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Chapter 15 - Chapter 15 Solutions to End-of-Chapter...

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Chapter 15 Solutions to End-of-Chapter Problems 15-1 1. Sales = $15,000,000; Inventory = $2,000,000; A/R = $3,000,000; A/P = $1,000,000;  COGS = 0.8(Sales); Interest on bank loan = 8%; CCC = ? CCC = Inventory conversion period + Average collection period – Payables deferral  period. Inventory conversion period =  day per    sold   goods   of Cost  Inventory 365 / )] 000 , 000 , 15 )($ 8 . 0 [( 000 , 000 , 2 $ 7123 . 876 , 32 $ 000 , 000 , 2 $ = 60.83 days. Average collection period =  Sales/365 s Receivable 365 / 000 , 000 , 15 $ 000 , 000 , 3 $ = 73 days. Payables deferral period =  sold/365   goods   of Cost  Payables 7123 . 876 , 32 $ 000 , 000 , 1 $ = 30.42 days. CCC = 60.83 + 73 – 30.42 = 103.41 days. 2. Lower inventories and receivables by 10% each and increase payables by 10%. Sales  and COGS remain the same. Inventory = $2,000,000  ×  0.9 = $1,800,000. A/R = $3,000,000  ×  0.9 = $2,700,000. A/P = $1,000,000  ×  1.1 = $1,100,000. Calculate new CCC:
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Inventory conversion period =  7123 . 876 , 32 $ 000 , 800 , 1 $ = 54.75 days. Average collection period =  365 / 000 , 000 , 15 $ 000 , 700 , 2 $ = 65.70 days. Payables deferral period =  7123 . 876 , 32 $ 000 , 100 , 1 $ = 33.46 days. New CCC = 54.75 + 65.70 – 33.46 = 86.99 days   87 days. 3. Cash freed up:  Inventory = (60.83 – 54.75)  ×  $32,876.7123 = $199,890.41.  Receivables = (73 – 65.70)  ×  $41,095.8904 = $300,000.  Payables = (33.46 – 30.42)  ×  $32,876.7123 = $99,945.2055. Cash   freed   up   =   $199,890.41   +   $300,000   –   $99,945.2055   =   $399,945.2045   $400,000. $400,000  ×  0.08 = $32,000 increase in pre-tax profit. 15-2 Sales = $10,000,000; A/R = $2,000,000; DSO = ? DSO=  Sales/365 s Receivable 365 / 000 , 000 , 10 $ 000 , 000 , 2 $ = 73 days. If all customers paid on time (assuming that it makes no sense for customers to pay earlier  than 30 days), then the firm’s DSO = 30 days.  If customers paid on time, the firm’s A/R =  30  ×  $10,000,000/365 = $821,917.81. Cash freed up = $2,000,000 – $821,917.81 = $1,178,082.19. 15-3 Purchases = $8,000,000; terms = 3/5 net 60; currently pays on Day 5 and takes discounts.
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Forgoes discounts; additional credit = ? $8,000,000/365  ×  55 days = $1,205,479.45. Nominal cost of trade credit =  55 5 36     97 3 ×  = 3.09%  ×  6.6364 = 20.52%. Effective cost of trade credit = (1 + 3/97) 365/55  – 1 = 1.2240 – 1 = 22.40%. Bank loan:  10%, interest paid monthly EAR = (1 + 0.10/12) 12  – 1 = 1.1047 – 1 = 10.47%. Because the effective cost of the bank loan is more than half the effective cost of the trade  credit, the bank loan should be used. 15-4 a. cycle conversion Cash period deferral Payables period collection s Receivable period conversion Inventory - + = 75 + 38 – 30 = 83 days. b. Average sales per day = $3,421,875/365 = $9,375. Investment in receivables = $9,375  ×  38 = $356,250.
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