Deck 7: Business Decisions, Capital Budgeting and Depreciation

Question 1

You are looking to invest $200,000.You have 3 possible investment options:
(I)A lump sum of $640,000 payable in 10 years
(II)An annuity paying $30,000 at the end of every years for 15 years
(III)A perpetuity paying $25,000 at the end of every year
Using the net present value method of business decision making,which option should be chosen,if any,if the cost of capital is j₁ = 12%?

A)(I)
B)(II)
C)(III)
D)None of them

Answer 1

(III)

Question 2

A company $100,000.They can invest this money in bonds with annual coupons yielding j₁ = 6%.There are two other investments available which each cost $100,000:
I.A perpetuity paying $6300 per year.
II.An investment paying $13,000 per year for the next 10 years.
The company can only choose one of the three investment options.Assuming the cost of capital is 6%.Which of the following is the correct answer? (Both the decision and explanation must be correct).

A)Invest in the bond because the NPV > 0.
B)Invest in the bond because it has the highest IRR.
C)Invest in I because it has the highest IRR.
D)Invest in II because the NPV > 0.

Answer 2

Invest in I because it has the highest IRR.

Question 3

You are deciding where to invest $100,000 and you have narrowed your choices to two options,I and II.Using the net present value method with a cost of capital of 10%,you have determined that NPV_I > NPV_II.Which of the following statements is true?

A)If both NPV_I and NPV_II are less than 0,then the internal rate of return (IRR)for option I may be less than the IRR for option II
B)If both NPV_I and NPV_II are greater than 0,then the IRR for option I may be greater than or may be less than the IRR for option II.
C)If both NPV_I and NPV_II are greater than 0,then the IRR for option I must be greater than the IRR for option II
D)No matter what,the IRR for both options must be greater than 10%,the
E)cost of capital.

Answer 3

If both NPV_I and NPV_II are greater than 0,then the IRR for option I may be greater than or may be less than the IRR for option II.

Question 4

Which of the following statements is (are)true?
(I)If an investment project has an internal rate of return (IRR)equal to the cost of capital,the net present value (NPV)for that project must be positive
(II)The NPV method implicitly assumes that all cash flows received can be reinvested at the cost of capital
(III)An initial investment of $100,000 is made,and the expected cash flows from this investment are $25,000 at the end of each of years one to six inclusive.The IRR on this investment (Rounded to the nearest ½%)is 13%.

A)I only
B)II only
C)III only
D)None are true

Question 5

23. Which of the following statements is (are) true? (NPV = net present value, IRR = internal rate of return; in both (I) and (II), the cost of capital > 0)

a. If the NPVs are same for two different projects (using the same cost of capital and same initial investment), they must also have same IRR.
b. If an investment ends up with an IRR < 0, then the NPV must also be less than 0.

A) I only
B) II only
C) I & II are true
D) Neither are true

Question 6

You have the opportunity to invest in a project which would require you to pay $50,000 now and another $100,000 in one year,with the promise of a return of $300,000 four years from now.You don't have the cash,but your rich uncle is willing to lend you the money,and would charge you interest at j₁ = 8% for the first 2 years and j₁ = 12% thereafter.What is your net present value (NPV)for this investment?

A)$48,063
B)$62,447
C)$77,916
D)$87,052

Question 7

A machine costs $15,000 and has an estimated lifetime of 8 years after which it could be sold for $3000.Annual maintenance costs are M.If the cost of capital is j₁ = 8%,the capitalized cost is $40,914.72.What is the value of M? (Answer to the nearest dollar)

A)$623
B)$945
C)$1113
D)$1477

Question 8

A company buys a machine that costs $50,000.It has an estimated useful lifetime of 10 years with no scrap value.It produces 5000 units of output per period.Annual maintenance costs are $2000.The cost of capital is j₁ = 10%.The capitalized cost is $101,372.70.What is the maximum amount the company should spend on increasing the machine's production by 60%? (If done so,there will be no change to the estimated lifetime or the annual maintenance costs;Answer to the nearest dollar)

A)$60,824
B)$38,164
C)$37,373
D)$13,358

Question 9

Which of the following statements is (are)true?
(I)If an investment project has an internal rate of return (IRR)equal to the cost of capital,the net present value (NPV)for that project must be positive.
(II)If the cumulative cash flows,∑ F_t,change signs more than once during the term of an investment,there may be more than one IRR.

