month, the use of $100,000 - $9,000 = $91,000 in the second month, and so on, for an average of $100,000/2 = $50,000 over the year. Since the interest expense is $8,000, the approximate cost is 16 percent, or twice the stated rate:

Approximate cost = = = 0.16 = 16%.


To find the exact effective annual rate, recognize that Jaws has received $100,000 and must make 12 monthly payments of $9,000:

PV =
100,000 =

Enter in n = 12, PV = 100000, and pmt = -9000 in a financial calculator, we find the monthly rate to be 1.2043%, which converts to an effective annual rate of 15.45 percent:

(1.012043)12 - 1.0 = 0.1545 = 15.45%,

which is close to the 16 percent approximate annual interest rate.

If the loan were for 90 days:

1. Simple interest. The brothers would have had to pay (0.08/4)($100,000) = 0.02($100,000) = $2,000 in interest after 3 months, plus repay the principal. In this case the nominal 2 percent rate must be converted to an annual rate, and the effective annual rate is 8.24 percent:

EARsimple = (1.02)4 - 1 = 1.0824 - 1 = 0.0824 = 8.24%.

In general, the shorter the maturity (within a year), the higher the effective cost of a simple loan.

2. Discount interest. If jaws borrows $100,000 face value at a nominal rate of 8 percent, discount interest, for 3 months, then m = 12/3 = 4, and the interest payment is (0.08/4)($100,000) = $2,000, so

EARdiscount =
= (1.0204)4 - 1 = 0.0842 = 8.42%.

Discount interest imposes less of a penalty on shorter-term than on longer-term loans.




3. Discount interest with compensating balance. Everything is the same as in #2 above, except that we must add the compensating balance term to the denominator.

EAR =
= (1.0227)4 - 1 = 0.0941 = 9.41%


g. How large would the loan actually be in each of the cases in part f?

Answer: Simple interest. The face value of the loan would be $100,000.

Discount interest. The face value of the loan is calculated as:

Face value = = = $108,695.65.

Discount interest with compensating balance. The face value of the loan is calculated as:

Face value = = = $121,951.22.

Installment loan. The face value of the loan is $100,000. Note that jaws would only have full use of the $100,000 for the first month and, over the course of the year, it would only have approximate use of $100,000/2 = $50,000.

Quarterly basis: simple interest. The face value of the loan is $100,000.

Discount interest. The face value is calculated as:

Face value = = = $102,040.82.
Discount interest with compensating balance. The face value of the loan is calculated as:

Face value = = = $113,636.36.