CHAPTER 19 - answer.doc

Solutions Manual

CHAPTER 19 ACCOUNTS RECEIVABLE AND INVENTORY MANAGEMENT SUGGESTED ANSWERS TO THE REVIEW QUESTIONS AND PROBLEMS I. Questions 1. Cash and marketable securities are generally used to meet the transaction needs of the firm and for contingency purposes. Because the funds must be available when needed, the primary concern should be with safety and liquidity rather than the maximum profits. 2. Float exists because of the delay time in check processing. Electronic funds transfer, or the electronic movement of funds between computer terminals, would eliminate the need for checks and thus eliminate float. 3. A firm could operate with a negative balance on the corporate books knowing float will carry them through at the bank. Checks written on the corporate books may not clear until many days later at the bank. For this reason, a negative account balance on the corporate books of ₱100,000 may still represent a positive balance at the bank. 4. By slowing down disbursements or the processing of checks against the corporate account, the firm is able to increase float and also to provide a source of short-term financing. 5. The average collection period, the ratio of bad debts to credit sales and the aging of accounts receivable. 6. Trade credit is usually granted on open account. The invoice is the credit instrument. 7. Credit costs: cost of debt, probability of default, and the cash discount. No-credit costs: lost sales. The sum of these is the carrying costs. 8. 1. Character:determines if a customer is willing to pay his or her

debts.

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2. Capacity: determines if a customer is able to pay debts out of

operating cash flow. 3. Capital:

determines the customer’s financial reserves in case problems occur with operating cash flow. 4. Collateral: assets that can be liquidated to pay off the loan in case of default. 5. Conditions: customer’s ability to weather an economic downturn and whether such a downturn is likely. 9. 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

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. 10. a. B: 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. b. A: Landlords have significantly greater collateral, and that collateral is not mobile. c. A: 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. d. B: Since A’s merchandise is perishable and B’s is not, B will probably have a longer credit period. e. A: Rugs are fairly standardized and they are transportable, while carpets are custom fit and are not particularly transportable. 11. The three main categories of inventory are: raw material (initial inputs to the firm’s production process), work-in-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

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for these inventory types in order to achieve the desired levels of finished goods. 12. 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 DuPont equation, an increase in total asset turnover, all else being equal, has a positive effect on ROE. 13. 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. 14. Since the price of components can decline quickly, Apple does not have inventory which is purchased and then declines quickly in value before it is sold. If this happens, the inventory may be sold at a loss. While this approach is valuable, it is difficult to implement. For example, Apple manufacturing plants will often have areas set aside that are for the suppliers. When parts are needed, it is a matter of going across the floor to get new parts. In fact, m0st computer manufacturers are trying to implement similar inventory systems. II. Multiple Choice Questions 1. 2. 3.

D B D

4. 5. 6.

A D C

7. 8. 9.

D C B

10. D 11. D 12. D

13.

D

III. Problems Problem 1 The firm’s average daily sales are its annual (credit) sales divided by 365 days. Average daily sales = ₱912,500/365 days = ₱2,500 The average collection period is the credit period plus the average days past the due date. Average collection period = 45 + 15 = 60 days

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The average investment in accounts receivable is determined by multiplying the average daily sales by the average collection period. Investment in accounts receivable = ₱2,500 x 60 = ₱150,000 Problem 2 a. The accounts receivable turnover is calculated by dividing 365 days by the average collection period of 25 days. Accounts receivable turnover = 365/25 = 15 times b. The average investment in accounts receivable is calculated by dividing credit sales by the accounts receivable turnover. Average investment in accounts receivable = ₱600,000/15 = ₱40,000 This method uses the total sales value of the accounts receivable. The cost (variable or total) is sometimes used as the relevant measure of the amount of funds tied up in accounts receivable. Using only variable cost as the relevant measure, the investment in accounts receivable would be ₱32,000 (₱40,000 x 0.80). Problem 3 a. The marginal pretax profits for each risk class are shown below:

1. Marginal profits on additional sales = Additional sales x CM = Additional sales x 0.15 2. Marginal increase in bad debt losses = Additional sales x Bad debt loss ratio 3. Marginal investment in A/R = (Additional sales/365) x 90 A = ₱12,330, B = ₱9,900, C = ₱4,950 19-4

A

Risk Class B

₱7,500

₱6,000

₱3,000

2,500

3,200

2,400

C

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Opportunity cost of marginal investment in AR = Marginal investment in A/R x Opportunity cost

