Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges

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374 Part 5 Business Applications

THE BOTTOM LINE

Review of chapter learning objectives:

Learning Objective

18.1

Compute depreciation using the straight-line method.

Example

1. On January 1, 2008, the local Pepsi-Cola bottling franchise purchased

a bottling machine for $320,000. Freight was added for $12,000. The

cost of installation was $68,000. It was estimated that the machine

had a useful life span of five years, after which there would be no

resale value. Using the straight-line method, determine the annual

amount of depreciation.

Answers: 1. $80,000 2. $7,520 3. $12,321 4. First year: $14,000; Second year: $12,000 5. First year: 20.00% rate,

$2,400 depreciation, $9,600 EBV; Second year: 32.00% rate, $3,840 depreciation, $5,760 EBV 6. 2008: $50;

2009: $200

18.6

Compute partial-year depreciation using the five

different primary depreciation methods covered.

6. On October 1, 2008, Corner Grocery bought and installed a new

cash register for $1,400. It has an estimated service life of 6 years

and an estimated scrap value of $200. The company decided to use

the straight-line method of depreciation. What was the depreciation

for 2008? What was it for 2009?

18.5

Compute depreciation for income tax purposes, using the

Modified Accelerated Cost Recovery System (MACRS).

5. Bank One bought new calculators in July for $12,000. Using the

MACRS method (5-year class), show the rate, depreciation, and

ending book value for the first 2 years.

18.4

Compute depreciation using the sum-of-the-years-digits

method.

4. A local Ford dealership purchased, for $60,000, a hydraulic lift unit

with an estimated life of 7 years and a scrap value of $4,000.

Compute the depreciation for each of the first 2 years using the

sum-of-the-digits method. Round to the nearest dollar.

18.3

Compute depreciation using the declining-balance

method.

3. For $56,000, a Gap clothing store bought display racks with an

estimated life of 20 years and a scrap value of $4,000. After 3 years,

this store closed and sold the display racks for $32,000. If the racks

were depreciated by the declining-balance method (150% annual

rate), how much less than the book value did the company receive?

Round to the nearest dollar.

18.2

Compute depreciation using the units-of-production

method.

2. The Yellow Cab Company bought a new taxi for $42,000 and

estimated its useful life to be 200,000 miles, after which it would

have a scrap value of $2,000. Compute the depreciation for the first

7 months if the vehicle had been driven 37,600 miles.

Chapter 18 Depreciation 375

SELF-CHECK

Review Problems for Chapter 18

1 Determine the annual declining-balance depreciation rate to be used for each of the following:

a. 150% declining balance, 12-year life

b. 200% declining balance, 8-year life

c. 125% declining balance, 5-year life

d. 200% declining balance, 5-year life

2 What fraction is to be used each year for sum-of-the-years-digits depreciation for an asset with a useful life

of 4 years?

3 For which depreciation method(s) is salvage value not subtracted to calculate depreciation?

4 Lopez Construction Company purchased construction equipment for $116,000 at the beginning of the year. It

is estimated that the equipment will have a useful life of 12 years and will have a scrap value of $8,000.

a. Calculate the annual depreciation if Lopez uses straight-line depreciation.

b. Calculate the book value of the equipment at the end of 5 years, assuming that Lopez uses straight-line

depreciation.

c. Compute the depreciation for the first year ending December 31 if Lopez purchased the equipment

September 1.

d. Determine the depreciation per hour if Lopez uses the straight-line method based on 120,000 hours of

useful life and an $8,000 scrap value.

e. Using the rate determined in (d), what is the depreciation for the year if the equipment is used for 2,360

hours?

5 Jurgenson Manufacturing uses the double-declining-balance method of depreciation. A piece of equipment

costing $37,500 has an estimated useful life of 5 years and an estimated scrap value of $2,700.

a. Compute the amount of depreciation taken in the second year.

b. What is the book value at the end of the second year?

6 Young Manufacturing uses the sum-of-the-years-digits method of depreciation. Equipment costing $37,500

has an estimated life of 5 years and an estimated scrap value of $2,700.

a. Compute the amount of depreciation expense for the second year.

b. What is the book value at the end of the second year?

