ie 2324 chap 12 homework with answers

7/24/2019 IE 2324 Chap 12 Homework With Answers

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IE 3301 ENGINEERING ECONOMIC ANALYSIS

Ch12 Problems - Solutions

Note: Corporate tax rates are used in problems.

12.1

A company wants to set up a new office in a country where corporate tax rate is asfollows: 15% of first $50,000 taxable income; 25% of next $25,000; 34% of next$25,000; and 39% of everything over $100,000. Executives estimate that they will havegross income of $500,000; total expenses of $300,000; $30,000 in allowable taxreductions; and a onetime business start-up tax credit of $8,000.

a. Determine the taxable income for the first year. b. How much should the company expect to pay in taxes?

Solution:

a) Taxable Income = Gross income − all expenditures except capital expendituresallowable deductions (depreciation and depletion charges)

= ($500,000 − $300,000) − $30,000 = $170,000 b) Income tax = 0.15 ($50,000) + 0.25 ($25,000) + 0.34 ($25,000) + 0.39 ($70,000)

− tax credits= $49,550 − 8,000 = $41,550

12.2A corporation in an industrialized state has a state taxable income of $150,000. If thestate has a corporate tax rate of 9.6% of taxable income,

a. Determine the total state and federal tax that the corporate must pay b. Compute its combined incremental state and federal income tax rate

Solution:

a) State Tax = 9.6% ($150,000) = $14,400Federal Taxable Income = $150,000 − $14,400 = $135,600 Federal Tax = $22,250 + 0.39 ($135,600 − $100,000) = $36,134 Total State + Federal Tax = $50,534

b) Combined incremental state and federal income tax rate:0.096 + 0.39 (1 − 0.096) = 0.4486 = 44.86%



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12.3A mining corporation purchased $120,000 of production machinery and depreciated itusing SOYD depreciation, a 5-year depreciation life, and zero salvage value. Thecorporation is a profitable one that has a 34% combined incremental tax rate. At the endof 5 years, the mining company changed its method of operation and sold the production

machinery for $40,000. During the 5 years the machinery was used, it reduced mineoperating costs by $32,000 a year, before taxes. If the company MARR is 12% after tax,was the investment in the machinery a satisfactory one? (Use present worth or rate ofreturn analysis)

Solution:

SOYD DepreciationSOYD = (N/2) (N + 1) = (5/2) 6 = 15Year 1 Depreciation = (5/15) ($120,000 − $0) = $40,000 Gradient = (−1/15) ($120,000 − $0) = −$8,000

NPW (12%) = $34,720 (P/A, 12%, 4) − $2,720 (P/G, 12%, 4) + $50,240 (P/F, 12%, 5) −$120,000

= $105,445 − $11,255 + $28,506 −$120,000 = +$2,726> 0 (Calculator solution:ROR = 12.88%)Therefore, investment was satisfactory.



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12.4An automaker is buying some special tools for $100,000. The tools are being depreciated by double declining balance depreciation using a 4-year depreciable life and a $6250salvage value. It is expected that the tools will actually be kept in service for 6 years andthen sold for $6250. The before-tax benefit of owning the tools is as follows:

Year Before-Tax Cash

Flow

1 $30,0002 $30,0003 $35,0004 $40,0005 $10,0006 $10,000

$6250 Selling price

Compute the after-tax rate of return for this investment situation, assuming a 46%

incremental tax rate. If after tax MARR is 15%, was this a satisfactory investment?

Solution:

DDB depreciation, dt =

NPW=0 = -100,000+39,200(P/F,i%,1)+ 27,700(P/F,i%,2)+ 24,650(P/F,i%,3)+24,475(P/F,i%,4)+ 5,400(P/F,i%,5)+ 11,650(P/F,i%,6)Estimate starting point for ROR

Total return for 6 years = (Sum of the benefits – Sum of the costs)/Sum of the costs= (133,075 – 100,000)/100,000 = 0.33075Average per year = 0.33075/6 = 0.055125 = 5.51%Try 6%, NPW=13,965Try 10%, NPW=3,694.69Try12%, NPW=-851.68Using linear interpolation, After-Tax Rate of Return, i = 11.6%, IRR < MARR = 15%,thus it was not a satisfactory investment.



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12.5Mr. Jones, a successful businessman, is considering erecting a small building on acommercial lot which he can buy for $30,000. A local company is willing to lease the building for 5 years at $9000 per year, paid at the end of each year. Mr. Jones could havethe building constructed for $82,000.

Mr. Jones has an annual taxable income from other sources which results in a combinedincremental tax rate of 27%. He could depreciate the property by modified acceleratedcost recovery system (MACRS) with midmonth convention. He believes that at the endof the 5-year lease he could easily sell the entire property (land and building) for$125,000 (assume the land is not expected to appreciate in value). Current tax law setsthe capital gains tax rate at 20%. What is the after tax present worth of this 5-year ventureif Mr. Jones uses a 10% after-tax MARR? Assume that the building was placed in serviceon January 1 and sold on December 31 after 5 years.

Solution:

The building is in the 39-year real property class. Land is a nondepreciable asset.