A)Both are true
B)I only
C)II only
D)Neither are true

Question 10

An investment of $724 will produce estimated cash flows of $250 at the end of each of the next four years.Which of the following would be reported as the internal rate of return (IRR)?

A)13.0%
B)13.5%
C)14.0%
D)14.3%

Question 11

You wish to invest $45,000 and you have three choices:
(I)Buy a perpetuity that provides annual payments of $1500,first payment one year from now
(II)Receive a single payment of $60,000 in 10 years
(III)Receive a single payment of $84,600 in 20 years
Rank the three investments from best to worst,based on the internal rate of return (IRR).

A)IRR _III > IRR _II > IRR _I
B)IRR _III > IRR _I > IRR _II
C)IRR I > IRR III > IRR II
D)IRR _I > IRR _II > IRR _III

Question 12

An investment of $724 will produce estimated cash flows of $250 at the end of each of the next four years.Which of the following would be reported as the internal rate of return,IRR? (Answer to the nearest 0.5%)

A)13.0%
B)13.5%
C)14.0%
D)14.5%

Question 13

Machine A has a purchase price of $500 and lasts for 10 years at which time it has a salvage value of $50.It produces 500 units per year.Machine B costs $500 and has a scrap value of $100 after 15 years.How many units per year should Machine B produce if a buyer is to be indifferent between the 2 machines if j₁ = 4%? Assume zero maintenance costs and answer to the nearest unit.

A)464
B)370
C)358
D)348

Question 14

You are given: F₀ = initial investment,F₁,F₂,…,F_n are the future net cash flows (where each is > 0).You are told that the sum of the future cash flows exceeds the initial investment.That is,
(F₁ + F₂ + … + F_n)> F₀.Which of the following statements is (are)true?
(I)IRR must be greater than 0.
(II)NPV must be greater than 0.

A)I only
B)II only
C)I & II are true
D)Neither are true

Question 15

A delivery van costing $24,000 has an estimated lifetime of 12 years at which time it will cost $1200 to dispose of it.Annual maintenance costs are $900.If the interest rate is j₁ = 9%,what is the capitalized cost of the van? (Answer to the nearest dollar)

A)$45,378
B)$46,578
C)$47,902
D)$49,102

Question 16

An investment of $3300 will produce estimated cash flows of $1000 at the end of each of the next four years.Which of the following would be reported as the internal rate of return (IRR)?

A)7.5%
B)8.0%
C)8.5%
D)9.0%

Question 17

A company needs to buy a machine to produce widgets.They have narrowed their choices to the following 3 machines:
Machine X - capitalized cost = $45,480
Machine Y - capitalized cost = $49,970,produces 10% more widgets per year than machine X
Machine Z - capitalized cost = $40,900,produces 10% fewer widgets per year than machine X
From a financial point of view,which machine should the company buy?

A)X
B)Y
C)Z

Question 18

Which of the following statements is true?
(I)If an investment project has an internal rate of return (IRR)equal to the cost of capital,the Net Present Value (NPV)for that project must be greater than 0
(II)If [CF₁ + CF₂ + … + CF_k] > CF₀,then the IRR will always be greater than 0.(CF_k = net cash flow at end of year k)

A)I & II are true
B)(I)only
C)(II)only
D)Neither statement is true

Question 19

You are given 3 investments,each costing $100,000:
(I)Government of Canada 10-year bond with a yield of j₂ = 5%
(II)An annuity paying $12,960 a year for 10 years
(III)A lump sum of $163,000 due in 10 years
Rank the above investments from highest net present value to lowest net present value.

A)I > II > III
B)II > III > I
C)II > I > III
D)III > I > II

Question 20

An insurance company has three investments available.Each costing $200,000:
(I)A Canadian government bonds to obtain a yield of j₂ = 6%.
(II)A perpetuity paying $5900 at the end of each half year.
(III)An ordinary annuity paying $13,200 every 6 months for 10 years.
Using j₂ = 6% as the cost of capital,rank the above investments from highest net present value to lowest net present value.

