Solution manual financial management 10e by keown chapter 20

CHAPTER 20

Accounts Receivable and
Inventory Management
CHAPTER ORIENTATION
The investment of funds in accounts receivable inventory involves a trade-off between
profitability and risk. For accounts receivable, this trade-off occurs as less creditworthy
customers with a higher probability of bad debts are taken on to increase sales. With
respect to inventory management, a larger investment in inventory leads to more efficient
production and speedier delivery, hence, increased sales. However, additional financing to
support the increase in inventory and increased handling and carrying costs is required. In
addition, the concept of total quality management and single-sourcing have had a major
impact on inventory purchasing.

CHAPTER OUTLINE
I.

Accounts receivable
A.

Typically, accounts receivable account for just over 20 percent of a firm's
assets.

B.

The size of the investment in accounts receivable varies from industry to
industry and is affected by several factors including the percentage of credit
sales to total sales, the level of sales and the credit and collection policies,
more specifically the terms of sale, the quality of customers and collection
efforts.

C.

Although all these factors affect the size of the investment, only the credit
and collection policies are decision variables under the control of the
financial manager.

D.

The terms of sale are generally stated in the form a/b net c, indicating that
the customer can deduct a percentage if the account is paid within b days;
otherwise, the account must be paid within c days.

240


E.

If the customer decides to forgo the discount and not pay until the final
payment date, the annualized opportunity cost of passing up this a%
discount and withholding payment until the cth day is determined as follows:
annualized opportunity
cost of forgoing the
discount

=

a
1 a

x

360
c b

Example: Given the trade credit terms of 2/10, net 30, what is the annualized
opportunity cost of passing up the 2 percent discount and withholding
payment until the 30th day?
Solution: Substituting the values from the example, we get
36.73% =
F.

A second decision variable in determining the size of the investment in
accounts receivable in addition to the trade credit terms is the type of
customer.
1.

G.

H.

0.02
360
x
1  0.02
30  10

The costs associated with extending credit to lower-quality
customers include:
a.

Increased costs of credit investigation

b.

Increased probability of customer default

c.

Increased collection costs

Analyzing the credit application is a major part of accounts receivable
management.
1.

Several avenues are open to the firm in considering the credit rating
of an applicant. Among these are financial statements, independent
credit ratings and reports, bank references, information from other
companies, and past experiences.

2.

One commonly used method for credit evaluation is called credit
scoring and involves the numerical evaluation of each applicant in
which an applicant receives a score based upon the answers to a
simple set of questions. The score is then evaluated relative to a
predetermined standard, its level relative to that standard determining
whether or not credit scoring should be extended to the applicant.
The major advantage of credit scoring is that it is inexpensive and
easy to perform.

The key to maintaining control over the collection of accounts receivable is
the fact that the probability of default increases with the age of the account.
1.

One common way of evaluating the current situation is ratio
analysis.
a.

examining the average collection period

b.

ratio of receivables to assets
241


c.
d.
e.

II.

ratio of credit sales to receivables (accounts receivable
turnover ratio)
amount of bad debts relative to sales over time
aging of accounts receivable schedule

I.

Once delinquent accounts have been identified, the third and final variable is

determined by the firm’s collection policies. A direct trade-off does exist
between collection expenses and lost goodwill on one hand and
noncollection of accounts on the other, and this trade-off is always part of
making the decision.

J.

Credit should be extended to the point that marginal profitability on
additional sales equals the required rate of return on the additional costs we
have to consider investment in inventories + receivables + change in cost of
cash discount to generate those sales.

Inventory
A.

Typically, inventory accounts for about four to five percent of a firm's
assets.

B.

The purpose of carrying inventories is to uncouple the operations of the
firm; that is, to make each function of the business independent of each
other function.

C.

As such, the decision with respect to the size of the investment in inventory
involves a basic trade-off between risk and return.

D.

The risk comes from the possibility of running out of inventory if too little
inventory is held, while the return aspect of this trade-off results because
increased inventory investment costs money.

E.

