4.6 Exercises

A. Problem:  Managing the Float at Anders Inc.

1. Disbursement float (uncashed cheques)	(7) (125,000)	+875,000
   Collection float (uncollected receipts)	(1) (145,000)	-145,000
   	Net float	+730,000

2. The net positive float indicates that Anders’ cash bank balance is greater than its book balance.  It has CAD 730,000 more in cash each day that it can use in operations or invest.

Anders could increase the net float by stretching the disbursement float further by mailing cheques from distant locations using remote disbursements.  The collection float could be reduced by arranging same day cheque settlement with their bank.

The net float measure does not include the benefit from accelerating collection of receipts by reducing the processing or mail float of their customers.  This could be done by introducing electronic payment, having cheques scanned and sent electronically, using preauthorized cheques, or implementing locked boxes or collection offices.  Before implementing these measures, their cost must be compared to their benefits,

B. Problem: Locked Boxes at Edson Telecom

Yes – benefits (CAD 1,445,000) exceed the costs (CAD 1,250,000).

Present value of savings from collecting earlier

(850) (425) = 361,250

(7 – 3) (361,250) = 1,445,000

Note:  Edson initially collects CAD 361,250 per day after waiting seven days.  If locked boxed are introduced and Edson only has to wait three days to collect, they will receive CAD 1,445,000 extra immediately and then will continue to collect CAD 361,250 each day in perpetuity with only a three-day delay.  The benefits from introducing locked boxes are immediate and one-time, so CAD 1,445,000 is the present value of any future benefits.  This amount should be compared against any costs.

Present value of cost locked boxes

(1 + i)³⁶⁵ – 1 = .025

i =.000068

(850) (.10) / (.000068) = 1,250,000

C. Problem: Investing in Treasury Bills at ABBA Company

[latex](1 + \frac{{\left( {100,000{\rm{\;}} - {\rm{\;}}\left( {99,245.48{\rm{\;}} + {\rm{\;}}200.00} \right)} \right)}}{{99,245.48}})[/latex]^365/180 – 1 = .0114 or 1.14%

(.0153) (180/365) (100,000) = 754.52

100,000 – 754.52 = 99,245.48

D. Problem: Optimal Credit Terms at Dexter Industries

Yes, the credit terms should be extended.

¹ (150,000 – 135,000) (.75)

² (.009) (135,000) – (.0135) (150,000)

³ (135,000) [latex](\frac{{30}}{{365}}[/latex]) = 11,095.89

(150,000) [latex](\frac{{45}}{{365}}[/latex]) = 18,493.15

(11,095.89 – 18,493.15) (.05) = <369.86>

⁴ (135,000) (.45) / 5 = 12,150

(150,000) (.45) / 5 = 13,500

(12,150 – 13,500) (.05) = <67.50>

E. Problem: Optimal Credit Terms at Jackson Inc.

Yes, the credit terms should be extended.

¹ (3,500,000 – 2,600,000) (.25)

² (2,600,000) (.85) (.02) = 44,200

(3,500,000) (.65) (.03) = 68,250

44,200 – 68,250 = <24,050>

³ (2,600,000) (.01) = 26,000

(3,500,000) (.02) = 70,000

26,000 – 70,000 = <44,000>

⁴ (2,600,000) (14/365) = 99,726.03

(3,500,000) (31/365) = 297,260.27

(99,726.03 – 297,260.27) (.05) = <9,876.71>

⁵ [latex]\frac{{\left( {2,600,000} \right)\left( {.4} \right)}}{5}[/latex] = 208,000

[latex]\frac{{\left( {3,500,000} \right)\left( {.4} \right)}}{5}[/latex]= 280,000

(208,000 – 280,000) (.05) = <3,600>

F. Problem: Optimal Credit Terms at Hoboken Company

Yes, the credit terms should be shortened.

