Answers and Solutions: 27 – 1
Chapter 27
Providing and Obtaining Credit
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
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.
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.
Answers and Solutions: 27 – 2
27-5 AR Sales Profit
a. The firm tightens its credit
standards. – – 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.
d. If the credit manager gets tough with past due accounts, sales will decline, as will
accounts receivable.
Answers and Solutions: 27 – 3
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
27-1 $25,000 interest-only loan, 11% nominal rate. Interest calculated as simple interest based
on 365-day year. Interest for 1st month = ?
27-2 $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 =
12
650,1$000,15$+
= $1,387.50.
Answers and Solutions: 27 – 4
27-3 a. Effective rate = 12%.
b. 0 1
| |
50,000 -50,000
2.01
−
= $62,500. The effective interest rate will still be 11.25%.
c. 0 1
| |
50,000 -50,000
– 4,375 (discount interest) 7,500
i = ?
i = ?
d. Approximate annual rate =
)/2000,50($
)000,50)($08.0(
=
000,25$
000,4$
= 16%.
Alternative b has the lowest effective interest rate.
27-4 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
Note that, if Gifts Galore actually needs $1,500,000 of funds, it will have to borrow
2.00225.01
000,500,1$
−−
=
7775.0
000,500,1$
= $1,929,260.45. The effective interest rate will still
be 12.088% ≈ 12.09%.
c. Installment loan:
27-5 Analysis of change:
Projected Income Projected Income
Statement Effect of Statement
Under Current Credit Policy Under New
Credit Policy Change Credit Policy
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
27-6 Analysis of change:
Projected Income Projected Income
Statement Effect of Statement
Under Current Credit Policy Under New
Credit Policy Change Credit Policy
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:
Answers and Solutions: 27 – 8
27-7 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%.
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%.
Answers and Solutions: 27 – 9
27-8 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.
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
$198,000 100%
27-9 a. Malone’s current accounts payable balance represents 60 days purchases. Daily
purchases can be calculated as
60
500$
= $8.33.
Answers and Solutions: 27 – 10
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.
c. Nonfree Trade Credit:
Nominal annual cost:
period
Discount
goutstandin is
credit Days
360
% Discount100
%Discount
−
−
=
20
360
99
1
= 18.18%.
0 1
| |
384.62 -384.62
-57.69 Discount interest +76.92
-76.92 Compensating balance -307.70
250.00
0 1
| |
641.03 -641.03
-96.15 Discount interest +128.21
-128.21 Compensating balance -512.82
416.67
Answers and Solutions: 27 – 12
d. Pro Forma Balance Sheet (Thousands of Dollars):
Casha $ 126.9 Accounts payable $ 250.0
Accounts receivable 450.0 Notes payableb 434.6
Answers and Solutions: 27 – 13
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
Face amount of loan =
0.65
5$251,515.1
0.200.151
5$251,515.1 =
−−
= $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
Answers and Solutions: 27 – 14
27-10 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.
rate
Nominal
=
98
2
30
360
= 24.49 ≈ 24.5%.
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:
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
Answers and Solutions: 27 – 15
SOLUTION TO SPREADSHEET PROBLEMS
27-11 The detailed solution for the spreadsheet problem, Ch27 P11 Build a Model Solution.xls,
is available on the textbook’s Web site.
Mini Case: 27- 16
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
Mini Case: 27 – 17
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
b. 2. What is its expected average daily sales (ADS)?
b. 3. What is its expected average accounts receivable (AR) level?
Answer: Accounts receivable (AR) = (DSO)(ADS) = 37($4,931) = $182,466. Thus, $182,466
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
Mini Case: 27- 18
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
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
Mini Case: 27 – 19
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 AR Sales ADS (AR)/(ADS)
Jan $100 $ 70
Feb 200 160
Mar 300 250 $600 $6.59 37.9
Apr 300
May 200
Jun 100
Mini Case: 27- 20
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.)
Mini Case: 27 – 21
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:
Mini Case: 27- 22
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) AR % AR %
0 – 30 $210 84%
31 – 60 40 16
61 – 90 0 0
$250 100%
Answer: Aging schedule:
Age of account March June
(days) AR % AR %
0 – 30 $210 Mar 84% $ 70 Jun 64%
Mini Case: 27 – 23
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
Month
Sales
Contribution
to AR
AR–to–
Sales Ratio
Month
Sales
Contribution
to A/R
AR–to–
Sales
Ratio
January
$100
$ 0
0%
April
February
200
40
20
May
March
300
210
70
June
Answer: Uncollected balances schedules:
Contribution to Ratio of month’s
Month Sales end-of-period AR AR to month’s sales
(1) (2) (3) (4)
Jan $100 $ 0 0%
Mini Case: 27- 24
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 AR–to-sales ratio to receivables
Jan $150 0% $ 0
Feb 300 20 60
Mar 500 70 350
projected March 31 AR balance = $410
Apr $400
May 300
Jun 200
Projected June 30 AR 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:
Mini Case: 27 – 25
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.
Mini Case: 27- 26
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 =
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
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.
Mini Case: 27 – 27
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) =
Mini Case: 27- 28
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
Mini Case: 27 – 29
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
Mini Case: 27- 30
p. The brothers need $100,000 and are considering a 1-year bank loan with a
quoted annual rate of 8%. The bank is offering the following alternatives: (1)
simple interest, (2) discount interest, (3) discount interest with a 10%
compensating balance, and (4) add-on interest on a 12-month installment loan.
What is the effective annual cost rate for each alternative? For the first three of
these assumptions, what is the effective rate if the loan is for 90 days, but
renewable? How large must the face value of the loan amount actually be in each
of the 4 alternatives to provide $100,000 in usable funds at the time the loan is
originated?
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
$100,000 principal repayment. For a 1-year simple interest loan, the nominal rate,
8 percent, is also the effective annual rate.
Mini Case: 27 – 31
Note that a timeline can also be used to calculate the effective annual rate of the
1-year discount loan:
0 1
| |
100,000 -100,000
-8,000 (discount interest)
92,000
With a financial calculator, enter N = 1, PV = 92000, PMT = 0, and FV = -100000
to solve for I/YR = 8.6957% ≈ 8.7%.
If the loan were for 90 days:
i = ?
Mini Case: 27- 32
3. If the loan is a discount loan, and a compensating balance is also required, then
the effective rate is calculated as follows:
Amount borrowed =
1.008.01
000,100$
−−
= $121,951.22.
The face value (the amount of the loan required to get the desired level
of usable funds) of the loan is calculated as:
Face value =
CB–RATE NOMINAL1
REQUIRED FUNDS
−
=
10.008.01
000,100$
−−
= $121,951.22.
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.
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%
The face value (the amount of the loan required to get the desired level of usable
funds) of the loan is $100,000. Note that the borrower would only have full use