There are several general types of inventory.
1.
Raw materials inventory consists of the basic materials that have
been purchased from other firms to be used in the firm's production
operations. This type of inventory uncouples the production function
from the purchasing function.
2.
Work in process inventory consists of partially finished goods that
require additional work before they become finished goods. This type
of inventory uncouples the various production operations.
3.
Finished goods inventory consists of goods on which the production
has been completed but the goods are not yet sold. This type of
inventory uncouples the production and sales function.
4.
Stock of cash inventory, already discussed in some detail in
preceding chapters, serves to make the payment of bills independent
of the collection of accounts due.

F.

In order to effectively manage the investment in inventory, two problems
must be dealt with: the order quantity problem and the order point problem.

G.

The order quantity problem involves the determination of the optimal order
size for an inventory item given its expected usage, carrying, and ordering
costs.
242


H.

The economic order quantity (EOQ) model attempts to determine the order
size that will minimize total inventory costs. The EOQ is given as
Q* =
where C

=

carrying cost per unit

O

=

ordering cost per order

S

=

total demand in units over the planning period

Q*

=

the optimal order quantity in units

I.

The order point problem attempts to answer the following question: How
low should inventory be depleted before it is reordered?

J.

In answering this question two factors become important:
1.

What is the usual procurement or delivery time and how much stock
is needed to accommodate this time period?

2.

How much safety stock does the management desire?

K.

Modification for safety stocks is necessary since the usage rate of inventory
is seldom stable over a given timetable.

L.

This safety stock is used to safeguard the firm against changes in order time
and receipt of shipped goods.

M.

The greater the uncertainty associated with forecasted demand or order time,
the larger the safety stock.
1.

The costs associated with running out of inventory will also
determine the safety stock levels.

2.
N.

A point is reached where it is too costly to carry a larger safety stock
given the associated risk.
Inflation can also have an impact on the level of inventory carried.
1.
Goods may be purchased in large quantities in anticipation of price
rises.
2.

O.

The cost of carrying goods may increase, causing a decline in Q*,
the optimal order quantity.

The just-in-time inventory control system is more than just an inventory
control system; it is a production and management system.
1.

Under this system, inventory is cut down to a minimum, and the time
and physical distance between the various production operations is
also minimized.

243


III.

2.

Actually the just-in-time inventory control system is just a new
approach to the EOQ model which tries to produce the lowest
average level of inventory possible.

3.

Average inventory is reduced by locating inventory supplies in
convenient locations and setting up restocking strategies that cut
time and thereby reduce the needed level of safety stock.

TQM and Inventory Purchasing management.
A.

The concept of total quality management has led to strong customer-supplier
relationships in an effort to increase quality.

B.

In many cases firms that only a few years ago placed an upper limit of 10 or
20 percent on the purchases of any part from a single supplier now rely on a
single supplier using the single-sourcing relationship.

C.

Single sourcing ties the interests of the supplier to the firm to which it
supplies and allows the supplier to provide input on production techniques
that might improve quality.

D.

Financially, the TQM view argues that higher quality will result in increased
sales and market share and as a result the traditional economic analysis of
inventory management is flawed.

ANSWERS TO
END-OF-CHAPTER QUESTIONS
20-1. The size of the investment in accounts receivable is determined primarily by these
factors:
(1)

The percentage of credit sales to total sales. While this factor plays a major
role in determining the investment in accounts receivable, it is generally not
within the control of the financial manager. In essence, the nature of the
business tends to determine the blend between credit sales and cash sales.

(2)

The level of sales. As sales increase, so will accounts receivable. Again,
this is not an effective decision tool.

(3)

Credit and collection policies. Specifically the terms of sale, the quality of
customer, and collection efforts are determinants of the level of investment
in receivables that are under the control of the financial manager.

20-2. (a)

1/20 net 50 means a 1 percent discount can be taken if the account is paid
within 20 days; otherwise, it can be paid within 50 days.

(b)

2/30 net 60 means a 2 percent discount can be taken if the account is paid
within 30 days; otherwise, it must be paid within 60 days.

(c)

Net 30 means there are no discounts offered and the account must be paid
within 30 days.