MACRS depreciation (building) schedule:

Year Depreciation

1 2.461%(82,000)=2,018.022-4 2.564%(82,000)=2102.485 2.461%(82,000)=2018.02

Capital gain = $125,000-(82,000+30,000) = $13,000Capital gain tax = 0.20*13,000 = $2600Depreciation recapture = 2018.02*2 + 2102.48 *3 = $ 10,343.48Depreciation recapture tax = 0.27 * 10,343.48 = $2,792.74

Total depreciation recapture and capital gain taxes= 2600+2792.74= $5,392.74

Year BTCF MACRS

Depreciation

Taxable

income

Income

taxes

ATCF

0 -82,000 Bld.0 -30,000 Land -112,0001 9,000 2,018.02 6981.98 -1,885.13 7,114.872 9,000 2102.48 6897.52 -1,862.33 7,137.673 9,000 2102.48 6897.52 -1,862.33 7,137.674 9,000 2102.48 6897.52 -1,862.33 7,137.675 9,000 2018.02 6981.98 -1,885.13 7114.87

5 125,000 23,427.94 -5,392.74 119,607.26

NPW(10%)= -112,000 + 7114.87 (P/F,10%,1) + 7137.67 (P/A,10%, 3)(P/F, 10%, 1) +7114.87(P/F,10%,5)+ 119,607.26 (P/F,10%, 5)

= -112,000 + 7114.87 (0.9091) + 7137.67 (2.487)(0.9091) + 7114.87 (0.6209)+119,607.26 (0.6209)

= - $ 10,712.32, thus this project would not be an acceptable investment.



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12.6A sales engineer has the following alternatives to consider in touring his sales territory.

a) Buy a new car for $14,500. Salvage value is expected to be about $5,000 after 3years. Maintenance and insurance cost is $1000 in the first year and increases atthe rate of $500/year in subsequent years. Daily operating expenses are $50/day

b)

Rent a similar car for $80/day

Based on a 12% after-tax rate of return, how many days per year must he use the car to justify its purchase? You may assume that this sales engineer is in the 30% corporateincremental tax bracket. Use MACRS depreciation.

Solution:

Let X = number of days car used per year. Automobiles are in the MACRS 5-year property class.

MV=$5000;BV=14500-(2900+4640+1392) = $5,568Capital loss on disposal = $568

NPW = −$14,500 + $21X (P/A, 12%, 3) + $170 (P/F, 12%, 1) + $342 (P/F, 12%, 2) + $4,188 (P/F, 12%, 3) = 0= −$14,500 + $21X (2.402) + $170 (0.8929) + $342 (0.7972) + $4,188 (0.7118) = 0

X = 220 days



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12.7Two mutually exclusive alternatives are being considered by a profitable corporationwith an annual taxable income between $5million and $10 million

Year Before-Tax cash flow

Alt. A Alt. B0 -3000 -50001 1000 10002 1000 12003 1000 14004 1000 26005 1000 2800

Both alternatives have a 5-year useful and depreciable life and no salvage value.Alternative A would be depreciated by sum-of-years-digits depreciation and alternative B by straight-line depreciation. If the after tax MARR is 10%, which alternative should be

selected? (use IRR analysis)

Solution:



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12.8A profitable corporation with $7 million in annual taxable income is considering twoalternatives:

Year Before-Tax cash flow

Alt. 1 Alt. 20 -$10,000 -$20,0001-10 4,500 4,50011-20 0 4,500

Both alternatives will be depreciated by straight-line depreciation assuming a 10-yeardepreciable life and no salvage value. Neither alternative is to be replaced at the end of itsuseful life. If the corporation has an after tax MARR of 10%, which alternative should itselect?Solve the problem by:a) Present worth analysis

b) Annual cash flow analysisc) Rate of return analysisd) Future worth analysise) Benefit-cost ratio analysis (basic, conventional form)

Solution:



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(a) To maximize NPW, choose Alternative 1 with a total present worth of $10,340.(b) To maximize (EUAB – EUAC), choose Alternative 1 with (EUAB – EUAC) =$1,215.(c) Based on the rate of return of 9.2% from investing in Alt. 2 instead of 1, note that theincrement is unacceptable. Choose Alternative 1.(d) To maximize Net Future Worth, choose Alternative 1 with a net future worth of$69,566.

(e) Because the 2− 1 increment has a B/C ratio =0.91, less than 1, reject the incrementand select Alternative 1.



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Partial Answers

12.1 a) $170,000; b) $41,550

12.2 a) $50,534; b) 44.86%

12.3 NPW>0; (ROR = 12.88%).Therefore, investment was satisfactory.

12.4 i = 11.6%

12.5 -$10,712.32,

12.6 220 days

12.7 choose B

12.8 a) Select Alt. 1, PW (10%) = $10,340; b) Select Alt. 1, EUAW (10%) = $1,215;

c) Select Alt. 1, IRR (2-1) = 9.2%

d) Select Alt. 1, FW (10%) = $69,566e) Select Alt.1, B/C=0.91

ie 2324 chap 12 homework with answers

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