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Maths. topic 2,3,4,5 Maths. topic 2,3,4,5 Presentation Transcript

  • 5-1Gateway Appliance toasters sell for $20 per unit, and the variablecost to produce them is $15. Gateway estimates that the fixed costsare $80,000.a. Compute the break-even point in units.b. Fill in the table below (in dollars) to illustrate the break-even point has been achieved.Sales ____________– Fixed costs ____________– Total variable costs ____________Net profit (loss) ____________
  • CHAPTER 5Solution: Gateway Appliance Fixed costs a. BE = Pr ice-variable cost per unit $80,000 $80,000 = = = 16,000 units $20 − $15 $5 b. Sales $320,000 (16,000 units × $20) –Fixed costs $ 80,000 –Total variable costs 240,000 (16,000 units × $15) Net profit (loss) $ 0
  • 5-25-2 Hazardous Toys Company produces boomerangs that sell for $8each and have a variable cost of $7.50. Fixed costs are $15,000.a. Compute the break-even point in units.b. Find the sales (in units) needed to earn a profit of $25,000.
  • 5-2Solution: The Hazardous Toys Company $15,000 a. BE = = 30,000 units $8.00 − $7.50 Profit + FC $25,000 + $15,000 b. Q = = (P − VC) $8.00 − $7.50 $40,000 = = 80,000 units $.50
  • 5-3Ensco Lighting Company has fixed costs of $100,000, sells its unitsfor $28, and has variable costs of $15.50 per unit.a.Compute the break-even point.b.Ms. Watts comes up with a new plan to cut fixed costs to $75,000.However, more labor will now be required, which will increasevariable costs per unit to $17. The sales price will remain at $28.What is the new break-even point?c.Under the new plan, what is likely to happen to profitability atvery high volume levels (compared to the old plan)?
  • CHAPTER 5Solution: Ensco Lighting Company Fixed costs a. BE = Pr ice −variable cost per unit $100,000 $100, 000 = = =8, 000 units $28 −$15.50 $12.505-3. (Continued) Fixed costs b. BE = Pr ice −variable cost per unit $75, 000 $75, 000 = = =6,818 units $28 −$17 $11 The breakeven level decreases. c. With less operating leverage and a smaller contribution margin, profitability is likely to be less at very high volume levels.
  • 5-11The Sterling Tire Company’s income statement for 2008 is as follows: STERLING TIRE COMPANY Income Statement For the Year Ended December 31, 2008 Sales (20,000 tires at $60 each) .................................. $1,200,000 Less: Variable costs (20,000 tires at $30) ................ 600,000 Fixed costs.............................................................. 400,000 Earnings before interest and taxes (EBIT) .................. 200,000 Interest expense ........................................................... 50,000 Earnings before taxes (EBT) ....................................... 150,000 Income tax expense (30%) .......................................... 45,000 Earnings after taxes (EAT) ......................................... $ 105,000 Given this income statement, compute the following: a. Degree of operating leverage. b. Degree of financial leverage. c. Degree of combined leverage. d. Break-even point in units.
  • SOLUTION 5-11 Sterling Tire Company Q = 20,000, P = $60, VC = $30, FC = $400,000, I = $50,000 Q(P −VC) a. DOL = Q(P −VC) −FC 20, 000($60 −$30) = 20, 000($60 − $30) −$400, 000 20, 000($30) = 20, 000($30) − $40, 000 $600, 000 $600, 000 = = =3.00x $600, 000 − $400, 000 $200, 0005-11. (Continued) EBIT $200, 000 b. DFL = = EBIT −I $200, 000 −$50, 000 $200, 000 = =1.33x $150, 000 Q (P −VC) c. DCL = Q(P −VC) −FC −I 20, 000($60 −$30) = 20, 000($60 −$30) − $400, 000 −$50, 000 $600, 000 $600, 000 = = =4x $600, 000 −$400, 000 −$50, 000 $150, 000
  • 5-12The Harmon Company manufactures skates. The company’s income statement for 2008 is as follows: HARMON COMPANY Income Statement For the Year Ended December 31, 2008 Sales (30,000 skates @ $25) ......................................................... $750,000 Less: Variable costs (30,000 skates at $7) ................................. 210,000 Fixed costs............................................................................... 270,000 Earnings before interest and taxes (EBIT) .................................... 270,000 Interest expense ............................................................................. 170,000 Earnings before taxes (EBT) ......................................................... 100,000 Income tax expense (35%) ............................................................ 35,000 Earnings after taxes (EAT) ........................................................... $ 65,000 Given this income statement, compute the following: a. Degree of operating leverage. b. Degree of financial leverage. c. Degree of combined leverage. d. Break-even point in units.