244


(d)

2/10, 1/30 net 60 means a two percent discount can be taken if the account is
paid within 10 days, and if paid after 10 days but before and up to 30 days, a
one percent discount can be taken; otherwise, the account must be paid within
60 days.

20-3. The purpose of an aging account is to provide a breakdown both in dollars and
percentage terms of the proportion of receivables that are past due. The same
function could essentially be handled through ratio analysis, provided accounts
receivable were broken down according to when they were due. However, an aging
account provides control over past due accounts in an extremely efficient manner.
20-4. If a credit manager experienced no bad debt losses over the past year, then credit
was probably not extended to enough customers. Ideally credit should be extended
to the point where marginal revenue from added sales due to increased credit is
equal to the marginal costs associated with increased bad debts, costs of
investigation, costs of collection, and increased required rate of return. Obviously
the credit manager was nowhere near this level if no bad debts were incurred.
20-5. Credit scoring involves the numerical evaluation of credit applicants based upon
their answers to simple questions. This score is then evaluated relative to a
predetermined standard, many times generated through the use of multiple
discriminant analysis; its level relative to the standard determining whether or not
credit should be extended to the applicant. The major advantage of credit scoring is
that it is inexpensive and easy to perform. Once standards are set, a computer or
clerical worker without specialized training can easily evaluate applicants.
20-6. The returns associated with a more liberal credit policy come from the fact that
extending credit to weaker customers or liberalizing the trade credit terms will
probably increase sales, resulting in a larger profit level. The risks involved largely
result from the increased possibility of extending credit that will eventually become
bad debts.
20-7. The logic behind marginal analysis is to examine the incremental or marginal

benefits, and incremental costs associated with any change in the credit policy; and
if this change produces more benefits than costs, the change should be made. If,
however, the incremental costs are greater than the incremental benefits, the
proposed change should be dropped.
20-8. The purpose of carrying inventories is to uncouple the operations of the firm; that
is, to make each function of the business independent of each other's function. By
uncoupling the various operations of the firm, delays or shutdowns in one area no
longer affect the production and sale of the final product. Raw materials inventory,
for example, uncouples the production function from the purchasing function.
Work in process inventory uncouples the various production operations.
20-9. Yes. The stock of cash carried by a firm is simply a special type of inventory. In
terms of uncoupling the various operations of the firm, the purpose of holding cash
is to make the payment of bills independent of the collection of accounts due.

245


20-10. In order to effectively control the investment in inventory, the firm must: (1)
determine the optimal order size for the inventory item, given its expected usage,
carrying, and ordering costs; (2) determine how low inventory should be allowed to
deplete before it is reordered.
20-11. The major assumptions of the EOQ model include:
(1) Constant or uniform demand.
(2) Constant unit price regardless of amount ordered.
(3) Constant carrying costs per unit.
(4) Constant ordering costs per order regardless of the size of the order.
(5) Instantaneous delivery.
(6) Independent orders.
20.12. The risk associated with the inventory investment is that if the level of inventory is
too low, the various functions of business will not be effectively uncoupled, and

delays in production and customer delivery will result. The return aspects of this
trade-off result because increased inventory investment costs money. As the size of
the inventory increases, the storage and handling cost, in addition to the required
rate of return on capital invested in inventory, will rise. Thus, the more inventory
the firm holds, the less risk they run of stocking out of inventory and the greater are
their inventory expenses.
20.13. Inflation affects the EOQ model by increasing carrying costs (C) which results in a
small EOQ level. In addition, if inflation is accompanied by major periodic price
increases, this may cause the EOQ model to lose its applicability and be replaced by
a policy of anticipatory buying; that is, buying in anticipation of a price increase in
order to secure the goods at a lower cost.
20-14. With single-sourcing, a company uses very few suppliers or, in many cases, a single
supplier as a source for a particular part or material. In this way the company has a
more direct influence and control over the quality performance of a supplier, since
the company accounts for a larger proportion of the supplier's volume. The
company and supplier can then enter into a partnership where the supplier agrees to
meet the quality standards of the customer. In this way the supplier can be brought
into the TQM program of the customer.
20-15. The TQM view argues that the traditional analysis is flawed in that it ignores the
fact that increased sales and market share result from better quality products and
that this increase in sales will more than offset the higher costs associated with
increased quality. In effect, it is argued that the benefits from quality improvement
are underestimated.