A)II > I > III
B)I > III > II
C)I > II > III
D)III > I > II

Question 21

Plastic trays last 8 years and cost $20 each.Metal trays last 24 years and cost $X.There is no salvage value for either type of tray.Trays need to be purchased today and are assumed to be needed forever.If the interest rate is j₁ = 6%,what value of X will the buyer be indifferent to purchasing plastic or metal trays?

A)$42.07
B)$102.68
C)$38.52
D)$40.42

Question 22

An investor is looking at purchasing a storage centre for his business and is evaluating two options.Option 1 is a storage centre that costs $200,000 has an estimated lifetime of 20 years and annual maintenance costs of $1000.Option 2 is a less expensive storage centre that costs $160,000 has an estimated lifetime of 14 years and annual maintenance costs of $2000.What is the absolute difference in the annual cost between Option 1 and Option 2? Assume the required return on his investments are j = 15% and there is no scrap value.(Answer to the nearest dollar).

A)$20,014
B)$3102
C)$3002
D)$19,014

Question 23

A machine costs $500,000.It has a useful life of 10 years,at the end of which there will be an additional cost of $50,000 for disposal.Maintenance costs for the machine are anticipated to be $20,000 per year.To the nearest $1000,what is the capitalized cost of the machine,if money is worth j₁ = 10%?

A)$967,000
B)$982,000
C)$1,028,000
D)$1,045,000

Question 24

A company needs to buy a machine to produce widgets.They have narrowed their choices to the following 4 machines:
Machine W - capitalized cost = $75,800
Machine X - capitalized cost = $87,500;produces 15% more widgets a year than machine W
Machine Y - capitalized cost = $67,500;produces 10% fewer widgets a year than machine W
Machine Z - capitalized cost = $60,500;produces 20% fewer widgets a year than machine W
From a financial point of view,which machine should the company buy?

A)W
B)X
C)Y
D)Z

Question 25

A machine is purchased for $100,000 and has a salvage value of $12,000 in 25 years.What is the total depreciation for the first 3 years,assuming the constant percentage method? (Answer to the nearest dollar)

A)$22,464
B)$15,601
C)$12,328
D)$6,863

Question 26

Machine X and Y each sell for $1,000 000 and each has a life of 17 years.Machine X produces 5000 units per year,has an annual maintenance expense of $10,000 and a salvage value of $33,750.Machine Y produces U units per year,has an annual maintenance expense of $11,000 and no salvage value.If the interest rate is j₁ = 8%,what does the value of U have to be for the two machines to be equivalent?

A)5042
B)5084
C)5357
D)5500

Question 27

A town is putting a new roof on its arena.A standard roof cost $600,000 and has an expected lifetime of 20 years with no salvage value.Another company has stated that they can add a preservative to the roof which will increase the lifetime of the roof by 10 years.Ignoring maintenance costs,what is the maximum amount the town should be willing to pay for the preservative if money is worth j₁ = 7%? (Answer to the nearest dollar).

A)$59,171
B)$87,760
C)$102,795
D)$118,342

Question 28

A company is considering buying a certain machine.There are there options:
• Machine 1 costs $6000 and will last 15 years with a scrap value of $800 and maintenance costs of $500 a year
• The capitalized cost for Machine 2 is $23,457
• The capitalized cost for Machine 3 is $25,500
It is known that machine 1 produces 30% less output than machine 2 and machine 3 produces 10% more output than machine 2.If j₁ = 7%,which of the following list is the rank of preference of machine to be purchased (ranked from best to worst machine)?

A)1,3,2
B)1,2,3
C)2,3,1
D)2,1,3

Question 29

A machine costs $10,000,has no scrap value at the end of 10 year estimated lifetime.Maintenance is $500 per year.How much can be spent on increasing the machine's productivity by 50%,if the salvage value remain same? If this is done,the annual maintenance cost would increase to $800 per year and the machine's lifetime would decrease to 8 years.The cost of capital is j₁ = 10%.

A)$2757
B)$5909
C)$4790
D)$6536

Question 30

A company needs to buy a machine to produce widgets and the annual interest rate is 9%.They have narrowed their choices to the following 3 machines:
Machine X - annual cost = $4,005
Machine Y - capitalized cost = $49,970,produces 10% more widgets per year than machine X
Machine Z - capitalized cost = $40,900,produces 10% fewer widgets per year than machine X
From a financial point of view,which machine should the company buy?