7 Calculate the depreciation expense for tax purposes using MACRS for each asset. Use Figure 18-1 on page

370 to determine the proper life and rate for each asset. (Round to the nearest dollar.)

a. Computer equipment purchased this year for $5,200.

b. Office furniture purchased 2 years ago for $8,500. (This is the third year.)

Answers to the Self-Check can be found in Appendix B at the back of the text.

376 Part 5 Business Applications

Notes

Chapter 18 Depreciation 377

Assignment 18.1: Business Depreciation

Name

Date Score

A (30 points) Solve the following depreciation problems. (points for correct answers as marked)

1. A pharmaceutical company has testing machines on which it estimates depreciation by the straight-line

method. The following table shows cost, estimated life, years used, and scrap value for each machine.

Find the annual depreciation, total depreciation, and book value after the indicated number of years of

use. ( point for each correct answer)

Total

Original Estimated Years Scrap Annual Depreciation

CostLife (years)Used Value Depreciation to Date Book Value

a. $30,000 10 8 $3,000

b. 48,000 7 6 $5,300

c. 84,000 8 5 none

d. 34,600 6 1 $1,000

2. Ace Delivery Service bought two new trucks. The following table shows the cost, scrap value, estimated life

(in miles), and mileage for the first year. Using the straight-line method based on mileage driven, compute

the first year’s depreciation and the book value at the end of the first year for each truck. (2 points for each

correct depreciation amount and 1 point for each correct book value)

Original Scrap Estimated Life Mileage for Depreciation Book Value

Cost Value (miles)First Year for First Year after 1 Year

a. $49,500 $1,500 150,000 21,700

b. $23,000 $ 600 80,000 9,500

3. Dole Fruit Company’s equipment cost $214,000. Its useful life is estimated to be 15 years, and its scrap

value is $4,000. The company uses straight-line depreciation. (2 points for each correct answer)

a. What is the annual depreciation?

b. What is the book value of the equipment at the end of 14 years?

$18,000

$14,000

$20,340$2,660

$42,556$6,944

$29,000$5,600$5,600

$31,500$52,500$10,500

$11,400$36,600$6,100

$8,400$21,600$2,700

Illustrative solution:

a. ($30,000 cost 2 $3,000 SV) 4 10 years 5 $2,700 annual depreciation

$2,700 3 8 years 5 $21,600 total depreciation to date

$30,000 2 $21,600 5 $8,400 book value

Illustrative solution:

a. $49,500 cost 2 $1,500 scrap value 5 $48,000 to be depreciated; $48,000 4 150,000 miles 5 $0.32 depreciation

per mile; 21,700 miles 3 $0.32 5 $6,944 depreciation first year; $49,500 original cost 2 $6,944 5 $42,556 book

value after 1 year

$214,000 2 $4,000 5 $210,000 total depreciation

$210,000 4 15 years 5$14,000 annual depreciation

$14,000 3 14 years 5 $196,000

$214,000 2 $196,000 5 $18,000 book value after 14 years

Learning Objectives

2 3 4

4. Carlucci and sons purchased a machine for $13,645 at the beginning of the year. Additional costs included

$250 freight and $175 for installation. It was estimated that the machine could be operated for 30,000

hours, after which its resale value would be $570. Determine the straight-line depreciation based on hours

of operation and the book value at the end of each of the first 7 years. (1 point for each correct answer)

Hours of

Year Operation Depreciation Book Value

1 2,300

2 2,750

3 2,500

4 2,480

5 2,800

6 3,100

7 2,950

Score for A (30)

B (56 points) Solve the following depreciation problems. Round dollar amounts to two decimal places.

(points for correct answers as marked)

5. Anderson Tool and Die Company owns a group of machines, the details of which are shown in the

following table. Anderson uses the double-declining-balance method of calculating depreciation.