2,466

2,376

6,485

4. Net change in pretax profits = Marginal profits – Marginal costs

₱2,534

₱424

(₱885)

* The contribution margin of 0.15 is calculated by subtracting the variable cost percentage from 1.00 or (1.00 – 0.85 = 0.15) Problem 4 Jazz Auto Supply should not adopt the change in the discount rate because the change results in a net disadvantage of ₱211. 1. Marginal profits on additional sales = Additional sales x Contribution margin = ₱0 x 0.25

₱

0

2. Current bad debt losses = Current sales x Current bad debt loss ratio = ₱400,000 x 0.03 = ₱12,000 New bad debt losses = New sales x New bad debt loss ratio = ₱400,000 x 0.025 = ₱10,000 Reduction in bad debt losses = Current bad debt losses – New bad debt losses = ₱12,000 − ₱10,000 3. Current average A/R balance = Current average daily sales x Current average collection period = (₱400,000/365) x 42 = ₱46,032 New average A/R balance = New average daily sales x New average collection period = (₱400,000/365) x 38 = ₱41,648

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Reduction in A/R investment = Current average A/R balance – New average A/R balance = ₱46,032 - ₱41,648 = ₱4,384 Earnings on funds released by reduction in A/R investment = Reduction in A/R x Required pretax rate of return = ₱4,384 x 0.18

789

4. Cost of current cash discount = Current sales x Current percentage taking discount x Current percentage discount = ₱400,000 x 0.45 x 0.01 = ₱1,800 Cost of new discount = New sales x New percentage taking discount x New percentage discount = ₱400,000 x 0.60 x 0.02 = ₱4,800 Cost of increase in cash discount = Cost of new cash discount – Cost of current cash discount = ₱4,800 − ₱1,800 5. Net advantage/disadvantage of changing credit terms = Marginal returns – Marginal costs = (₱0 + ₱2,000 + ₱789) − ₱3,000

3,000

(₱211)

Problem 5 a. S = 12,000; O = ₱50; C = ₱0.10 Q* =

(2) (12,000) (₱50) = 3,464 gallons ₱0.10

b. The average inventory is determined by dividing the economic order quantity, Q* by 2, as follows: Average inventory = 3,464/2 = 1,732 gallons

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c. C = ₱0.10; Q* = 3,464; S = 12,000 ; O = ₱50 Total inventory costs = CQ/2 + SO/Q TIC = [(0.10) (3,464) / 2] + [(12,000) (₱50) / 3,464) = ₱346 per month d. Q* = 3,464; Average daily demand = 12,000/30days T* = Q*/Average daily demand T* = 3,464 / (12,000/30 days) = 9 days e. S = 12,000; Q* = 3,464 N* = S/Q* N* = 12,000 / 3,464 = 3 orders per month

or

Time period = 30; T = 9 N* = Time period/T* N* = 30 / 9 = 3 orders per month Problem 6 a. S = 36,000; O = ₱100; C = ₱5 Q* =

(2) (36,000) (₱100) = 1,200 fruit cakes ₱5

b. Q* = 1,200 ; SS = 3,000 Average inventory (Qa) = [(Q*/2) + SS] Qa = [(1,200 / 2) + 3,000] = 3,600 fruit cakes c. S = 36,000; Q* = 1,200 N* = S/Q* N* = 36,000 / 1,200 = 30 orders per year

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d. Fruitcake Specialists’ total inventory cost is found by multiplying the average inventory, 3,600 fruit cakes, by the carrying cost per unit, ₱5, and then adding the product of the orders per year, 30, multiplied by the ordering costs per order, ₱100. Total inventory costs = (3,600) (₱5) + (30) (₱100) = ₱21,000 e. SS = 3,000; S = 36,000; Time period = 365 ; n = 5 Qr = SS + (S/Time period) (n) Qr = 3,000 + (36,000 / 365) (5) = 3,495 fruitcakes Problem 7 The costs per period are the same whether or not credit is offered; so we can ignore the production costs. The firm currently has sales of, and collects ₱110 x 2,000 = ₱220,000 per period. If credit is offered, sales will rise to ₱120 x 2,000 = ₱240,000. Defaults will be 4 percent of sales, so the cash inflow under the new policy will be .96 x ₱240,000 = ₱230,400. This amounts to an extra ₱10,400 every period. At 2 percent per period, the PV is ₱10,400/.02 = ₱520,000. If the switch is made, Dama de Noche will give up this month’s revenues of ₱220,000; so the NPV of the switch is ₱300,000. If only half of the customers take the credit, then the NPV is half as large: ₱150,000. So, regardless of what percentage of customers takes the credit, the NPV is positive. Thus, the change is a good idea. Problem 8 The cash flow from the old policy is the quantity sold times the price, so: Cash flow from old policy = 40,000(₱510) = ₱20,400,000 The cash flow from the new policy is the quantity sold times the new price, all times one minus the default rate, so: Cash flow from new policy = 40,000(₱537) (1 – .03) = ₱20,835,600 The incremental cash flow is the difference in the two cash flows, so: 19-8