  • SOLUTION:5-12. Harmon CompanyQ = 30,000, P = $25, VC = $7, FC = $270,000, I = $170,000 Q(P −VC)a. DOL = Q(P −VC) −FC 30, 000($25 −$7) = 30, 000($25 − $7) −$270, 000 30, 000($18) = 30, 000($18) − $270, 000 $540, 000 $540, 000 = = =2x $540, 000 − $270, 000 $270, 000 EBIT $270, 000b. DFL = = EBIT −I $270, 000 − $170, 000 $270, 000 = =2.7x $100, 000c. Q(P −VC) DCL = Q(P −VC) −FC −I 30, 000($25 − $7) = 30, 000($25 −$7) − $270, 000 −$170, 000 30, 000($18) $540, 000 = = =5.4x 30, 000($18) − $440, 000 $100, 000 $270,000d. BE = =15, 000 units $25 − $7
  • 5-14U.S. Steal has the following income statement data: Total Operating Units Variable Fixed Total Total Income Sold Costs Costs Costs Revenue (Loss) 40,000 $ 80,000 $50,000 $130,000 $160,000 $30,000 60,000 120,000 50,000 170,000 240,000 70,000 a. Compute DOL based on the formula below (see page for an example): Percent change in operating income DOL= Percent change in units sold b. Confirm that your answer to part a is correct by recomputing DOL using formula 5–3 on page. There may be a slight difference due to rounding. Q(P − VC) DOL= Q (P − VC) − FC Q represents beginning units sold (all calculations should be done at this level). P can be found by dividing total revenue by units sold. VC can be found by dividing total variable costs by units sold.
  • 5-14. U. S. Steal Percent change in operating income a. DOL = Percent change in units sold $40, 000 30, 000 ×100 133% = = =2.66 20, 000 50% 40, 000 ×1005-14. (Continued) Q(P −VC) b. DOL = Q(P −VC) −FC Q =40,000 Total revenue $160, 000 P = = =$4 Units sold 40, 000 Total variable costs $80, 000 VC = = =$2 Units sold 40, 000 FC =$50,000 40,000 ($4 −$2) $80, 000DOL = = 40, 000($4 −$2) −$50, 000 $80, 000 − $50, 000 $80, 000 = =$2.67 $30, 000
  • 6-1Gary’s Pipe and Steel company expects sales nextyear to be $800,000 if the economy is strong,$500,000 if the economy is steady, and $350,000 ifthe economy is weak. Gary believes there is a 20percent probability the economy will be strong, a50 percent probability of a steady economy, and a30 percent probability of a weak economy.What is the expected level of sales for next year?
  • 6-1 Gary’s Pipe and Steel Company State of ExpectedEconomy Sales Probability Outcome Strong $800,000 .20 $160,000 Steady 500,000 .50 250,000 Weak 350,000 .30 105,000 Expected level of sales = $515,000
  • 6-2Nile Riverboat Co., a major boat building companyhighly sensitive to the economy, expects profitsnext year to be $2,000,000 if the economy is strong,$1,200,000 if the economy is steady, and minus$400,000 if the economy is weak. Mr. Nile believesthere is a 30 percent probability of a strongeconomy, a 40 percent probability of a steadyeconomy, and a 30 percent probability of a weakeconomy. What is the expected value of profits fornext year?
  • 6-2 Nile Riverboat Co. State of ExpectedEconomy Profits Probability Outcome Strong 2,000,000 .30 $600,000 Steady 1,200,000 .40 480,000 Weak –400,000 .30 –120,000 Expected level of profits = $960,000
  • 6-3Tobin Supplies Company expects sales next year tobe $500,000. Inventory and accounts receivable willincrease $90,000 to accommodate this sales level.The company has a steady profit margin of 12percent with a 40 percent dividend payout. Howmuch external financing will Tobin SuppliesCompany have to seek? Assume there is noincrease in liabilities other than that which willoccur with the external financing.