A)X
B)Y
C)Z
D)Cannot be determined

Question 31

A certain machine costs $500,000 new.It has a useful life of 20 years,at the end of which it can be sold for $50,000.Maintenance costs for the machine are anticipated to be $12,000 per year.What is the annual cost of the machine,if money is worth j₁ = 12%?

A)$652,045
B)$518,245
C)$78,245
D)$66,000

Question 32

A company needs a machine that will produce widgets.They have found that there are only three machines available,with the following information:
Machine X - Capitalized cost = $73,692
Machine Y - Capitalized cost = $62,135,produces 15% fewer widgets than machine X
Machine Z - Capitalized cost = $88,930,produces 20% more widgets than machine X
>From a strictly financial point of view,rank the machines in the order: best,2^nd best,worst.

A)X,Z,Y
B)Y,Z,X
C)Z,X,Y
D)Y,X,Z

Question 33

A basic Flabberjabber,which lasts only 1 year,costs $5000 with a scrap value of $750 at the end of 1 year.A deluxe Flabberjabber,which lasts for n-years,can be purchased for $20,000 with scrap value $2500.Assume there are no maintenance costs for either model.Both Flabberjabbers perform exactly the same task.What is the minimum value of n so that a deluxe model would be a better buy than the basic model,if money is worth j₁ = 10%? (Answer to the nearest whole number. )

A)3 years
B)4 years
C)5 years
D)6 years

Question 34

A company buys a machine costing $75,000.The machine has no scrap value at the end of its estimated lifetime of 15 years.It has annual maintenance expenses of $1000,and is expected to produce 2000 units per year.The capitalized cost of the machine at j₁ = 7% is $131,922.72.The company wishes to increase the machine's productivity by 10% per year.If this is done,the cost,estimated lifetime and scrap value remain unchanged,but maintenance costs will increase by $X per year.What is the value of X?

A)$923.45
B)$1015.80
C)$1100.00
D)$1319.23

Question 35

A machine costs $15,000 and has an estimated lifetime of 8 years after which it could be sold for $3000.Annual maintenance costs are M.If the cost of capital is j₁ = 8%,the capitalized cost is $40,914.72.What is the value of M? (Answer to the nearest dollar)

A)$623
B)$945
C)$826
D)$1477

Question 36

Machine A has a purchase price of $500 and lasts for 10 years at which time it has a salvage value of $50.It produces 500 units per year.Machine B costs $500 and has a scrap value of $100 after 15 years.How many units per year should Machine B produce if a buyer is to be indifferent between the 2 machines if j₁ = 4%? Assume zero maintenance costs and answer to the nearest unit.

A)464
B)370
C)358
D)348

Question 37

Machine 1 has a capitalized cost of $74,000.Machine 2 has a cost of $C,a scrap value estimated at $5000,an estimated lifetime of 10 years and annual maintenance costs of $2000.Machine 2 produces 20% more output per year than Machine 1.If j₁ = 8%,what is the value of C so that machine 1 and 2 are economically equivalent? (Answer to the nearest dollar)

A)$36,564
B)$34,248
C)$31,932
D)$28,620

Question 38

A company buys a machine and then buys an upgrade which increases its productivity by 100%.The total cost of the machine and the upgrade is $10,000.The upgraded machine has no scrap value at the end of its 10-year estimated lifetime and maintenance is $500 per year.If there was no upgrade,the maintenance would be only $300 per year and the machine's lifetime would be 14 years (scrap value would still be $0).If the upgraded and non-upgraded machines are economically equivalent and if the cost of capital is j₁ = 10%,how much less is the cost of the original (non-upgraded)machine?

A)$4374
B)$4700
C)$5626
D)$5937

Question 39

A machine costing $5000 is estimated to have a useful lifetime of 5 years and a scrap value of $500.It is expected to run for 20,000 hours.You are given that the actual production hours in the first three years are: 5000 in year 1,4400 in year 2,and 4000 in year 3.What is the book value of this machine at the end of three years?

A)$3015
B)$1985
C)$1650
D)$1485

Question 40

A machine costs $500,000 new.It has a useful life of 20 years,at the end of which it can be sold for $S.Maintenance costs are $15,000 at the end of each year.If the cost of capital is j₁ = 12%,the capitalized cost of the machine is $675,000.What is the value of S?