¹ (465,000 – 500,000) (.20)

² (500,000) (.3) (.03) = 4,500

(465,000) (.0) (.0) = 0

4,500 – 0 = 4,500

³ (500,000) (.02) = 10,000

(465,000) (.0175) = 8,137.50

10,000 – 8,137.50 = 1,862.50

⁴ (500,000) (⁵45/365) = 61,643.84

(465,000) (30/365) = 38,219.18

(61,643.84 – 38,219.18) (.05) = 1,171.23

⁵ (.7) (60) + (.3) (10) = 45

⁶ [latex]\frac{{\left( {500,000} \right)\left( {.5} \right)}}{6}[/latex] = 41,666.67

[latex]\frac{{\left( {465,000} \right)\left( {.5} \right)}}{6}[/latex] = 38,750.00

(41,666.67 – 38,750.00) (.05) = 145.83

G. Problem: EOQ, Safety Stock, Re-order Point at Holland Ltd.

1. [latex]\sqrt {\frac{{\left( 2 \right)\;\left( {13,000} \right)\left( {5.35} \right)}}{{2.45}}}[/latex] = 238

2.

EOQ is the optimal order size, but a company must also determine when to place the order.  For example, if it takes 10 days on average for an order to be processed and delivered by the supplier and demand is normally 20 units daily, then the re-order point is 200 units.  As the company waits for the order to arrive, they should have sufficient inventory to satisfy demand.  The re-order point is also called the minimum and the maximum is equal to the re-order point plus the EOQ.

¹ 13,000 / 238 = 54.62

A safety stock of 150 units will minimize total stockout and carrying costs.

2. (5) ([latex]\frac{{13,000}}{{260}}[/latex])+ 150  = 400 units

On average, the company uses 13,000 units a year and works 260 days a year so on average uses 13,000/260=50 units per day. Since the company must wait 5 days to get the units after placing an order, they need to place an order when inventory falls to 250 units (5 days times 50 units per day). This is the average amount of inventory used during the reorder time, ie between the time an order is placed and inventory arrives. Note that it is the same as the expected sales during the period in the first table above. This is the reorder point.

Also note that this usage is not constant, but follows a probability given in the table for the 5-day period it takes to receive an order. Given this variability, if they wait until they reach 250 units in stock, there is a chance they will use more than average in any given week and so run out. Given they place an order when they reach 250 units (zero safety stock – the first line in the 2nd table above), there is a 5% chance they will actually need 400 units, leaving them 150 units short, and a 25% chance they will need 350 units, leaving them 100 units short. The expected stockout costs are the probability * stock-out-units * stock-out-cost-per-unit * orders-per-year = expected-stockout-costs. The carrying costs in that table are the safety stock (which lowers the probability of a stock out occurring) times the carrying cost per unit, so with 100 units of safety stock, the carrying cost is 100 * $2.45 per unit = $245. The total cost for any level of safety stock is the sum of the stockout costs and the carrying costs.

The 2nd table shows that costs are lowest when the company maintains 150 units of safety stock, and this means it must reorder when inventory falls to 400 units (250 units expected to be used while waiting for a shipment plus 150 units of safety stock). Note that in this case, the reorder point is greater than the economic order quantity which means the company must either order more than the EOQ each time they reach the reorder point or must place an order before inventory falls to the 400-unit level.

3. Stock out costs were very high compared to carrying costs, so the maximum safety stock level of 150 units is justified. If stockout costs fall and carry costs rise like it might with expensive products due to financing and security costs, the safety stock level may be less than the maximum.  Assuming a stable re-order period, the safety stock should not exceed the difference between maximum and average demand during the re-order period.  If the re-order period is unstable, the maximum safety stock will increase.

H. Problem: EOQ, Safety Stock, Re-order Point at Ashern Inc.

1. [latex]\sqrt {\frac{{\left( 2 \right)\;\left( {26,000} \right)\left( {57.76} \right)}}{{\left( {.05} \right)\left( {95.32} \right)}}}[/latex] = 794

2. (13) (125) – (10) (100) = 625 units

Note: The re-order period is no longer stable, so the safety stock is equal to the maximum re-order period times the maximum demand minus the average re-order period times the average demand.  Carrying costs were not considered as re-stocking costs are very high in comparison.

