Financial Mathematics 3: Depreciation

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Financial Mathematics 3: Depreciation

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Financial mathematics 3: Depreciation

Student Book - Series MContents

Topics

Practice Tests

Topic 1 - Modelling depreciation __ /__ /__

Topic 1 - Topic test A __ /__ /__

Topic 2 - Straight-line depreciation __ /__ /__

Topic 2 - Topic test B __ /__ /__

Topic 3 - Declining balance method __ /__ /__

Topic 4 - Comparison of methods __ /__ /__

Topic 5 - Depreciation as a tax deduction __ /__ /__

Date completed

Author of The Topics and Topic Tests: AS Kalra

iiFinancial mathematics 3: Depreciation

Mathletics Instant Workbooks – Series M Copyright © 3P Learning

1


Financial mathematics 3: DepreciationMathletics Instant Workbooks – Series M Copyright © 3P Learning

Topic 1 - Modelling depreciation

126 EXCEL HSC GENERAL MATHEMATICS REVISION & EXAM WORKBOOK

CHAPTER 10Financial Mathematics – Depreciation

Modelling depreciation

QUESTION 1 The graph below shows how $1000 depreciates at the different rates of 25% p.a., 15% p.a. and5% p.a. over 8 years.

EXCEL HSC GENERALMATHEMATICS

pages 69-73

5%

15%

25%

$1000

$900

$800

$700

$600

$500

$400

$300

$200

$100

1 2 3 4 5 6 7 8

Time (Years)

a Using the graph find:

i the value of $1000 after 6 years at 5% p.a. depreciation

ii the amount by which $1000 depreciates in 3 years at 25% p.a.

iii the depreciation of $1000 in the fifth year at 15% p.a.

iv the salvage value of a car bought for $24 000, 4 years ago, at 15% p.a. depreciation.

b Use the formula S = 1000(0.8)n to complete the table of values, correct to two decimal places.

n 0 1 2 3 4 5 6 7 8

S

c The above formula gives the value of $1000 if depreciating at 20% p.a.. Sketch this on the above graph.

2



Topic 2 - Straight-line depreciation (1)

127CHAPTER 10 – Financial Mathematics – Depreciation

Straight-line depreciation (1)

QUESTION 1 Use the straight-line formula to find the current value of an asset where:

a purchase price $18 000, depreciation $750 per year, after 12 years

b purchase price $9500, depreciation $1200 per year, after 5 years.

QUESTION 2 A business purchased a new delivery van for $21 000. Depreciation is allowed at $2500 per year.

a What is the depreciated value at the end of 6 years?

b Why wouldn’t you use the above depreciation allowance for 9 years? Briefly explain.

QUESTION 3 A 9 year old machine is currently valued at $7500. If its purchase price was $24 375 find theamount of depreciation allowed each year.

QUESTION 4 The curtains of a house cost $12 000. It is expected that the curtains will have an effective lifeof 10 years and will then be sold for $1500. Find:

a the annual depreciation

b the annual depreciation as a percentage of the cost price.

Financial Mathematics – Depreciation EXCEL HSC GENERALMATHEMATICS

pages 69-71

3



Topic 2 - Straight-line depreciation (2)


Straight-line depreciation (2)

QUESTION 1 Using the straight-line method of depreciation, $108 has been apportioned each year on a rotaryhoe. The salvage value is $359 after 5 years. Find the purchase price of the rotary hoe.

QUESTION 2 A farmer purchased machinery and assessed that one machine worth $25 000 had a useful life of8 years. Its scrap value after 8 years was estimated at $5000. The straight-line method ofdepreciation will be used.

a Calculate the annual depreciation of the machine.

b Complete the table to show the salvage value after each year.