  • SOLUTION:6-3. Tobin Supplies Company$500,000 Sales .12 Profit margin 60,000 Net income– 24,000 Dividends (40%)$ 36,000 Increase in retained earnings$ 90,000 Increase in assets– 36,000 Increase in retained earnings$ 54,000 External funds needed
  • 6-4 Shamrock Diamonds expects sales next year to be $3,000,000. Inventory and accounts receivable will increase $420,000 to accommodate this sales level. The company has a steady profit margin of 10 percent with a 25 percent dividend payout. How much external financing will the firm have to seek?
  • SOLUTION:6-4. Shamrock Diamonds$3,000,000 Sales .10 Profit margin 300,000 Net income 75,000 Dividends (25%)$ 225,000 Increase in retained earnings 420,000 Increase in assets – 225,000 Increase in retained earnings$ 195,000 External funds needed
  • 6-7Procter Micro-Computers, Inc., requires $1,200,000in financing over the next two years. The firm canborrow the funds for two years at 9.5 percentinterest per year. Mr. Procter decides to doeconomic forecasting and determines that if heutilizes short-term financing instead, he will pay6.55 percent interest in the first year and 10.95percent interest in the second year. Determine thetotal two-year interest cost under each plan. Whichplan is less costly?
  • 6-7 Procter-Mini-Computers, Inc. Cost of Two Year Fixed Cost Financing$1,200,000 borrowed × 9.5% per annum × 2 years = $228,000 interest Cost of Two Year Variable Short-term Financing1st year $1,200,000 × 6.55% per annum = $ 78,600 interest cost nd2 year $1,200,000 × 10.95% per annum = $131,400 interest cost $210,000 two-year totalThe short-term plan is less costly.
  • 6-1111. Colter Steel has $4,200,000 in assets. Temporary current assets ......................... $1,000,000 Permanent current assets .......................... 2,000,000 Fixed assets .............................................. 1,200,000 Total assets ......................................... $4,200,000 Short-term rates are 8 percent. Long-term rates are 13 percent. Earnings before interest and taxes are $996,000. The tax rate is 40 percent. If long-term financing is perfectly matched (synchronized) with long-term asset needs, and the same is true of short-term financing, what will earnings after taxes be? For a graphical example of perfectly matched plans, see Figure 6-5.
  • SOLUTION:6-11. Colter SteelLong-term financing equals: Permanent current assets $2,000,000 Fixed assets 1,200,000 $3,200,000Short-term financing equals: Temporary current assets $1,000,000Long-term interest expense = 13% × $3,200,000 = $ 416,000Short-term interest expense = 8% × 1,000,000 = 80,000Total interest expense $ 496,000Earnings before interest and taxes $ 996,000 Interest expense 496,000Earnings before taxes $ 500,000 Taxes (40%) 200,000Earnings after taxes $ 300,000
  • 6-12In problem 11, assume the term structure ofinterest rates becomes inverted, with short-termrates going to 11 percent and long-term rates 4percentage points lower than short-term rates.If all other factors in the problem remainunchanged, what will earnings after taxes be?
  • SOLUTION:6-12. Colter Steel (Continued) Long-term interest expense = 7% × $3,200,000 = $224,000 Short-term interest expense = 11% × 1,000,000 = 110,000 Total interest expense $334,000 Earnings before interest and taxes $996,000 Interest expense 334,000 Earnings before taxes $662,000 Taxes (40%) 264,800Earnings after taxes $397,200
  • 6-15Using the expectations hypothesis theory for the term structure of interest rates, determine the expected return for securities with maturities of two, three, and four years based on the following data. Do an analysis similar to that in Table 6-6. 1-year T-bill at beginning of year 1 6% 1-year T-bill at beginning of year 2 7% 1-year T-bill at beginning of year 3 9% 1-year T-bill at beginning of year 4 11%
  • SOLUTION:6-15.2 year security (6% + 7%)/2 = 6.5%3 year security (6% + 7% + 9%)/3 = 7.33%4 year security (6% + 7% + 9% + 11%)/4 = 8.25%
  • 18-1Sherwin Paperboard Company expects to sell 600 units inJanuary, 700 units in February, and 1,200 units in March.January’s ending inventory is 800 units. Expected sales forthe whole year are 12,000 units. Sherwin has decided on alevel production schedule of 1,000 units (12,000 units/12months = 1,000 units per month). What is the expectedend-of-month inventory for January, February, and March?Show the beginning inventory, production, and sales foreach month to arrive at ending inventory.
