CHAPTER 20
CREDIT AND INVENTORY MANAGEMENT
Answers to Concepts Review and Critical Thinking Questions
1.
a.
b.
c.
d.
e.
2.
Trade credit is usually granted on open account. The invoice is the credit instrument.
3.
Credit costs: cost of debt, probability of default, and the cash discount
No-credit costs: lost sales
The sum of these are the carrying costs.
4.
1.
2.
3.
Character:
Capacity:
Capital:
4.
5.
Collateral:
Conditions:
1.
2.
3.
4.
5.
6.
7.
Perishability and collateral value
Consumer demand
Cost, profitability, and standardization
Credit risk
The size of the account
Competition
Customer type
5.
A sight draft is a commercial draft that is payable immediately.
A time draft is a commercial draft that does not require immediate payment.
A bankers acceptance is when a bank guarantees the future payment of a commercial draft.
A promissory note is an IOU that the customer signs.
A trade acceptance is when the buyer accepts the commercial draft and promises to pay it in the future.
determines if a customer is willing to pay his or her debts.
determines if a customer is able to pay debts out of operating cash flow.
determines the customer’s financial reserves in case problems occur with opera-ting cash
flow.
assets that can be liquidated to pay off the loan in case of default.
customer’s ability to weather an economic downturn and whether such a down-turn is
likely.
If the credit period exceeds a customer’s operating cycle, then the firm is financing the receivables and other
aspects of the customer’s business that go beyond the purchase of the selling firm’s merchandise.
6.
a.
B:
b.
c.
A:
A:
d.
e.
B:
A:
A is likely to sell for cash only, unless the product really works. If it does, then they might grant
longer credit periods to entice buyers.
Landlords have significantly greater collateral, and that collateral is not mobile.
Since A’s customers turn over inventory less frequently, they have a longer inventory period, and
thus, will most likely have a longer credit period as well.
Since A’s merchandise is perishable and B’s is not, B will probably have a longer credit period.
Rugs are fairly standardized and they are transportable, while carpets are custom fit and are not
particularly transportable.
7.
The three main categories of inventory are: raw material (initial inputs to the firm’s production process), workin-progress (partially completed products), and finished goods (products ready for sale). From the firm’s
perspective, the demand for finished goods is independent from the demand for the other types of inventory.
The demand for raw material and work-in-progress is derived from, or dependent on, the firm’s needs for these
inventory types in order to achieve the desired levels of finished goods.
8.
JIT systems reduce inventory amounts. Assuming no adverse effects on sales, inventory turnover will increase.
Since assets will decrease, total asset turnover will also increase. Recalling the Du Pont equation, an increase
in total asset turnover, all else being equal, has a positive effect on ROE.
412
9.
Carrying costs should be equal to order costs. Since the carrying costs are low relative to the order costs, the
firm should increase the inventory level.
10. It would be a one-time boost. The drop in liquidity is not as bad as it seems since it came from inventory
reduction, and the quick ratio, for example, is unchanged. The firm decreased its leverage as well.
Solutions to Questions and Problems
Basic
1.
a.
b.
c.
30 days until account overdue; remittance: 200($60) = $12,000
3% discount; 10 day discount period; remittance: .97($12,000) = $11,640
implicit interest: $12,000 – 11,640 = $360; 30 – 10 = 20 days credit
2.
Receivables turnover = 365/70 = 5.21428571 times
Average receivables = $90 million/5.21428571 = $17,260,274
3.
a.
b.
4.
Average accounts receivable = 5 weeks’ sales = 5($20,000) = $100,000
5.
Nominal interest rate = .02/.98 = .0204 for 45 – 8 = 37 days
EAR = (1.020408)365/37 – 1 = 22.05%
a.
.03/.97 = .03093; EAR = (1.03093) 365/37 – 1 = 35.05%
b.
EAR = (1.020408)365/52 – 1 = 15.24%
c.
EAR = (1.020408)365/30 – 1 = 27.86%
6.
Receivables turnover = 365/61 = 5.9836066 times
Annual credit sales = 5.9836066($40,000) = $239,344.26
7.