A)Less than $50,000
B)At least $50,000,but less than $65,000
C)At least $65,000,but less than $80,000
D)At least $80,000

Question 41

Equipment costing $40,000 is to be depreciated over 15 years,at which time it will be sold for scrap for $4,000.Let R_s = depreciation expense for the 6^th year under the straight line method and R_c = depreciation expense for the 6^th year under the constant percentage method with rate of depreciation d = 20%.What is | R_s -R_c |?

A)$569.52
B)$302.85
C)$221.44
D)$45.23

Question 42

A piece of equipment is depreciated over 5-years.It costs $5000 and has a scrap value of $500.For the first 2-years,the straight line method is used.For the last 3-years,the constant percentage method is used with a depreciation rate of d.What value of d is needed?

A)36.9%
B)43.0%
C)45.0%
D)46.1%

Question 43

A machine,with an original cost of $28,000,depreciates to $4000 over 20 years.If the constant percentage method of depreciation is used,what is the earliest year end where the machine will be depreciated to less than half of its original value? (Round up the answer to the nearest whole number)

A)9 years
B)8 years
C)5 years
D)6 years

Question 44

Equipment that was purchased three years ago has a depreciation expense in year 3 of R₃ = $735 assuming the constant percentage method and d = 15%.Determine the original cost of this equipment,C.(Answer to the nearest dollar)

A)$7979
B)$6782
C)$5765
D)$5635

Question 45

A mine $2,000,000 and is said to contain 80,000 tons of ore.When all the ore has been mined,the land can be sold for $100,000.If the book value of the mine after 3 years is $1,080,000,how many tons of ore have been mined up to that point?

A)34,526
B)36,800
C)37,895
D)38,737

Question 46

A gravel pit is purchased for $200,000 and has expected usable gravel equal to 40,000 truck loads,with yearly production as follows (in truck loads): year 1 -10,500 ;year 2 - 9,600 ;year 3 - 8,300 ;year 4 - 6,700 ;year 5 - 4,900.When all the usable gravel has been extracted,the land can be sold for $30,000.What is the book value of the land after 3 years?

A)$120,700
B)$79,300
C)$58,000
D)$49,300

Question 47

An asset was purchased 10 years ago for $150,000.It useful lifetime was estimated to be 15 years,so the asset has 5 years left before being sold for $5000 (scrap value).If this asset is depreciated using the straight-line method,what is the book value of the asset now?

A)$15,536.16
B)$50,000.00
C)$53,333.33
D)$101,666.67

Question 48

A machine costing $5000 is estimated to have a useful lifetime of 5 years and a scrap value of $500.It is expected to run for 20,000 hours.You are given that the actual production hours in the first three years are: 5000 in year 1,4400 in year 2,and 4000 in year 3.What is the book value of this machine at the end of three years?

A)$3015
B)$1985
C)$1650
D)$1485

Question 49

A machines costing $10,000 is estimated to have a useful lifetime of n years and a scrap value of $500.It is expected to run for 25,000 hours over n years.The actual hours the machine runs are: 2000 hours in year 1,1500 hours in year 2 and 800 in year 3.What is the book value of the machine at the end of 3-years?

A)$9600
B)$8280
C)$8670
D)$8366

Question 50

An asset with an initial value of $15,000 has a salvage value of $2000 after 10 years.What is the absolute value of the difference between the depreciation expenses entered in the books in the seventh year under the straight-line method and under the declining-balance method?

A)$682.88
B)$482.87
C)$631.99
D)$2239.43

Question 51

A computer is depreciated over 3 years.It costs $2300 and has an estimated scrap value of $200.The straight-line method is used for the first year.For the last two years,the constant percentage method is used,with depreciation rate d.In order to depreciate the computer from $2300 to $200 by the end of 3 years,what value of d is needed?

A)63.9%
B)64.6%
C)70.5%
D)87.5%

Question 52

A machine costing $100,000 has a useful lifetime of 15 years with an estimated scrap value of $10,000.What is the book value of the machine at the end of the third year under the constant percentage method of depreciation? (Answer to the nearest dollar)

A)$63,096
B)$63,163
C)$63,606
D)$73,564

Question 53

A plot of land is purchased for $1.5 million.It is said to contain 300,000 tons of ore.It will take five years to mine all the ore after which the land will be worth $300,000.They expected to mine 60,000 tons of ore in each of the first two years.What is the book value of the mine after two years?