Compute the depreciation for the specific years indicated. (2 points for each correct answer)

Original Estimated Scrap

CostLife (years) Value Year Depreciation Year Depreciation

a. $32,000 16 $1,200 1 3

b. $25,800 5 $3,000 3 5

c. $ 8,000 4 $ 300 2 3

d. $15,000 10 — 3 5

e. $12,600 8 $1,200 2 4

f. $95,000 20 — 3 5

$6,232.95$7,695.00

$1,328.91$2,362.50

$1,228.80$1,920.00

$1,000.00$2,000.00

$343.68$3,715.20

$3,062.50$4,000.00

$5,574.00$1,327.50

$6,901.50$1,395.00

$8,296.50$1,260.00

$9,556.50$1,116.00

$10,672.50$1,125.00

$11,797.50$1,237.50

$13,035.00$1,035.00

378 Part 5 Business Applications

Assignment 18.1 Continued

Illustrative solution:

Year 1: $13,645 1 $250 1 $175 5 $14,070 full cost

$14,070 2 $570 5 $13,500 total depreciation

$13,500 4 30,000 5 $0.45 depreciation per hour

2,300 3 $0.45 5 $1,035 depreciation first year

$14,070 2 $1,035 5 $13,035 book value end of first year

Year 2: 2,750 3 $0.45 5 $1,237.50 depreciation second year

$13,035 2 $1,237.50 5 $11,797.50 book value end of second year

Illustrative solutions:

a. 100% 4 16 years 5 6.25% 3 2 5 12.5% annual rate b. 100% 4 5 yrs 5 20% 3 2 5 40% annual rate

$32,000 3 12.5% 5 $4,000 depreciation first year $25,800 3 40% 5 $10,320 depreciation first year

$32,000 2 $4,000 5 $28,000 new balance $25,800 2 $10,320 5 $15,480 new balance

$28,000 3 12.5% 5 $3,500 depreciation second year $15,480 3 40% 5 $6,192 depreciation second year

$28,000 2 $3,500 5 $24,500 new balance $15,480 2 $6,192 5 $9,288 new balance

$24,500 3 12.5% 5 $3,062.50 depreciation third year $9,288 3 40% 5 $3,715.20 depreciation third year

$9,288 2 $3,715.20 5 $5,572.80 new balance

$5,572.80 3 40% 5 $2,229.12 depreciation fourth year

$5,572.80 2 $2,229.12 5 $3,343.68 new balance

$3,343.68 2 $3,000 scrap value 5 $343.68 depreciation fifth year

(40% in year 5 would decrease book value below scrap value)

6. Machinery purchased from Telecom, Inc., by Blazedales cost $69,800. Depreciation was determined by

the double-declining-balance method for an estimated life of 16 years. Compute the following:

a. Book value after 4 years (8 points):

$40,915.47

Chapter 18 Depreciation 379

Assignment 18.1 Continued

100% 4 16 5 6.25%; 6.25% 3 2 5 12.5% annual rate

$69,800 3 0.125 5 $8,725 depreciation first year

$69,800 2 $8,725 5 $61,075 new balance

$61,075 3 0.125 5 $7,634.38 depreciation second year

$61,075.00 2 $7,634.38 5 $53,440.62 new balance

$53,440.62 3 0.125 5 $6,680.08 depreciation third year

$53,440.62 2 $6,680.08 5 $46,760.54 new balance

$46,760.54 3 0.125 5 $5,845.07 depreciation fourth year

$46,760.54 2 $5,845.07 5 $40,915.47 book value after 4 years

100% 4 20 5 5%; 5% 3 2 5 10% annual rate

$31,500 3 0.10 5 $3,150 depreciation first year

$31,500 2 $3,150 5 $28,350 new balance

$28,350 3 0.10 5 $2,835 depreciation second year

$28,350 2 $2,835 5 $25,515 new balance

$25,515 3 0.10 5 $2,551.50 depreciation third year

$25,515 2 $2,551.50 5 $22,963.50 new balance

$22,963.50 3 0.10 5 $2,296.35 depreciation fourth year

$22,963.50 2 $2,296.35 5 $20,667.15 new balance

$20,667.15 3 0.10 5 $2,066.72 depreciation fifth year

$20,667.15 2 $2,066.72 5 $18,600.43 new balance

$18,600.43 3 0.10 5 $1,860.04 depreciation sixth year

$18,600.43 2 $1,860.04 5 $16,740.39 book value at end of sixth year

$16,740.39 2 $15,200 5 $1,540.39 loss

$40,915.47 3 0.125 5 $5,114.43 depreciation fifth year

$40,915.47 2 $5,114.43 5 $35,801.04 new balance

$35,801.04 3 0.125 5 $4,475.13 depreciation sixth year

$35,801.04 2 $4,475.13 5 $31,325.91 new balance

$69,800 2 $31,325.91 5 $38,474.09 total depreciation after 6 years

b. Total depreciation after 6 years (4 points):

$38,474.09

7. The Dugan Manufacturing Company bought an engine for $31,500. The engine had an estimated life

of 20 years and a scrap value of $5,250. After 6 years, the company went out of business and sold the

engine for $15,200. If the machine was depreciated by the double-declining-balance method, how

much did the company lose on the sale (the difference between the book value and the selling price)?