246


SOLUTIONS TO
END-OF-CHAPTER PROBLEMS
Solutions to Problem Set A

a
360
x
1 a
c b

20-1A.

where a
b
c

=
=
=

amount of the discount
the discount period
the net period

0.02
360
x
1  0.02
50  10

= 18.37%

a
360

x
1 a
c b

20-2A.

where a
b
c

=
=
=

amount of the discount
the discount period
the net period

0.02
360
x
1  0.02
30  20

= 73.47%

20-3A.
a
360
x

1 a
c b
where a
b
c

=
=
=

(a)

0.01
x
1  0.01

360
20  10

=

36.36%

(b)

0.02
1  0.02

360
30  10

=

36.73%

(c)

0.03
360
x
1  0.03
30  10

=

55.67%

(d)

0.03
360
x
1  0.03
60  10

=

22.27%

x

amount of the discount
the discount period
the net period

247


(e)

0.03
360
x
1  0.03
90  10

=

13.92%

(f)

0.05
360
x
1  0.05
60  10

=

37.89%

20-4A.
Applicant #1
Z =
Z =
Z =

3.3(0.2) + 1.0(0.2) + 0.6(1.2) + 1.4(0.3) + 1.2(0.5)
0.66 + 0.2 + 0.72 + 0.42 + 0.6
2.6 < 2.7 thus, reject

Applicant #2
Z =
Z =
Z =

3.3(0.2) + 1.0(0.8) + 0.6(1.0) + 1.4(0.3) + 1.2(0.8)
0.66 + 0.8 + 0.6 + 0.42 + 0.96
3.44 > 2.7 thus, accept

Applicant #3
Z =
Z =
Z =

3.3(0.2) + 1.0(0.7) + 0.6(0.6) + 1.4(0.3) + 1.2(0.4)
0.66 + 0.7 + 0.36 + 0.42 + 0.48
2.62 < 2.7 thus, reject

Applicant #4
Z =
Z =
Z =

3.3(0.1) + 1.0(0.4) + 0.6(1.2) + 1.4(0.4) + 1.2(0.4)
0.33 + 0.4 + 0.72 + 0.56 + 0.48
2.49 < 2.7 thus, reject

Applicant #5
Z =
Z =
Z =

3.3(0.3) + 1.0(0.7) + 0.6(0.5) + 1.4(0.4) + 1.2(0.7)
0.99 + 0.7 + 0.30 + 0.56 + 0.84
3.39 > 2.7 thus, accept

Applicant #6
Z =
Z =
Z =

3.3(0.2) + 1.0(0.5) + 0.6(0.5) + 1.4(0.4) + 1.2(0.4)
0.66 + 0.5 + 0.30 + 0.56 + 0.48
2.5 < 2.7 thus, reject

20-5A.
(a)

Sales  cost of goods sold
Sales

=

Gross Profit Margin

$600,000  Cost of goods sold
$600,000

=

0.10

Cost of goods sold

=

$540,000

248


(b)

(c)

(d)

Cost of goods sold

Average inventory

=

Inventory turnover ratio

$540,000
Average inventory

=

6

Average inventory

=

$90,000

Inventory turnover ratio

=

360
Average Collection Period

Inventory turnover

=

Inventory turnover ratio

=

9 times

Cost of goods sold
Average inventory

=

9 times

$480,000
Average inventory

=

9 times

Average inventory

=

$53,333

Cost of goods sold
Average inventory

=

Inventory turnover ratio

$1,150,000
Average inventory

=

5

Average inventory

=

$230,000

(1 - Gross profit margin) (Sales)

=

(0.86)($25,000,000)

Cost of Goods Sold

=

$21,500,000 cost of goods

=

8 times

$21,500,000
Average inventory

=

8 times

Average inventory

=

$ 2,687,500

Inventory turnover ratio =

20-6A.