Total credit sales = 3,000($400) = $1,200,000
ACP = .50(10) + .50(30) = 20 days
Receivables turnover = 365/20 = 18.25 times
Average receivables = $1,200,000/18.25 = $65,753.42
ACP = .6(10 days) + .4(30 days) = 18 days
Average balance = 1,200($2,200)(18)(12/365) = $1,562,301.37
If the firm increases the cash discount, then more people will pay sooner, thus lowering the average collection
period. If the ACP declines, receivables turnover increases, which will lead to a decrease in average
receivables.
8.
ACP = 20 + 12 = 32 days
Receivables turnover = 365/32 = 11.40625 times
Receivables = $6M/11.40625 = $526,027.40
9.
a.
b.
c.
d.
NPV = –$1.4M + (1 – .005)($1.8M)/1.03 = $338,834.95 per unit; fill the order.
NPV = 0 = –$1.4M + (1 – )($1.8M)/1.03 ;  = .1989 = 19.89%
NPV = –$1.4M + (1 – .005)($1.8M – 1.4M)/.03 = $11,866,666.67 per unit; fill the order.
NPV = 0 = –$1.4M + (1 – )($1.8M – 1.4M)/.03 ;  = .895 = 89.5%
It is assumed that if a person has paid his or her bills in the past, then they will pay their bills in the
future. This implies that if someone doesn’t default when credit is first granted, then they will be a good
customer far into the future, and the possible gains from the future business outweigh the possible losses
from granting credit the first time.
10. Cost of switching = $750(1,100) + $400(1,220 – 1,100) = $873,000
Perpetual benefit of switching = ($750 – 400)(1,220 – 1,100) = $42,000
413
NPV = –$873,000 + $42,000/.015 = $1,927,000
The firm will have to bear the cost of sales for one month before they receive any revenue from credit sales,
which is why the initial cost is for one month. Receivables will grow over the one month credit period and will
then remain about stable with payments and new sales offsetting one another.
11. Carrying costs = (2,000/2)($40) = $40,000
Order costs = (52)($1,100) = $57,200
EOQ = [2(52)(2,000)($1,100)/$40] 1/2 = 2,391.65
The firm’s policy is not optimal, since the costs are not equal. The company should increase the order size and
decrease the number of orders.
12. Carrying costs = (170/2)($45) = $3,825
Restocking costs = 52($48) = $2,496
EOQ = [2(52)(170)($48)/$45]1/2 = 137.33
Number of orders per year = 52(170)/137.33 = 64.37 times
The firm’s policy is not optimal, since the costs are not equal. The company should decrease the order size and
increase the number of orders.
Intermediate
13. Carrying costs = (Q/2)  CC ;
CC  (Q/2) = F  (T/Q)
Q2 = 2  F  T /CC
Q = [2F  T /CC]1/2 = EOQ
restocking costs = F  (T/Q)