  • SOLUTION:6-18. Sherwin Paperboard Company Beginning Production Ending Inventory + (level) – Sales = InventoryJanuary 800 1,000 600 1,200February 1,200 1,000 700 1,500March 1,500 1,000 1,200 1,300
  • 7-4Thompson Wood Products has credit sales of$2,160,000 and accounts receivable of $288,000.Compute the value of the average collection period.
  • 7-4. Thompson Wood Products Accounts ReceivableAverage collection period = Average daily credit sales $288,000 = $2,160,000 / 360 $288,000 = = 48days $6,000
  • 7-5 Lone Star Petroleum Co. has annual creditsales of $2,880,000 and accounts receivable of$272,000. Compute the value of the averagecollection period.
  • 7-5. Lone Star Petroleum Co. Accounts ReceivableAverage collection period = Average daily credit sales $272,000 = $2,288,000 / 360 $272,000 = 8,000 = 34days
  • 7-6Knight Roundtable Co. has annual credit sales of$1,080,000 and an average collection period of 32days in 2008. Assume a 360-day year. What is thecompany’s average accounts receivable balance?Accounts receivable are equal to the average dailycredit sales times the average collection period
  • 7-6 Knight Roundtable Co. $1,080,000annual credit sales = $3,000credit sales a day 360days per year$3,000 average × 32 average = $96,000 average accountsdaily credit sales collection period receivable balance
  • 7-9Hubbell Electronic Wiring Company has anaverage collection period of 35 days. The accountsreceivable balance is $105,000. What is the value ofits credit sales?
  • 7-9 Hubbell Electronic Wiring Company Accounts receivableAverage collection period = Average daily credit sales $105,000 35 days =  credit sales     360  $105,000 Credit sales/360 = 35 days Credit sales/360 = $3,000 credit sales per day Credit sales = $3,000 × 360 = $1,080,000
  • 7-11Nowlin Pipe & Steel has projected sales of 72,000 pipes this year, an ordering cost of $6 per order, and carrying costs of $2.40 per pipe. a. What is the economic ordering quantity? b. How many orders wil be placed during the year? c. What wil the average inventory be?
  • 7-11 Nowlin Pipe and Steel Company 2SO 2 × 72,000 × $6a. EOQ = = C $2.40 $864,000 = = 360,000 = 600 units $2.40b. 72,000 units/600 units = 120 ordersc. EOQ/2 = 600/2 = 300 units (average inventory)
  • 7-12Howe Corporation is trying to improve its inventory control system and has installed an online computer at its retail stores. Howe anticipates sales of 126,000 units per year, an ordering cost of $4 per order, and carrying costs of $1.008 per unit. a. What is the economic ordering quantity? b. How many orders will be placed during the year? c. What will the average inventory be? d. What is the total cost of inventory expected to be?
  • 7-12 Howe Corp. 2SO 2 × 126,000 × $4a. EOQ = = = 1,000 units C $1.008b. 126,000 units/1,000 units = 126 ordersc. EOQ/2 = 1,000/2 = 500 units (average inventory)d. 126 orders × $4 ordering cost = $ 504 500 units × $1.008 carrying cost per unit = 504 Total costs = $1,008
  • 7-13(See Problem 12 for basic data.) In the second year,Howe Corporation finds it can reduce orderingcosts to $1 per order but that carrying costs willstay the same at $1.008 per unit.a. Recompute a, b, c, and d in Problem 12 forthe second year.b. Now compare years one and two and explainwhat happened
  • 7-13 Howe Corp. (Continued) 2SO 2 ×126, 000 ×$1a. EOQ = = C $1.008 $252, 000 = = 250, 000 =500 units $1.008 126,000 units/500 units = 252 orders EOQ/2 = 500/2 = 250 units (average inventory) 252 orders × $1 ordering cost = $252 250 units × $1.008 carrying cost per unit = 252 Total costs = $504b. The number of units ordered declines 50%, while the number of orders doubles. The average inventory and total costs both decline by one-half. Notice that the total cost did not decline in equal percentage to the decline in ordering costs. This is because the change in EOQ and other variables (½) is proportional to the square root of the change in ordering costs (¼).
