maths. topic 2,3,4,5

5-1

Gateway Appliance toasters sell for $20 per unit, and the variable cost to produce them is $15. Gateway estimates that the fixed costs are $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 5

Solution:

Gateway Appliance

a. Fixed costs

BEPr ice-variable cost per unit

$80,000 $80,00016,000 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

5-2

5-2 Hazardous Toys Company produces boomerangs that sell for $8 each 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

a. $15,000

BE 30,000 units$8.00 $7.50

b. Profit FC $25,000 $15,000Q

(P VC) $8.00 $7.50

$40,00080,000 units

$.50

5-3

Ensco Lighting Company has fixed costs of $100,000, sells its units for $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 increase variable 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 at very high volume levels (compared to the old plan)?

CHAPTER 5Solution:

Ensco Lighting Company

a. Fixed costs

BEPr ice variable cost per unit

$100,000 $100,0008,000 units

$28 $15.50 $12.50

5-3. (Continued)

b. Fixed costs

BEPr ice variable cost per unit

$75,000 $75,0006,818 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 5-11Sterling Tire Company

Q = 20,000, P = $60, VC = $30, FC = $400,000, I = $50,000

a. Q(P VC)

DOLQ(P VC) FC

20,000($60 $30)

20,000($60 $30) $400,000

20,000($30)

20,000($30) $40,000

$600,000 $600,0003.00x

$600,000 $400,000 $200,000

5-11. (Continued)

b. EBIT $200,000

DFLEBIT I $200,000 $50,000

$200,0001.33x

$150,000

c. Q (P VC)DCL

Q(P VC) FC I

20,000($60 $30)

20,000($60 $30) $400,000 $50,000

$600,000 $600,0004x

$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 Company

Q = 30,000, P = $25, VC = $7, FC = $270,000, I = $170,000

a. Q(P VC)

DOLQ(P VC) FC

30,000($25 $7)

30,000($25 $7) $270,000

30,000($18)

30,000($18) $270,000

$540,000 $540,0002x

$540,000 $270,000 $270,000

b. EBIT $270,000

DFLEBIT I $270,000 $170,000

$270,0002.7x

$100,000

c. Q(P VC)DCL

Q(P VC) FC I

30,000($25 $7)

30,000($25 $7) $270,000 $170,000

30,000($18) $540,0005.4x

30,000($18) $440,000 $100,000

d. $270,000

BE 15,000 units$25 $7

5-14U.S. Steal has the following income statement data:

Units Sold

Total Variable

Costs Fixed Costs

Total Costs

Total Revenue

Operating Income (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

a. Percent change in operating incomeDOL

Percent change in units sold

$40,000133%30,000 100 2.66

20,000 50%40,000 100

5-14. (Continued)

b. Q(P VC)

DOLQ(P VC) FC

Q 40,000

Total revenue $160,000P $4

Units sold 40,000

Total variable costs $80,000VC $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

6-1

Gary’s Pipe and Steel company expects sales next year to be $800,000 if the economy is strong, $500,000 if the economy is steady, and $350,000 if the economy is weak. Gary believes there is a 20 percent probability the economy will be strong, a 50 percent probability of a steady economy, and a 30 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 Economy Sales Probability

Expected 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

6-2

Nile Riverboat Co., a major boat building company highly sensitive to the economy, expects profits next 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 believes there is a 30 percent probability of a strong economy, a 40 percent probability of a steady economy, and a 30 percent probability of a weak economy. What is the expected value of profits for next year?

6-2Nile Riverboat Co.

State of Economy Profits Probability

Expected 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

6-3

Tobin Supplies Company expects sales next year to be $500,000. Inventory and accounts receivable will increase $90,000 to accommodate this sales level. The company has a steady profit margin of 12 percent with a 40 percent dividend payout. How much external financing will Tobin Supplies Company have to seek? Assume there is no increase in liabilities other than that which will occur 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

6-7

Procter Micro-Computers, Inc., requires $1,200,000 in financing over the next two years. The firm can borrow the funds for two years at 9.5 percent interest per year. Mr. Procter decides to do economic forecasting and determines that if he utilizes short-term financing instead, he will pay 6.55 percent interest in the first year and 10.95 percent interest in the second year. Determine the total two-year interest cost under each plan. Which plan 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 Financing

1st year $1,200,000 × 6.55% per annum = $ 78,600 interest cost 2nd year $1,200,000 × 10.95% per annum = $131,400 interest cost $210,000 two-year total The short-term plan is less costly.

6-11

11. 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 Steel

Long-term financing equals:

Permanent current assets $2,000,000 Fixed assets 1,200,000 $3,200,000

Short-term financing equals:

Temporary current assets $1,000,000

Long-term interest expense = 13% × $3,200,000 = $ 416,000 Short-term interest expense = 8% × 1,000,000 = 80,000 Total interest expense $ 496,000 Earnings before interest and taxes $ 996,000 Interest expense 496,000 Earnings before taxes $ 500,000 Taxes (40%) 200,000 Earnings after taxes $ 300,000

6-12

In problem 11, assume the term structure of interest rates becomes inverted, with short-term rates going to 11 percent and long-term rates 4 percentage points lower than short-term rates.If all other factors in the problem remain unchanged, 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%) 264,800

Earnings after taxes $397,200

6-15

Using 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%

18-1

Sherwin Paperboard Company expects to sell 600 units in January, 700 units in February, and 1,200 units in March. January’s ending inventory is 800 units. Expected sales for the whole year are 12,000 units. Sherwin has decided on a level production schedule of 1,000 units (12,000 units/12 months = 1,000 units per month). What is the expected end-of-month inventory for January, February, and March? Show the beginning inventory, production, and sales for each month to arrive at ending inventory.