14. Cash flow from old policy = ($70 – 40)(3,200) = $96,000
Cash flow from new policy = ($75 – 40)(3,500) = $122,500
Incremental cash flow = $122,500 – 96,000 = $26,500
NPV = –[($70)(3,200) + ($40)(3,500 – 3,200)] + $26,500/.03 = $647,333.33
15. Cash flow from old policy = ($315 – 240)(3,000) = $225,000
Cash flow from new policy = ($320 – 245)(3,100) = $232,500
Incremental cash flow = $232,500 – 225,000 = $7,500
NPV = –[($315)(3,000) + ($245 – 240)(3,000) + ($245)(3,100 – 3,000)] + ($7,500/.02) = –$609,500
Challenge
16. NPV = 0 = –($70)(3,200) – ($40)(Q – 3,200) + [($75 – 40)(Q) – ($70 – 40)(3,200)]/.03
0 = –224,000 – 40Q + 128,000 + 1,166.67Q – 3,200,000
1,126.67Q = 3,296,000; Q* = 2,925.44
17. NPV = 0 = –($70)(3,200) – ($40)(3,300 – 3,200) + [(P – 40)(3,300) – ($70 – 40)(3,200)]/.03
0 = –224,000 – 4,000 + 110,000P – 7,600,000
110,000P = 7,828,000; P* = $71.16
18. NPV = 0 = –[($315)(3,000) + ($245 – 240)(3,000) + ($245)(3,100 – 3,000)] + [(P – 245)(3,100) – ($315 –
240)(3,000)]/.02
0 = –945,000 – 15,000 – 24,500 + 155,000P – 49,225,000
155,000P = 50,209,500; P * = $323.93
19. The company places an order every five days. Number of orders per year = 365/5 = 73 times.
If an order was received before the store opened on Monday, then Monday should be included in the day count
required to determine the next point in time to reorder. The next order should be placed five days later which
would normally be after the close of business on Friday. If the supplier is not open on Friday evening and
414
assuming that the supplier is not open on the weekend, the order should be placed just before the close of
business on Friday.
APPENDIX 20A
1.
Cash flow from old policy = 50,000($562.50) = $28,125,000
Cash flow from new policy = 50,000($593.75)(1 – .09) = $27,015,625
Incremental cash flow = $27,015,625 – 28,125,000 = - $1,109,375
NPV = –$28,125,000 - $1,109,375/.04 = -$55,859,375.
Since NPV is negative the change in credit policy is not advisable.
2.
a.
b.
c.
d.
110.13/113.54 = .97; credit terms: 3/22, net 50
2,175($110.13) = $239,532.75 (at a maximum)
Since the quantity sold does not change, variable cost is the same under either plan.
No, because d –  = 3.0003 – 12 = –9%, the NPV will be negative; NPV = –2,175($110.13) +
(2,175)($113.54)(.03003 – .12)/(.015) = –$1,720,736.
The breakeven credit price is P(1 + r)/(1 – ) = $110.13(1.015)/(.88) = $127.02, which implies that the
breakeven discount is 1 – (110.13/127.02) = 13.3%.
NPV = –2,175($110.13) + (2,175)($127.02)(.133 – .12)/(.015)  0 Small difference due to rounding
3.
a.
b.
c.
NPV = –18($1,920) + (1 – .24)(18)($2,700)/1.02 = $1,651.76; the order should be taken.
NPV = 0 = –18($1,920) + (1 – )(18)($2,700)/1.02;  = .2747 = 27.47%
Effectively, the cash discount is $300/$2,700 = 11.11%. Since the discount rate is less than the default
rate, credit should not be granted. The firm would be better off taking the $2,400 up-front than taking a
76% chance of making $2,700.
4.
a.
Cash discount = 1 – ($40/$43) = 6.98%
Default probability = 1 – .90 = .10
Since the default probability is greater than the cash discount, credit should not be granted; the NPV of
doing so is negative.
Due to the increase in both quantity sold and credit price when credit is granted, an additional
incremental cost is incurred of (3,630)($23 – 19) + (3,850 – 3,630)($23) = $19,580.
NPV = 0 = –$19,580 – (3,630)($40) + {3,850[(1 – .10)P – $23] – 3,630($40 – 19)}/(1.008399/30 – 1);
164,780(0.02765) + 76,230 = 3,465P – 88,550; P = $48.87
NPV = 3,630(19) – .90(3,850)23 – 3,630(40) – 3,850(2.20) + {3,850[0.90(43 – 23) – 2.20]
– 3,630(40 – 19)}/(1.008399/30 – 1)
= –$164,395 – $556,914.12 = –$721,309.12, so credit should not be extended
b.
c.
5.
Old Cashflow
= (P – v)Q
New Cashflow
= (P – v)(1 – a)Q + aQ [(1 – )P – v]
Incremental Cashflow = –(P – v)Q + (P – v)(1 – a)Q + aQ [(1 – )P – v]
= (P – v)(Q – Q) + aQ [(1 – )P – P]
 (P - v)(Q - Q)  aQ{(1 -  )P - P 
Thus, NPV = (P – v)(Q – Q) – aPQ + 

R


415