Step 1:

360
45

Estimate the Change in Profit.

249


=

=
=
Step 2:

($1,000,000 x .20) - ($1,000,000 x .08)
$200,000 - $80,000
$120,000

Estimate the cost of additional investment in accounts receivable
and inventory.
Estimate the additional investment in accounts receivable:
=
=
=

($6,000,000 / 360) x 90 - ($5,000,000 / 360) x 60
$1,500,000 - $833,333
$666,667

Additional accounts receivable and inventory times the required
rate of return:
=
=
Step 3:

Estimate the change in the cost of the cash discount
=

Step 4:

($666,667 + $50,000) .15
$107,500

$0 (no change)

Compare incremental revenues with incremental costs.
=
=
=

Step 1 - (Step 2 + Step 3)
$120,000 - $107,500
$12,500

The policy should be adopted.
20-7A.

Step 1:

Estimate the Change in Profit.
=
=
=

Step 2:

($1,500,000 x .20) - ($1,500,000 x .09)
$300,000 - $135,000
$165,000

Estimate the cost of additional investment in accounts receivable
and inventory.
Estimate the additional investment in accounts receivable:
=
=
=

($12,500,000 / 360) x 45 - ($11,000,000 / 360) x 30
$1,562,500 - $916,667
$645,833

Additional accounts receivable and inventory times the required
rate of return:
250


=
=
Step 3:

($645,833 + $75,000) .15
$108,125

Estimate the change in the cost of the cash discount
=

Step 4:

$0 (no change)

Compare the incremental revenues with the incremental costs.
=
=
=

Step 1 - (Step 2 + Step 3)
$165,000 - $108,125
$56,875

The policy should be adopted.
20-8A.
(a)

Q*

=

2SO
C

=

2(3000)10
0.10

=

600,000

=

(b)

775 units

Total costs

=

S
Q
  C +   O
2
Q

Order one time:

=

 3000 
 3000 

 $.10 + 
 $10
 2 
 3000 

=

$150 + $10

=

$160

Order four times: =

 750 
 3000 

 $.10 + 
 $10
 2 
 750 

=

$37.50 + $40

=

$77.50

251


 600 
 3000 

 $.10 + 
 $10

 2 
 600 

Order five times: =
=

$30.00 + $50.00

=

$80
 300 
 3000 

 $0.10 + 
 $10
 2 
 300 

Order ten times: =

Order 15 times:

(c)

(1)
(2)
(3)
(4)
(5)

(6)

(a)

Q*

=

$15.00 + $100

=

$115

=

 200 
 3000 

 $0.10 + 
 $10
 2 
 200 

=

$10 + $150

=

$160

constant or uniform demand
constant unit price
constant carrying costs
constant ordering costs
instantaneous delivery
independent orders

20-9A.
=

2SO
C

=

2(20,000)50
0.25

=
(b)

2828 boxes

It assumes among other things that the rolls are not perishable.
assumptions include:
(1) constant or uniform demand
(2) constant unit price
(3) constant carrying costs

(4) constant ordering costs
(5) instantaneous delivery
(6) independent orders

252

Other


20-10A.
(a)

Q*

=

2SO
C
2(50,000)500
75

=
=
(b)

816.4967 units or 816 units

Total costs

=

S
Q
  C +   O
2
Q

=

 816 
 50,000 

 $75 + 
 $500
 2 
 816 

=

$30,600 + $30,637

=

$61,237

Note that carrying cost ($30,600) differs from ordering cost ($30,637) due to a $37
rounding error. Recall that Q* was rounded down by .4967 units.
20-11A.
(a)

Q*

=

2SO
C

=

2(500,000)90
.40

=

15,000 Units

(b)

500,000
15,000

(c)

Inventory order point = delivery time stock + safety stock

(d)

=

Average inventory

33 1/3 orders per year

=

1
x 500,000 + 15,000
50

=

10,000 + 15,000

=

25,000 units

=

EOQ
+ safety time stock
2

=

15,000
+ 15,000
2

=

7,500 + 15,000

=

22,500 units

253


20-12A.
(a)

