“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
Maths. topic 2,3,4,5
1. 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) ____________
2. CHAPTER 5
Solution:
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
3. 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.
4. 5-2
Solution:
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. 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)?
6. CHAPTER 5
Solution:
Ensco Lighting Company
Fixed costs
a. BE =
Pr ice −variable cost per unit
$100,000 $100, 000
= = =8, 000 units
$28 −$15.50 $12.50
5-3. (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.
7. 5-11
The 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.
9. 5-12
The 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.
11. 5-14
U.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.
12. 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 ×100
5-14. (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, 000
DOL = =
40, 000($4 −$2) −$50, 000 $80, 000 − $50, 000
$80, 000
= =$2.67
$30, 000
13. 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?
14. 6-1
Gary’s Pipe and Steel Company
State of Expected
Economy 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
15. 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?
16. 6-2
Nile Riverboat Co.
State of Expected
Economy 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
17. 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.
18. 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
19. 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?
20. 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
21. 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?
22. 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
nd
2 year $1,200,000 × 10.95% per annum = $131,400 interest cost
$210,000 two-year total
The short-term plan is less costly.
23. 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.
24. 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
25. 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?
26. 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
27. 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%
29. 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.
30. 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
31. 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.
32. 7-4.
Thompson Wood Products
Accounts Receivable
Average collection period =
Average daily credit sales
$288,000
=
$2,160,000 / 360
$288,000
= = 48days
$6,000
33. 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.
34. 7-5.
Lone Star Petroleum Co.
Accounts Receivable
Average collection period =
Average daily credit sales
$272,000
=
$2,288,000 / 360
$272,000
=
8,000
= 34days
35. 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
36. 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 accounts
daily credit sales collection period receivable balance
37. 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?
38. 7-9
Hubbell Electronic Wiring Company
Accounts receivable
Average 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
39. 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 wil be placed during the year?
c. What wil the average inventory be?
40. 7-11
Nowlin Pipe and Steel Company
2SO 2 × 72,000 × $6
a. EOQ = =
C $2.40
$864,000
= = 360,000 = 600 units
$2.40
b. 72,000 units/600 units = 120 orders
c. EOQ/2 = 600/2 = 300 units (average inventory)
41. 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?
42. 7-12
Howe Corp.
2SO 2 × 126,000 × $4
a. EOQ = = = 1,000 units
C $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
43. 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
44. 7-13
Howe Corp. (Continued)
2SO 2 ×126, 000 ×$1
a. 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 = $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).
45. 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.
46. 8-1
Cost of not Discount % 360
taking a cash = ×
discount 100% − Disc.% Final due date −
Discount period
a. Cost of 2% 360
= × = 2.04% × 12.00 = 24.48%
lost discount 98% 40 − 10
b. Cost of 2% 360
= × = 2.04% × 24.00 = 48.96%
lost discount 98% 30 − 15
c. Cost of 2% 360
= × = 2.04% × 10.29 = 20.99%
lost discount 98% 45 − 10
d. Cost of 3% 360
= × = 3.09% × 4.50 = 13.91%
lost discount 97% 90 − 10
47. 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?
48. 8-2
Delilah’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% 360
taking 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 of
the loan (18.36% vs. 13%). The firm should borrow the money
and take the cash discount.
49. 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?
51. 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?
52. 8-5
I.M. Boring
Effective 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%
53. 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)
54. 8-7
Mo and Chris’ Sporting Goods
Dollar cost of loan =
Days loan is outstanding
Amount Borrowed × Interest rate ×
Days in the year (360)
20
= $14,500 × 12% ×
360
1
= $14,500 × 12% ×
18
= $14,500 × .67% = $97.15
55. 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?
56. 8-8
Sampson Orange Juice Company
a. 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 = $76,000
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.
57. 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?
58. 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
59. 8-10
Digital 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 amount
borrowed, what is the effective rate on the $400,000 actually being used?
60. 8-10
Digital Access, Inc.
Amount needed
a. Amount 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, 000
= 11.5%
$400, 000
61. 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.
62. 8-15
a. 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%
63. 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.
64. 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%
65. 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?
66. 8-18
Paul Promptly
Cost of not taking = Discount % × 360
a 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 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.
67. 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.
68. 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