SOLUTION:6-18.

Sherwin Paperboard Company

Beginning Production Ending Inventory + (level) – Sales = Inventory

January 800 1,000 600 1,200 February 1,200 1,000 700 1,500 March 1,500 1,000 1,200 1,300

7-4

Thompson 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

$288,00048days

$6,000

7-5

Lone Star Petroleum Co. has annual credit sales of $2,880,000 and accounts receivable of $272,000. Compute the value of the average collection 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

7-6

Knight Roundtable Co. has annual credit sales of $1,080,000 and an average collection period of 32 days in 2008. Assume a 360-day year. What is the company’s average accounts receivable balance? Accounts receivable are equal to the average daily credit 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

7-9

Hubbell Electronic Wiring Company has an average collection period of 35 days. The accounts receivable balance is $105,000. What is the value of its credit sales?

7-9

Hubbell Electronic Wiring Company

Accounts receivableAverage collection period

Average daily credit sales

$105,00035 days

credit sales360

$105,000Credit sales/360

35 days

Credit sales/360 $3,000 credit sales per day

Credit sales $3,

000 360 $1,080,000

7-11

Nowlin 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 will be placed during the year? c. What will the average inventory be?

7-11

Nowlin Pipe and Steel Company

a. 2SO 2 72,000 $6EOQ

C $2.40

$864,000360,000 600 units

$2.40

b. 72,000 units/600 units = 120 orders

c. EOQ/2 = 600/2 = 300 units (average inventory)

7-12

Howe 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.

a. 2SO 2 126,000 $4

EOQ 1,000 unitsC $1.008

b. 126,000 units/1,000 units = 126 orders

c. 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 ordering costs to $1 per order but that carrying costs will stay the same at $1.008 per unit.a. Recompute a, b, c, and d in Problem 12 for the second year.b. Now compare years one and two and explain what happened

7-13Howe Corp. (Continued)

a. 2SO 2 126,000 $1EOQ

C $1.008

$252,000250,000 500 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 = $504

b. 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.

8-1

Cost of not Discount % 360taking a cash =

100% Disc.% Final due date discountDiscount period

a. 2% 360Cost of 2.04% 12.00 24.48%lost discount 98% 40 10

b. 2% 360Cost of = 2.04% 24.00 48.96%lost discount 98% 30 15

c.

2% 360Cost of = 2.04% 10.29 20.99%lost discount 98% 45 10

d.

3% 360Cost of = 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?

8-2Delilah’s Haircuts

First, compute the cost of not taking the cash discount and compare this figure to the cost of the loan.

Cost of not Discount% 360taking a cash =

100% Disc.% final due date discount perioddiscount

2% 360

98% 55 15

2.04% 9 18.36%

The cost of not taking the cash discount is greater than the cost of the loan (18.36% vs. 13%). The firm should borrow the money and 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. Boring

Interest Days per year (360)Effective rate on a =discounted loan Princ. Int. Days loan is outstanding

$650 360 $6501

$5,000 $650 360 $4,350

14.94%

8-7

Mo 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 Goods

Dollar cost of loan =

Days loan is outstandingAmount Borrowed Interest rate

Days in the year (360)

20$14,500 12%

3601

$14,500 12%18

$14,500 .67% $97.15

8-8

Sampson 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?

8-8Sampson Orange Juice Company

a. Net credit position = accounts receivable – accounts payable

Average Daily AverageAccounts rec.= Credit Purchases Payment Period

$196,000 $7,000 28

Average Daily AverageAccounts payable = Credit Purchases Payment Period

$120,000 $6,000 20

Net Credit Position = $196,000 – $120,000 = $76,000

b. 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 $30,0001 1 12.5%

$300,000 $60,000 $240,000

8-10

Digital Access, Inc., needs $400,000 in funds for a project.

a. With a compensating balance requirement of 20 percent, how much will the firm need to borrow?

b. Given your answer to part a and a stated interest rate of 9 percent on the total amount borrowed, what is the effective rate on the $400,000 actually being used?

8-10

Digital Access, Inc.

a.

Amount neededAmount to be borrowed =

1 C

$400,000 $400,000

1 .20 .80

$500,000

b. $500,000 total amount borrowed

9% Interest rate

$ 45,000 Interest

$45,00011.5%

$400,000

8-15

Your company plans to borrow $5 million for 12 months, and your banker gives you a stated rate of 14 percent interest. You would like to know the effective rate of interest for the following types 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 $4,500,000

b. Discounted interest

$700,000 $700,000

1 16.28%$5,000,000 $700,000 $4,300,000

c. An installment loan with 12 payments

2 12 $700,000 $16,800,000

25.85%13 $5,000,000 $65,000,000

d. Discounted interest with a 5% compensating balance

$700,000/($5,000,000 – $700,000 – $250,000) = 17.28%

8-16

If 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.

8-16

a. $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 Principal

b. (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%

8-18

Mr. 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 in 60 days rather than the 70 days allowed so he is sure the payments are never late. What is Mr. Promptly’s cost of not taking the cash discount?

8-18

Paul Promptly

Discount % 360Cost of not taking = a cash discount 100% Disc.% Payment dateDiscount 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 extra days (60-10), instead of 60 extra days (70-10). Mr. Promptly’s suppliers are offering terms of 3/10, net 70. Mr. Promptly is effectively accepting terms of 3/10, net 60.

8-20

In problem 19, if the compensating balance requirement were 10 percent instead of 25 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 less than the cost of passing up the discount. Ogden Timber Company should borrow the funds and take the discount

Q

End

1-69

Q & A

1-70

Thank You.

1-71