(20 points)

$1,540.39

Score for B (56)

C (14 points) Solve the following depreciation problems. (1 point for each correct answer)

The Western Salvage Service bought three trucks. The following table shows the cost, estimated life, and

resale estimate for each truck. Use the sum-of-the-years-digits method to find each truck’s depreciation

for the first and second years of use. Round answers to the nearest dollar.

Depreciation for Depreciation for

Original CostEstimated Life Resale Estimate First Year Second Year

a. $36,000 6 yr $6,000

b. $48,000 5 yr 8,000

c. $60,000 7 yr 12,000

$10,286$12,000

$10,667$13,333

$7,143$8,571

380 Part 5 Business Applications

Assignment 18.1 Continued

Illustrative solution:

a. or 1 1 2 1 3 1 4 1 5 1 6 5 21

$36,000 2 $6,000 5 $30,000 total depreciation

First year: Second year:

3 $30,000 5 $7,143

3 $30,000 5 $8,571

(6 1 1)6

5 21,

9. Use the information in problem 8b to compute the amount of depreciation for years 3–5.

Year 3:

Year 4:

Year 5:

$2,667

$5,333

$8,000

Year 3:

Year 4:

Year 5:

3 $40,000 5 $2,667

3 $40,000 5 $5,333

3 $40,000 5 $8,000

10. Use the information in problem 8 to compute the amount of depreciation for each vehicle for the first 2

years using the straight-line method. Round to the nearest dollar.

a. b. c.

$13,714$16,000$10,000

a. ($36,000 2 $6,000) 4 6 5 $5,000; $5,000 3 2 5 $10,000

b. ($48,000 2 $8,000) 4 5 5 $8,000; $8,000 3 2 5 $16,000

c. ($60,000 2 $12,000) 4 7 5 $6,857; $6,857 3 2 5 $13,714

11. Which method of depreciation would give the smaller amount of write-off, and how much less would it

be for the three vehicles for the first 2 years?

straight-line $22,286straig

SYD: ($8,571 1 $7,143) 1 ($13,333 1 $10,667) 1 ($12,000 1 $10,286) 5 $62,000

SL: $10,000 1 $16,000 1 $13,714 5 $39,714

Difference: $62,000 2 $39,714 5 $22,286

Score for C (14)

Chapter 18 Depreciation 381

Assignment 18.2: Business Depreciation

Name

Date Score

A (43 points) Solve the following depreciation problems. Round dollar amounts to two decimal places.

(points for correct answers as marked)

1. An architect bought drafting equipment for $7,500. Its estimated life was 6 years, and its scrap value was

$300. At the end of 4 years, the equipment wears out and is sold for scrap for $225. (4 points for each

correct answer)

a. By the straight-line method, how much difference is there between the book value and the cash value of the

equipment on the date of the sale?

b. In April 2000, a computer and software costing $18,000 are purchased. Its estimated life is 5 years. What is the

book value of the new computing equipment on December 31, 2001? Use MACRS.

2. E, F, and G were partners in a small textile company. They spent $54,000 for equipment that they agreed

would last 8 years and have a resale value of 5% of cost. The three partners couldn’t agree on the

depreciation method to use. E was in favor of using the double-declining-balance system, F insisted on

the 150%-declining-balance method, and G was sure that the sum-of-the-years-digits method would be

better. Show the depreciation for the first 4 years for each method in the following table. At the end of 4

years, what would be the book value under each of the three methods? (2 points for each correct

depreciation amount, 1 point for each correct total, and 1 point for the correct book value)

Year Double-DB 150%-DB SYD

Total

Book value

3. Baxter Company owned assets that cost $240,000. Depreciation was figured at a straight-line rate of 6.5%

per year. After 12 years, the company sold the assets for $150,000. How much greater was the selling price

than the book value at the time of the sale? (5 points)