  • 8-1 Compute the cost of not taking the following cash discounts.a.2/10, net 40.b.2/15, net 30.c. 2/10, net 45.d.3/10, net 90.
  • 8-1Cost of not Discount % 360taking a cash = ×discount 100% − Disc.% Final due date − Discount perioda. Cost of 2% 360 = × = 2.04% × 12.00 = 24.48% lost discount 98% 40 − 10b. Cost of 2% 360 = × = 2.04% × 24.00 = 48.96% lost discount 98% 30 − 15c. Cost of 2% 360 = × = 2.04% × 10.29 = 20.99% lost discount 98% 45 − 10d. Cost of 3% 360 = × = 3.09% × 4.50 = 13.91% lost discount 97% 90 − 10
  • 8-2 Delilah’s Haircuts can borrow from its bank at 13 percent to take a cash discount. The terms of the cash discount are 2/15, net 55. Should the firm borrow the funds?
  • 8-2 Delilah’s HaircutsFirst, compute the cost of not taking the cash discount andcompare this figure to the cost of the loan.Cost of not Discount% 360taking a cash = ×discount 100% − Disc.% final due date − discount period 2% 360 = × 98% 55 − 15 = 2.04% × 9 = 18.36%The cost of not taking the cash discount is greater than the cost ofthe loan (18.36% vs. 13%). The firm should borrow the moneyand take the cash discount.
  • 8-3 Your bank will lend you $4,000 for 45 days at a cost of $50 interest. What is your effective rate of interest?
  • 8-3
  • 8-5 I. M. Boring borrows $5,000 for one year at 13 percent interest. What is the effective rate of interest if the loan is discounted?
  • 8-5 I.M. BoringEffective rate on a = Interest × Days per year (360)discounted loan Princ. − Int. Days loan is outstanding $650 360 $650 = × = ×1 $5,000 − $650 360 $4,350 = 14.94%
  • 8-7Mo and Chris’s Sporting Goods, Inc., borrows $14,500 for 20 days at 12 percent interest. What is the dollar cost of the loan? Use the formula: Dollar cost Amount Interest Days loan is outstanding = × × of loan borrowed rate Days in the year (360)
  • 8-7 Mo and Chris’ Sporting GoodsDollar cost of loan = Days loan is outstandingAmount Borrowed × Interest rate × Days in the year (360) 20 = $14,500 × 12% × 360 1 = $14,500 × 12% × 18 = $14,500 × .67% = $97.15
  • 8-8Sampson Orange Juice Company normally takes 20 days to pay for its average daily credit purchases of $6,000. Its average daily sales are $7,000, and it collects accounts in 28 days. a. What is its net credit position? That is, compute its accounts receivable and accounts payable and subtract the latter from the former. Accounts receivable = Average daily credit sales × Average collection period Accounts payable = Average daily credit purchases × Average payment period b. If the firm extends its average payment period from 20 days to 35 days (and all else remains the same), what is the firm’s new net credit position? Has it improved its cash flow?
  • 8-8 Sampson Orange Juice Companya. Net credit position = accounts receivable – accounts payable Accounts rec.= Average Daily × Average Credit Purchases Payment Period $196,000 = $7,000 × 28 Accounts payable = Average Daily × Average Credit Purchases Payment Period $120,000 = $6,000 × 20 Net Credit Position = $196,000 – $120,000 = $76,000b. Accounts Receivable will remain at $196,000 Accounts Payable = $6,000 × 35 = 210,000 Net Credit Position ($ 14,000) The firm has improved its cash flow position. Instead of extending $76,000 more in credit (funds) than it is receiving, it has reversed the position and is the net recipient of $14,000 in credit.