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Incremental cash flow = ₱20,835,600 – 20,400,000 = ₱435,600 The cash flows from the new policy are a perpetuity. The cost is the old cash flow, so the NPV of the decision to switch is: NPV = –₱20,400,000 + ₱435,600/.025 = –₱2,976,000 Problem 9 a.

The old price as a percentage of the new price is: ₱90/₱91.84 = .98 So the discount is: Discount = 1 – .98 = .02 or 2% The credit terms will be: Credit terms: 2/15, net 30

b.

We are unable to determine for certain since no information is given concerning the percentage of customers who will take the discount. However, the maximum receivables would occur if all customers took the credit, so: Receivables = 3,300(₱90) =  ₱ 297,000 (at a maximum)

c.

Since the quantity sold does not change, variable cost is the same under either plan.

d.

No, because: d –  = .02 – .11 = –.09 or –9% Therefore the NPV will be negative. The NPV is: NPV = –3,300(₱90) + (3,300) (₱91.84) (.02 – .11)/(.01) = –₱3,023,592 The breakeven credit price is: P (1 + r) / (1 –) = ₱90 (1.01)/ (.89) =  ₱ 102.13 This implies that the breakeven discount is: Breakeven discount = 1 – (₱90/₱102.13) = .1188 or 11.88%

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The NPV at this discount rate is: NPV = –3,300(₱90) + (3,300) (₱102.13) (.1188 – .11)/(.01) NPV  0 Problem 10 a.

The cost of the credit policy switch is the quantity sold times the variable cost. The cash inflow is the price times the quantity sold, times one minus the default rate. This is a one-time, lump sum, so we need to discount this value one period. Doing so, we find the NPV is: NPV = –15(₱760) + (1 – .2) (15) (₱1,140)/1.02 = ₱2,011.76 The order should be taken since the NPV is positive.

b.

To find the breakeven default rate, , we just need to set the NPV equal to zero and solve for the breakeven default rate. Doing so, we get: NPV = 0 = –15(₱760) + (1 –) (12) (₱1,140)/1.02  = .3200 or 32.00%

c.

Effectively, the cash discount is: Cash discount = (₱1,140 – 1,090) / ₱1,140 = .0439 or 4.39% Since the discount rate is less than the default rate, credit should not be granted. The firm would be better off taking the ₱1,090 up-front than taking an 80% chance of making ₱1,140.

Problem 11 a.

The cash discount is: Cash discount = (₱75 – 71) / ₱75 = .0533 or 5.33% The default probability is one minus the probability of payment, or: Default probability = 1 – .90 = .10 19-10

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Since the default probability is greater than the cash discount, credit should not be granted; the NPV of doing so is negative. b.

Due to the increase in both quantity sold and credit price when credit is granted, an additional incremental cost is incurred of: Additional cost = (6,200) (₱33 – 32) + (6,900 – 6,200) (₱33) Additional cost = ₱29,300 The breakeven price under these assumptions is: NPV = 0 = –₱29,300 – (6,200) (₱71) + {6,900 [(1 – .10) P – ₱33] – 6,200(₱71 – 32)} / (1.00753 – 1) NPV = –₱34,100 – 440,200 + 273,940.31P – 10,044,478.08 – 10,666,468.16 ₱21,185,246.24 = ₱273,940.31P P = ₱77.34

c.

The credit report is an additional cost, so we have to include it in our analysis. The NPV when using the credit reports is: NPV = 6,200 (32) – .90 (6,900) 33 – 6,200 (71) – 6,900 (₱1.50) + {6,900 [0.90 (75 – 33) – 1.50] – 6,200 (71 – 32)} / (1.00753 – 1) NPV = ₱198,400 – 204,930 – 440,200 – 10,350 + 384,457.73 NPV = –₱72,622.27 The reports should not be purchased and credit should not be granted.

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