A)$1,020,000
B)$720,000
C)$900,000
D)$600,000

Question 54

A company just bought some equipment for $10,000 today.It is estimated to last 15 years at which time it will be worth $1500.Initially,the company uses the constant percentage method to depreciate the asset.After 5 years,the accountants of the company change their minds and switch to the straight line method.What is the book value of the equipment after 10 years?

A)$2218.52
B)$2656.65
C)$2968.53
D)$3406.64

Question 55

A company has office equipment costing $10,000.The book value of the equipment after one year,using the constant percentage method of depreciation,is $8000.What is the total depreciation at the end of 3 years?

A)$4880
B)$5120
C)$6000
D)Cannot be determined

Question 56

A company has office equipment costing $10,000.The book value of the equipment after two years,using the constant percentage method of depreciation,is $8000.What is the total depreciation at the end of 4 years?

A)$3600
B)$4000
C)$5904
D)$6400

Question 57

A machine costing $42,246 is expected to last 10 years with a scrap value of $4000.The machine is depreciated using the constant percentage method with d = 21%.After 5 years,the depreciation method is changed to the straight-line method for the final 5 years.What is the book value after 7 years?

A)$7799.60
B)$8112.88
C)$8661.11
D)$9399.60

Question 58

An airplane costing $5 million is expected to be flown 800,000 miles over its lifetime of 8 years,at which time it can be sold for $400,000.After 6 years,the total depreciation using the physical service method is $3.8 million.How many miles is the airplane flown in total over its last 2 years (years 7 and 8)? (Answer to the nearest mile)

A)128,000
B)139,130
C)192,000
D)208,696

Question 59

A machine is purchased for $100,000 and has a salvage (scrap)value of $10,000 in 20 years.What is the total depreciation for the first 3 years,assuming the constant percentage method? (Answer to the nearest dollar)

A)$70,795
B)$63,096
C)$36,904
D)$29,205

Question 60

A company has an asset that cost $20,000.It is estimated to last 8 years.It is to be depreciated 32% every year using the constant percentage method.What is the scrap value of the asset?

A)$430.27
B)$914.33
C)$1344.60
D)The asset has no scrap value since the constant percentage method is being used

Question 61

A gravel pit is purchased for $200,000 and has expected usable gravel equal to 40,000 truck loads,with yearly production as follows (in truck loads): year 1 = 10,500 ;year 2 = 9,600 ;year 3 = 8,300 ;year 4 = 6,700 ;year 5 = 4,900.When all the usable gravel has been extracted,the land can be sold for $30,000.What is the book value of the land after 3 years?

A)$120,700
B)$58,000
C)$79,300
D)$49,300

Question 62

A machine is purchased for $10,000 and has an expected life of 8 years,at which time its salvage value is $500.What is the book value at the end of six years using the constant percentage method of depreciation?

A)$1,057.37
B)$1423.76
C)$1213.99
D)$1537.65

Question 63

A company buys two machines.Machine A is expected to last 14 years and costs $2450.Machine B is expected to last 10 years and costs $Y.Both machines have a salvage value of $1050 and both use the straight line method of depreciation.At the end of the 9^th year,machine A and machine B have a same book value.What is Y?

A)$6050
B)$5400
C)$2050
D)$16,550

Question 64

A piece of equipment costing $50,000 is expected to last 15 years,after which it will have a salvage value of $5000.For the first 3 years,the constant percentage method is used for depreciation with a 20% rate of depreciation.After that,the company switches to the straight line method of depreciation.What is the book value of the equipment 6-years after it was purchased?

A)$16,600
B)$17,280
C)$19,200
D)$20,450

Question 65

An office machine costing $2000 is being depreciated over 10 years using the constant-percentage method.The book value after 4-years is $480.20.What is the scrap (salvage)value of the machine?

A)$56.50
B)$58.14
C)$128.41
D)$235.30

Question 66

An airplane costing $5 million is expected to be flown 800,000 miles over its lifetime of 8 years,at which time it can be sold for $400,000.After 6 years,the book value of the plane using the physical service method is $1.2 million.How many miles is the airplane flown in total over its first 6? (Answer to the nearest mile)

A)591,304
B)608,000
C)660,870
D)672,000