  • 8-9 Maxim Air Filters, Inc., plans to borrow $300,000 for one year. Northeast National Bank will lend the money at 10 percent interest and requires a compensating balance of 20 percent. What is the effective rate of interest?
  • 8-9 Maxim Air Filters, Inc. Effective rate of interest with 20% compensating balance = Interest rate 10% 10% = = = 12.5% ( 1 − C) ( 1 − .2 ) .8 or Interest Days of the year (360) ×Principal − Compensating balance Days loan is outstanding $30,000 $30,000= ×1 = × 1 = 12.5% $300,000 − $60,000 $240,000
  • 8-10Digital Access, Inc., needs $400,000 in funds for a project. a. With a compensating balance requirement of 20 percent, how much wil the firm need to borrow?b. Given your answer to part a and a stated interest rate of 9 percent on the total amountborrowed, what is the effective rate on the $400,000 actually being used?
  • 8-10 Digital Access, Inc. Amount neededa. Amount to be borrowed = ( 1 − C) $400, 000 $400, 000 = = ( 1 − .20 ) .80 = $500, 000b. $500,000 total amount borrowed 9% Interest rate $ 45,000 Interest $45, 000 = 11.5% $400, 000
  • 8-15Your company plans to borrow $5 million for 12 months, and your banker gives you a stated rateof 14 percent interest. You would like to know the effective rate of interest for the followingtypes of loans. (Each of the following parts stands alone.) a. Simple 14 percent interest with a 10 percent compensating balance. b. Discounted interest. c. An installment loan (12 payments). d. Discounted interest with a 5 percent compensating balance.
  • 8-15a. Simple interest with a 10% compensating balance $700, 000 $700, 000 ×1 = = 15.56% $5, 000, 000 − $500, 000 $4,500, 000b. Discounted interest $700, 000 $700, 000 ×1 = = 16.28% $5, 000, 000 − $700, 000 $4,300, 000c. An installment loan with 12 payments 2 × 12 × $700, 000 $16,800, 000 = = 25.85% 13 × $5, 000, 000 $65, 000, 000d. Discounted interest with a 5% compensating balance $700,000/($5,000,000 – $700,000 – $250,000) = 17.28%
  • 8-16If you borrow $12,000 at $900 interest for one year, what is your effective interest rate for the following payment plans? a. Annual payment. b. Semiannual payments. c. Quarterly payments. d. Monthly payments.
  • 8-16a. $900/$12,000 = 7.5% Use formula 8-6 for b, c, and d. Rate on installment loan = 2 × Annual no. of payments × Interest ( Total no. of payments + 1) × Principalb. (2 × 2 × $900)/(3 × $12,000) = $3,600/$36,000 = 10.00%c. (2 × 4 × $900)/(5 × $12,000) = $7,200/$60,000 = 12.00%d. (2 × 12 × $900)/(13 × $12,000) = $21,600/$156,000 = 13.85%
  • 8-18Mr. Paul Promptly is a very cautious businessman. His supplier offers trade credit terms of 3/10,net 70. Mr. Promptly never takes the discount offered, but he pays his suppliers in60 days rather than the 70 days allowed so he is sure the payments are never late. What isMr. Promptly’s cost of not taking the cash discount?
  • 8-18 Paul PromptlyCost of not taking = Discount % × 360a cash discount 100% − Disc.% Payment date − Discount period 3% 360 = × 100% − 3% 60 − 10 = 3.09% × 7.2 = 22.25%In this problem, Mr. Promptly has the use of funds for 50 extradays (60-10), instead of 60 extra days (70-10). Mr. Promptly’ssuppliers are offering terms of 3/10, net 70. Mr. Promptly iseffectively accepting terms of 3/10, net 60.
  • 8-20 In problem 19, if the compensating balance requirement were 10 percent instead of25 percent, would you change your answer? Do the appropriate calculation.
  • 8-20 The Ogden Time Company (Continued) Effective rate of interest with a 10% compensating balance requirement: Interest rate 15% 15% = = = = 16.67% ( 1 − C) ( 1 − .1) ( .9 )The answer now changes. The effective cost of the loan, 16.67%, is lessthan the cost of passing up the discount. Ogden Timber Company shouldborrow the funds and take the discount
  • 1-69Q End
  • 1-70 Q&A
  • 1-71Thank You.