Fundamentals of coroprate finance 7th ross westerfield CH20

Chapter20 •Cash and Liquidity Management McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights reserved Chapter 20 – Index of Sample Problems • • • • • Slide # 02 - 09 Slide # 10 - 11 Slide # 12 - 16 Slide # 17 - 21 Slide # 22 - 25 Float Cost of float Lockbox net present value BAT model Miller-Orr model 2: Float On an average day, your firm receives 50 checks These checks, on average, are worth $250 each The average collection delay is days Also each day, your firm writes about 25 checks These checks are worth an average of $400 and clear your bank in an average of days What is the amount of the collection float? What is the amount of the disbursement float? What is the amount of the net float? 3: Float Collection float = Firm' s available balance - Firm' s book balance = $0 − (50 × $250 × 3) = -$37,500 Disbursement float = Firm' s available balance - Firm' s book balance = (25 × $400 × 6) - $0 = $60,000 Net float = Collection float + Disbursement float = - $37,500 + $60,000 = $22,500 4: Float Your firm has decided to contract with only three customers who each pay you monthly as follows: Customer A B C Check Amount $60,000 $40,000 $50,000 What is the average daily float amount? Collection delay days days days 5: Float Item Amount Delay Total float $60,000 ×4 = $240,000 $40,000 ×5 = $200,000 $50,000 ×2 = $100,000 Total: Average daily float = $540,000 Total float $540,000 = = $18,000 Total days 30 6: Float Your firm has decided to contract with only three customers who each pay you monthly as follows: Customer A B C Check Amount $60,000 $40,000 $50,000 Collection delay days days days What is the amount of the average daily receipts? What is the weighted average delay? 7: Float Total receipts Average daily receipts = Total days $60,000 + $40,000 + $50,000 = 30 $150,000 = 30 = $5,000 8: Float Amount Weight Delay Weighted average delay $ 60,000 60/150 = 4000 400 × = 1.6000 $ 40,000 40/150 = 2667 2667 × = 1.3335 $ 50,000 50/150 = 3333 3333 × = 6666 $150,000 1.000 Total = 3.6001 9: Float Average daily float = Average daily receipts × Weighted average delay = $5,000 × 3.6001 = $18,000.50 = $18,000 12: Cost of float What is the most this firm should pay to eliminate its collection float entirely? Maximum cost = PV of the float = $4,800 What is the highest daily fee this firm should pay to eliminate its collection float entirely? Maximum daily fee = Total float × Daily interest rate = $4,800 × 0003 = $1.44 13: Lockbox net present value You are considering implementing a lockbox system and have gathered this information: Average daily lockbox payments = 1,200 Average size of payment = $750 Daily interest rate of Treasury bills = 01% Bank charge per check = $.21 Reduction in mail time = 1.5 days Reduction in processing time = 1.0 day Reduction in clearing time = day What is the NPV of this lockbox arrangement? 14: Lockbox net present value NPV = Average daily collections × Reduction in delay = (1,200 × $750) × (1.5 + + 5) − 1,200 × $.21 0001 = $900,000 × − $2,520,000 = $2,700,000 − $2,520,000 = $180,000 See the next slide for another approach Daily cost Daily interest rate 15: Lockbox net present value Daily cost = 1,200 × $.21 = $252 Daily savings = 1,200 × $750 × (1.5 + + 5) × 0001 = $270 Daily profit = $270 - $252 = $18 $18 NPV of daily profit = = $180,000 0001 See the next slide for a slightly different approach 16: Lockbox Daily cost = 1,200 × $.21 = $252 PV of daily cost = $252 = $2,520,000 0001 Daily savings = 1,200 × $750 × (1.5 + + 5) × 0001 = $270 PV of daily savings = $270 = $2,700,000 0001 NPV = $2,700,000 - $2,520,000 = $180,000 17: BAT model Your firm utilizes $165,000 a week to pay bills The standard deviation of these cash flows is $20,000 The fixed cost of transferring funds is $48 a transfer The applicable interest rate is 6% The firm has established a lower cash balance limit of $100,000 Answer these five questions using the BAT model: What is the optimal initial cash balance? What is the optimal average cash balance? What is the opportunity cost of holding cash? What is the trading cost of holding cash? What is the total cost of holding cash? 18: BAT model What is the optimal initial cash balance? C* = = (2T × F) R × $165,000 × 52 × $48 06 $823,680,000 = 06 = $117,166.55 = $117,167 19: BAT model What is the optimal average cash balance? C * $117,167 = = $58,583.50 = $58,584 2 What is the opportunity cost of holding cash? $58,584 ×.06 = $3,515.04 = $3,515 20: BAT model What is the trading cost of holding cash? Optimal initial cash balance $117,167 = = 7101 weeks Weekly cash need $165,000 Total weeks per year 52 = 73.229 This is the number of transfers per year Cash balance duration 7101 Cost of transfer × Number of transfers per year = $48 × 73.229 = $3,514.99 = $3,515 21: BAT model What is the total cost of holding cash? Total cost = Opportunity cost + Trading cost = $3,515 + $3,515 = $7,030 22: Miller-Orr model Your firm utilizes $130,000 a week to pay bills The standard deviation of these cash flows is $15,000 The fixed cost of transferring funds is $51 a transfer Your firm has established a lower cash balance limit of $80,000 The weekly interest rate is 067% Use the Miller-Orr model to answer these three questions What is the optimal initial cash balance? What is the optimum upper limit? What is the average cash balance? 23: Miller-Orr model What is the optimal initial cash balance? 1 / 3 σ  C* = L +  × F ×  R  4  33333 3 $15,000   = $80,000 +  × $51×  00067   = $80,000 + $23,417.26 = $103,417.26 = $103,417 24: Miller-Orr model What is the optimum upper limit? U* = (3 × C*) − (2 × L) = (3 × $103,417) − (2 × $80,000) = $310,251 − $160,000 = $150,251 25: Miller-Orr model What is the average cash balance? (4 × C*) - L Average cash balance = (4 × $103,417) − $80,000 = = $111,222.67 = $111,223 Chapter20 •End of Chapter 20 McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights reserved ... worth an average of $400 and clear your bank in an average of days What is the amount of the collection float? What is the amount of the disbursement float? What is the amount of the net float?... entirely? 11: Cost of float What the is the present value of the float? PV of the float = Total float = Average daily receipts × Average delay = $1,200 × = $4,800 12: Cost of float What is the... $270 Daily profit = $270 - $252 = $18 $18 NPV of daily profit = = $180,000 0001 See the next slide for a slightly different approach 16: Lockbox Daily cost = 1,200 × $.21 = $252 PV of daily cost