EOQ

=

2SO
C

=

2(500,000)(100)
.50

=

14,142 units: but since orders must be placed in 200unit lots, the effective EOQ becomes 14,200 units

=

35.2 orders per year

(b)

500,000
14,200

(c)

Inventory order point = Delivery time stock + safety stock

(d-a)

EOQ

=

=

4
50

=

40,000 + 5,000

=

45,000 units

x 500,000 + 5,000

2(500,000)(100)
2.5

=

6,324.5 =

=

6,325 units, but since orders must be placed in 200 unit
lots the effective EOQ becomes 6,400

=

78.1 orders per year

(d-b)

500,000
6,400

(d-c)

4
x 500,000 + 5,000
50
=

40,000 + 5,000

=

45,000 units

6,325

(d-d) Yes, as carrying costs rise the EOQ level drops and the number of orders per
year rises which means that on average less inventory will be kept on hand.

254


SOLUTION TO INTEGRATIVE PROBLEM
Accounts Receivable
1.

2.

The size of the investment in accounts receivable is determined primarily by these
factors:
(a)

The percentage of credit sales to total sales. While this factor plays a major
role in determining the investment in accounts receivable, it is generally not
within the control of the financial manager. In essence, the nature of the
business tends to determine the blend between credit sales and cash sales.

(b)

The level of sales. As sales increase, so will accounts receivable. Again,
this is not an effective decision tool.

(c)

Credit and collection policies. Specifically the terms of sale, the quality of
customer, and collection efforts are determinants of the level of investment
in receivables that are under the control of the financial manager.

(a)

a
360
x
1 a
c b
where a
b
c
x

3.

(a)

=
=
=

= 18.18%

a
360
x
1 a
c b
where a
b
c
x

4.

Step 1:

Step 2:

=
=
=

amount of the discount
the discount period
the net period

= 24.49%
Estimate the Change in Profit.
=

=
=

5.

amount of the discount
the discount period
the net period

($1,000,000 x .25) - ($1,000,000 x .08)
$250,000 - $80,000
$170,000

Estimate the cost of additional investment in account receivable and
inventory.
Estimate the additional investment in accounts receivable:
=
=
=

($8,000,000 / 360) x 75 - ($7,000,000 / 360) x 60
$1,666,667 - $1,166,667
$500,000

255


Additional accounts receivable and inventory times the required rate of
return:
=

=
6.

Step 3:

Estimate the change in the cost of the cash discount
=
=
=

7.

Step 4:

($500,000 + $50,000) .15
$82,500
($8,000,000 x .02 x .50) - ($7,000,000 x .01 x .50)
$80,000 - $35,000
$45,000

Compare the incremental revenues with the incremental costs.
=
=
=

Step 1 - (Step 2 + Step 3)
$170,000 - ($82,500 + $45,000)
$42,500

The policy should be adopted.

Inventory Management

1.

EOQ

=

2SO
C

=

2(250,000)100
1

=

7,071 units or 7,100 units

=

35.2 orders per year

2.

250,000
7,100

3.

Inventory order point = Delivery time stock + safety stock

4.

Average inventory

=

1
x 250,000 + 5,000
50

=

5,000 + 5,000

=

10,000 units

=

EOQ
2

=

7,100
+ 5,000

2

=

8,550 units

+ Safety stock

256


5.

EOQ

Elasticity of
EOQ with
respect to a
double in sales

6.

EOQ

Elasticity of
EOQ with
respect to a
double in
carrying costs

7.

EOQ

Elasticity of
EOQ with
respect to a
double in
ordering costs

=

2(500,000)100
1

=

10,000 units

=

% Δ EOQ
% Δ Sales

=

Δ EOQ
EOQ
Δ Sales
Sales

=

 10,000  7,100 
 500,000  250,000 

 / 

7,100
250,000





=

.4085
1.0

=

= .4085 or 40.85%

2( 250,000)100
2

=

5,000

=

%  EOQ
%  Carrying Costs

=

5,000  7,100
7,100
= -29.58%
2 1
1

=

2(250,000)200
1

=

10,000

=

%  EOQ
%  Ordering Costs

257

=

10,000  7,100
7,100
= 40.85%
200  100
100

8.