3. (10) [latex](\frac{{26,000}}{{260}})[/latex] + 625 = 1,625 units

I. Problem: Specific Assignment Accounts Receivable at York Ltd.

1. [latex]\frac{{3,685.07\; + \;3,500}}{{245,000}}[/latex] = .0293

[latex]{\left( {1 + \;.0293} \right)^{365/90}}[/latex] – 1 = .1243 or 12.43%

(245,000) (.061) [latex](\frac{{90}}{{365}}[/latex]) = 3,685.07

(.01) (350,000) = 3,500

(350,000) (.7) = 245,000

2. The 1.0% processing fee significantly raised the effective annual cost of borrowing. These are higher-risk receivables so the bank required a specific assignment instead of a general assignment.  A specific assignment involves a more thorough credit assessment and a lien against the assets.  With this improved security arrangement, the company can usually borrow a higher percentage of the value of the receivables, so the added cost may be worth it.  York’s customers could also be notified to pay the bank directly if the bank is uncertain of payment, but this could be disruptive for customers and cause them to question the firm’s financial stability.

J. Problem: Specific Assignment Inventory at Hansen Inc.

1. [latex]\frac{{7,895.58\; + \;3,000}}{{525,000}}[/latex] = .0208    [latex]{\left( {1 + \;.0208} \right)^{365/90}}[/latex] – 1 = .0869 or 8.69%

(525,000) (.061) [latex](\frac{{90}}{{365}}[/latex]) = 7,896.58

(750,000) (.7) = 525,000

2. The bank wants to ensure the price received for the inventory is reasonable and the proceeds are used to pay down the loan first.  Companies sometimes sell stock at below market prices during a period of financial distress when they are short of cash.

K. Problem: Factoring of Accounts Receivable at Willobey Industries

1.

[latex]\frac{{3,500.00\; + \;3,205.48}}{{200,000}}[/latex] = .0335    [latex]{\left( {1 + \;.0335} \right)^{365/90}}[/latex] – 1 = .1431 or 14.31%

2. 50,000 – 3,500 – 3,205.48 – 38,500 = 4,794.52

L. Problem: Operating Loan versus Factoring at Helca Ltd.

1. Factoring is the preferred form of financing.
   

   	Operating Loan	Factoring
   Sales volume	CAD 15,000,000	CAD 15,750,0008
   A/R turnover in days	28.8 days1	25.92 days9
   Average A/R	CAD 1,200,0002	CAD 1,134,00010
   Loan	CAD 900,0003	CAD 963,90011
   Customer discounts	CAD 120,0004	0
   Factor commission	0	CAD 393,75012
   Interest expense	CAD 37,8005	CAD 62,65413
   Collection department	CAD 207,5006	0
   Bad debts	CAD 225,0007	0
   Total	CAD 590,300	CAD 456,404

   ¹ (.4) (15) + (.6) (38) (Includes float and a bit of worst-case assumptions)

   ²(28.8) (15,000,000) / 360

   ³(1,200,000) (.75)

   ⁴(15,000,000) (.40) (.02)

   ⁵(900,000) (.042)

   ⁶Hecla spends CAD 200,000 on salaries and another CAD 7,500 for credit information operating its credit department.

   ⁷(15,000,000) (.015)

   ⁸(15,000,000) (1 + .05)

   ⁹(28.8) (1 – .10)

   ¹⁰(25.92) (15,750,000) / 360

   ¹¹ (1,134,000) (.85)

   ¹²(.025) (15,750,000)

   ¹³(.065) (963,900)

   Small firms like Hecla may likely find that factoring is more efficient than in-house collections because they do not need to operate their own collections department.

M. Problem: Issuing Commercial Paper at Jackson Company

1. (1 +[latex]\frac{{63,997.50}}{{\left( {10,500,000\; - \;\;63,997.50} \right)}}[/latex]) ^365/90 – 1 = 0.0251 or 2.51%

2. Companies sometimes operate their own commercial paper programs to eliminate the dealer fees to lower the effective annual cost. There are still large fixed costs related to operating such a program, so only companies with sizeable financing requirements would benefit from this option.