Score for A (43)

$97,200

$16,950$23,533.54$17,085.94

$37,050$30,466.46$36,914.06

$7,125$5,430.82$5,695.31

$8,550$6,684.08$7,593.75

$9,975$8,226.56$10,125.00

$11,400$10,125.00$13,500.00

$8,640

$2,475

$7,500 2 $300 5 $7,200 total depreciation

$7,200 4 6 years 5 $1,200 annual depreciation

$1,200 3 4 years 5 $4,800

$7,500 2 $4,800 5 $2,700 book value

$2,700 2 $225 5 $2,475

20% 1 32% 5 52% recovery for 2000 and 2001

$18,000 3 0.52 5 $9,360 depreciation

$18,000 2 $9,360 5 $8,640 book value

$240,000 3 0.065 5 $15,600 depreciation per year

$15,600 3 12 years 5 $187,200 depreciation for 12 years

$240,000 2 $187,200 5 $52,800 book value after 12 years

$150,000 2 $52,800 5 $97,200

Learning Objectives

4 5 6

B (57 points) Solve the following depreciation problems.(points for correct answers as marked)

On March 1, Jarvis Realty spent $16,000 for a new company car with an estimated life of 4 years and an

estimated scrap value of $4,000. Jarvis Realty elected to use the straight-line method for depreciation. On

the same date, Carter Realty bought an identical car at the same price and also estimated the car’s life and

scrap value to be 4 years and $4,000, respectively. Carter Realty, however, chose the sum-of-the-years-digits

method for depreciation.

a. At the end of the first year (10 months of use) and second year, how much depreciation did each company

calculate? (3 points for each correct answer)

Jarvis: Year 1 Carter: Year 1

Year 2 Year 2

b. At the end of the second year, which company had more recorded accumulated depreciation, and what was the

difference in the amounts? (5 points)

c. True or false: At the end of the fourth year, Carter Realty will have recorded more accumulated depreciation than

Jarvis Realty. Explain your answer. (4 points)

5. In May 2001, Jian & Ming bought a light-duty truck for $20,800. One year later, they bought an additional

truck for $21,800. In June 2003, a third truck was purchased for $23,500. Use MACRS (5-year class) to

determine the total allowable cost recovery for 2003. (12 points)

6. David Marcus purchased new office furniture July 15, 2008, for $28,100. Use MACRS (7-year class) to

show the rate, depreciation, and beginning and ending book values for 2008, 2009, and 2010. Round to the

nearest dollar. (2 points for each correct answer)

Beginning Ending

Year Rate Cost Depreciation Book Value Book Value

2008 3 $28,100 5

2009 3 $28,100 5

2010 3 $28,100 5

Score for B (57)

$12,288$17,203$4,91517.49%

$17,203$24,085$6,88224.49%

$24,085$28,100$4,01514.29%

$15,670

false

Carter Realty, by $2,300

$3,800$3,000

$4,000

$2,500

382 Part 5 Business Applications

Assignment 18.2 Continued

Jarvis (SL) Year 1: ($16,000 2 $4,000)

Year 2:

Carter (SYD) Year 1: ($16,000 2 $4,000)

Year 2: a$12,000 3

b 1 a$12,000 3

b 5 $3,800

5 $4,000

$12,000 3

5 $3,000

5 $2,500

($4,000 1 $3,800) 2 ($2,500 1 $3,000) 5 $2,300

At the end of the fourth year, the estimated life of both cars will be over. Each company will have recorded the

same amount of accumulated depreciation ($16,000 cost 2 $4,000 SV 5 $12,000)

2001 truck: $20,800 3 0.1920 5 $ 3,993.60 or $ 3,994

2002 truck: $21,800 3 0.32 5 6,976.00 or 6,976

2003 truck: $23,500 3 0.20 5 

 4,700.00 or  4,700

Total cost recovery for 2003: $15,669.60 or $15,670

Financial

Statements

Chapter 19 Financial Statements 383

Learning Objectives

By studying this chapter and completing all assignments, you will be able to:

Analyze balance sheets, comparing items and periods.

Analyze income statements, comparing items and periods.

Compute commonly used business operating ratios.

Learning Objective