The selling price of the item does not enter the EOQ equation and does not affect
the level of EOQ. The EOQ equation attempts to minimize costs and as such the
selling price does not enter into its calculation; thus the elasticity of EOQ with
respect to the selling price is 0.

9.

The major assumptions of the EOQ model include:
(1)
(2)
(3)
(4)
(5)
(6)

Constant or uniform demand.
Constant unit price regardless of amount ordered.
Constant carrying costs per unit.
Constant ordering costs per order regardless of the size of the order.

Instantaneous delivery.
Independent orders.

10.

Inflation affects the EOQ model by increasing carrying costs (C) which results in a
small EOQ level. In addition if inflation is accompanied by major periodic price
increases this may cause the EOQ model to lose its applicability and be replaced by
a policy of anticipatory buying, that is, buying in anticipation of a price increase in
order to secure the goods at a lower cost.

11.

A decrease in the average delivery time decreases the inventory order point.
Inventory can be ordered when there is a lower level of inventory. Safety stock
may also be reduced. The total level of inventory held will decrease in this
situation.

12.

If ordering costs decrease, then it is more economical to order more often and the
EOQ decreases. This in turn means that less inventory on average will be held.

Solutions to Problem Set B
20-1B.

a
360
x
1 a

c b
where a
b
c

=
=
=

0.02
360
x
1  0.02
60  10

amount of the discount
the discount period
the net period
= 14.69%

258


a
360
x
1 a
c b

20-2B.

where a
b
c
x

=
=
=

amount of the discount
the discount period
the net period

= 36.73%

a
360
x
1 a
c b

20-3B.

where a

=

amount of the discount

b

=

the discount period

c

=

the net period

(a)

0.01
360
x
= 24.24%
1  0.01
20  5

(b)

0.02
360
x
= 10.50%
1  0.02
90  20

(c)

0.01
360
x
= 4.55%
1  0.01
100  20

(d)

0.04
360
x
= 37.50%
1  0.04
50  10

(e)

0.05
360
x
= 23.68%
1  0.05
100  20

(f)

0.05

360
x
= 94.74%
1  0.05
50  30

259


20-4B. Applicant #1
Z

=

3.3(0.3) + 1.0(0.4) + 0.6(1.2) + 1.4(0.3) + 1.2(0.5)

Z

=

0.99 + 0.4 + 0.72 + 0.42 + 0.6

Z

=

3.13 > 2.7 thus, accept

Z

=

3.3(0.2) + 1.0(0.6) + 0.6(1.3) + 1.4(0.4) + 1.2(0.3)

Z

=

0.66 + 0.6 + 0.78 + 0.56 + 0.36

Z

=

2.96 > 2.7 thus, accept

Z

=

3.3(0.2) + 1.0(0.7) + 0.6(0.6) + 1.4(0.3) + 1.2(0.2)

Z

=

0.66 + 0.7 + 0.36 + 0.42 + 0.24

Z

=

2.38 < 2.7 thus, reject

Z

=

3.3(0.1) + 1.0(0.5) + 0.6(1.8) + 1.4(0.5) + 1.2(0.4)

Z

=

0.33 + 0.5 + 1.08 + 0.7 + 0.48

Z

=

3.09 > 2.7 thus, accept

Z

=

3.3(0.5) + 1.0(0.7) + 0.6(0.5) + 1.4(0.4) + 1.2(0.6)

Z

=

1.65 + 0.7 + 0.30 + 0.56 + 0.72

Z

=

3.93 > 2.7 thus, accept

Z

=

3.3(0.2) + 1.0(0.4) + 0.6(0.2) + 1.4(0.4) + 1.2(0.4)