Year Previous value Depreciation Salvage value

1 $25 000

2

3

4

5

6

7

8 $5000

c Draw a graph showing the salvage value over the eight years.


pages 69-71

$25 000

$20 000

$15 000

$10 000

$5000

0 1 2 3 4 5 6 7 8

Number of years

Salv

age

valu

e

4



Topic 3 - Declining balance method (1)


Declining balance method (1)

QUESTION 1 Use the declining balance formula to find the salvage value of an asset with:

a purchase price $6000, depreciation rate 5% p.a., after 4 years

b purchase price $24 000, rate of depreciation 8% p.a., after 7 years.

QUESTION 2 A car bought for $45 000 is depreciating at a rate of 12% p.a. of its value from the previous year.Write down its salvage value (current value) after 5 years.

QUESTION 3 Arnie bought a tractor in 1998 for $54 000, which has been depreciating at 15% p.a.. Two yearslater he bought a second tractor for $48 000, which has been depreciating at 17.5% p.a. . Whichtractor has the greater salvage value in 2008? Justify your answer.

QUESTION 4 The salvage value of a machine after 10 years is $5670. If it depreciated at the rate of 18.5% p.a.,what was the cost price (to the nearest dollar)?


pages 71-73

5



Topic 3 - Declining balance method (2)


Declining balance method (2)

QUESTION 1 A machine was purchased for $32 500 and had a scrap value of $8500 after 5 years. Find itsdeclining-balance depreciation rate as a percentage correct to 1 decimal place.

QUESTION 2 A machine bought for $25 000 depreciates at 20% p.a..

a What is its salvage value after 8 years, to the nearest dollar?

b Complete the table to show the salvage value each year. (Give the salvage value to the nearest dollar.)

Year Previous value Depreciation Salvage value

1 $25 000

2

3

4

5

6

7

8

c Draw a graph showing the salvage value over time.


pages 71-73

$25 000

$20 000

$15 000

$10 000

$5000

0 1 2 3 4 5 6 7 8

Number of years

Salv

age

valu

e

6




Comparison of methods

QUESTION 1 An industrial sewing machine was bought for $11 000.

a Using the straight-line method of depreciation, what would be the value of the sewing machine after 5 yearsif it is depreciating at $1500 per year?

b Using the declining balance method of depreciation at 20% p.a., would the machine be worth more or lessafter 5 years? Justify your answer.

QUESTION 2 A machine, bought for $18 500, was depreciated at 12% p.a..

a What was the salvage value of the machine after 7 years?

b What amount of depreciation per year, using the straight-line method, would produce the same result?

QUESTION 3 A pump was bought for $4600.

a What is it worth after 1 year if it depreciates by $483.

b What is this amount of depreciation as a percentage of the cost price?

c If the pump continues to depreciate at $483 per year, how many years will it be before the value of the pumpfalls below $1000?

d If the pump depreciates at the rate found in part b, how many years will it be before the value of the pumpfalls below $1000? (Use estimation and refinement.)


pages 69-73Topic 4 - Comparison of methods

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Depreciation as a tax deduction

QUESTION 1 John is a contractor who makes round bale silage. The table below shows the items he has beendepreciating, using the declining-balance method, in his tax returns. The previous value is thevalue at the end of the previous financial year.

Item Rate Previous value Depreciation Current value

Tractor 1 10% $43 000

Tractor 2 10% $35 800

Hay rake 8% $5000

Baler 15% $24 000

Mower 12% $8700

Wrapper 18% $12 000

a Complete the table.

b What is the total depreciation allowed as a tax deduction?

c If John bought a second hay rake on October 1, for what fraction of the financial year can he claim a taxdeduction?

d If the new hay rake cost $12 500 and is depreciated at 8% p.a., find the amount he can claim as a taxdeduction.

QUESTION 2 Sharon uses the straight-line method of depreciation. For a computer that she bought on February1, 2003 for $1800 she claims $150 as a tax deduction.

a What is the salvage value of the computer on July 1, 2003?

b How much is the depreciation each year?

c What is the value of the computer on July 1, 2006?