Z

=

0.66 + 0.4 + 0.12 + 0.56 + 0.48

Z

=

2.22 < 2.7 thus, reject

Applicant #2

Applicant #3

Applicant #4

Applicant #5

Applicant #6

260


20-5B. (a)

(b)

Sales  cost of goods sold
Sales

=

Gross Profit Margin

$550,000  Cost of goods sold
$550,000

=

0.10

Cost of goods sold

=

$495,000

Cost of goods sold
Average inventory

=

Inventory turnover ratio

$495,000
Average inventory

=

5

Average inventory

=

$99,000

Inventory turnover ratio

=

360

Average Collection Period

Inventory turnover

=

360
35

Inventory turnover ratio

=

10.286 times

Cost of goods sold
Average inventory

=

10.286 times

$480,000
Average inventory

=

10.286 times

Average inventory

=

$46,665.37

=

Inventory turnover ratio

$1,250,000
Average inventory

=

6

Average inventory

=

$208,333

(c)

261


(d)

20-6B. Step 1:

Step 2:

(1 - Gross profit margin) (Sales)

=

cost of goods

(0.85)($25,000,000)

=

$21,250,000

Inventory turnover ratio =

=

7.2 times

$21,250,000
Average inventory

=

7.2 times

Average inventory

=

$ 2,951,389

Estimate the Change in Profit.
=

($1,000,000 x .20) - ($1,000,000 x .08)

=

$200,000 - $80,000

=

$120,000

Estimate the cost of additional investment in accounts receivable and
inventory.
Estimate the additional investment in accounts receivable:
=

($7,000,000 / 360) x 90 - ($6,000,000 / 360) x 40

=

$1,750,000 - $666,667

=

$1,083,333

Additional accounts receivable and inventory times the required rate of
return:

Step 3:

=

($1,083,333 + $40,000) .15

=

$168,500

Estimate the change in the cost of the cash discount
=

Step 4:

$0 (no change)

Compare the incremental revenues with the incremental costs.
=

Step 1

-

(Step 2 + Step 3)

=

$120,000 - $168,500

=

- $48,500

The policy should not be adopted.

262


20-7B. Step 1:

Estimate the Change in Profit.

Step 2:

=

($1,000,000 x .20) - ($1,000,000 x .08)

=

$200,000 - $80,000

=

$120,000

Estimate the cost of additional investment in accounts receivable and
inventory.
Estimate the additional investment in accounts receivable:
=

($18,000,000 / 360) x 50 - ($17,000,000 / 360) x 30

=

$2,500,000 - $1,416,667

=

$1,083,333

Additional accounts receivable and inventory times the required rate of
return:

Step 3:

=

($1,083,333 + $60,000) .15

=

$171,500

Estimate the change in the cost of the cash discount
=

Step 4:

$0 (no change)

Compare the incremental revenues with the incremental costs.
=

Step 1 - (Step 2 + Step 3)

=

$120,000 - $171,500

=

- $51,500

The change should not be made.
20-8B.
(a)

Q*

=

2SO
C

=

2(3500)9
0 .2

=

315,000

=

561.2 units

263


(b)

Total costs

S
Q
=   C +   O
2
Q

Order one time:

=

 3500 
 3500 

 $.20 + 
 $9
 2 
 3500 

=

$350 + $9

=

$359

=

 875 
 3500 

 $.20 + 
 $9
 2 
 875 

=

$87.50 + $36

=

$123.50

=

 700 
 3500 

 $.20 + 
 $9
 2 
 700 

=

$70.00 + $45.00

=

$115

=

 350 
 3500 

 $0.20 + 
 $9

 2 
 350 

=

$35.00 + $90

=

$125

=

 234 
 3500 

 $0.20 + 
 $9
 2 
 234 

=

$23.40 + $134.62

=

$158.02

Order four times:

Order five times:

Order ten times:

Order 15 times:

(c)

20-9B.

(1)
(2)
(3)
(4)
(5)
(6)

constant or uniform demand
constant unit price
constant carrying costs
constant ordering costs
instantaneous delivery
independent orders

(a)

Q*
=

2(21,000)55
0.20

=

3,398.5 boxes

264

=

2SO
C