QUESTION 3 Cameron’s Mowing Service bought a new ride-on mower for $3600 on September 1. Find theamount of depreciation the business can claim as a tax deduction on the next tax return if thedeclining balance method is used at 12% p.a..


pages 69-73Topic 5 - Depreciation as a tax deduction


TOPIC TEST SECTION I

Instructions • 8 multiple choice questions• Each question is worth 1 mark• Fill in only ONE CIRCLE• Calculators may be used

Time allowed: 10 minutes Total marks: 8

1 An asset depreciates using the straight-line method. If its purchase price was $9750 and its salvage valueis $2175 after 6 years, how much is the amount of depreciation apportioned per year?

A $1625 B $1262.50 C $938.75 D $1515

2 Furniture valued at $32 000 depreciates at a rate of 10% p.a., find the value of the furniture after3 years.

A $23 328 B $28 800 C $25 600 D None of these

3 The value of a car depreciates by 12% of its value each year. If its price was $45 000 when new, what willbe its value (to the nearest dollar) at the end of 5 years?

A $24 650 B $23 843 C $23 961 D $23 748

4 A truck was bought for $87 000 on April 1. If it depreciates using the declining-balance method at15% p.a., the amount of depreciation that can be claimed as a tax deduction that financial year isclosest to:

A $9980 B $3460 C $3260 D $13 050

5 A quad bike depreciates by $750 per year. If its salvage value after 7 years is $3000, its purchase pricewas:

A $8250 B $9000 C $7500 D $5250

6 Each year a computer depreciates by 20% of its value at the beginning of that year. A new computer costs$4300. What will be its value at the end of the second year?

A $2752 B $2863 C $2850 D none of these

7 A van was bought 6 years ago and has been depreciating using the declining-balance method at 12% p.a..Its salvage value is $12 540. Its purchase price was closest to:

A $25 080 B $27 000 C $23 750 D $33 250

8 A chainsaw is depreciated by the straight-line method, with $85 being apportioned each year. Thepurchase price of the chainsaw was $690 and its current salvage value is $180. How old is thechainsaw?

A 4 years B 5 years C 6 years D 7 years

Financial Mathematics – Depreciation

8Total marks achieved for PART A

8Financial mathematics 3: Depreciation


Instructions •8 multiple-choice questions •Each question is worth 1 mark •Fill in only ONE CIRCLE •Calculators may be used

Time allowed: 10 minutes Total marks = 8

Financial mathematics 3: DepreciationTopic Test PART A

Instructions •This section consists of 5 questions •Show all necessary working

Time allowed: 15 minutes Total marks = 12

Financial mathematics 3: DepreciationTopic Test PART B




TOPIC TEST SECTION II

Instructions • This section consists of 5 questions• Show all necessary working

Time allowed: 15 minutes Total marks: 12

9 An overlocker is bought for $675. It is depreciated using the straight-line method. The amount of depreciationallocated in the first year is 10% of the purchase price. 1 mark eacha Find the amount of depreciation apportioned each year.

b Find the salvage value of the overlocker after 5 years.

10 A business buys new machinery for $80 000 that depreciates at the rate of 20% of its previous value eachyear. After three years, find: 1 mark each

a its salvage value

b the total amount of depreciation.

11 Furniture was purchased for $32 000 and had a salvage value of $4000 after 7 years. 2 marks each

a Find the amount of depreciation apportioned per year if the straight-line method was used.




b Find the rate, as a percentage correct to 1 decimal place, if the declining-balance method was used.

12 Find the amount of depreciation that can be claimed on the tax return if a pressure cleaner was bought for$868 on March 1 and the straight-line method of depreciation is to be used, apportioning $180 each year.

2 marks

13 A table lamp, costing $1500 when new, depreciates at the rate of 20% of its previous value each year. Afterhow many years will its value be approximately $300? (Make an estimate and refine.) 2 marks

Total marks achieved for PART B 12

Financial Mathematics 3: Depreciation

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