NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
Version A 1
IE 343 Midterm Exam 2
April 6, 2012
Version A
Closed book, closed notes.
50 minutes
Write your printed name in the spaces provided above on every page.
Show all of your work in the spaces provided.
Interest rate tables are provided for you to use in questions that require numerical answers.
Exam 2 has three Parts totally 5 Problems with 105 Points:
Part I – 3 Old Problems, totally 76 Points. The old problems are selected from
Homework, Quizzes, Lecture Notes Examples and Textbook Examples with numbers
changed.
Part II – 1 New Problem, 24 Points.
Part III – 1 Bonus Problem, 5 Points.
You are suggested to do Part I first, and then part II. Part III is optional.
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
Version A 2
Part I – 3 Old Problems, totally 76 Points: old problems selected from Homework, Quizzes,
Lecture Notes Examples or Textbook Examples
Question 1 (35 Points)
We consider four design alternatives D1, D2, D3, D4 each with a useful life of 5 years. The
MARR is 20%.
D1 D2 D3 D4
Initial Investment: $100 $300 $150 $200
Annual Revenues: $50 $90 $70 $65
Annual Expenses: $20 $15 $15 $20
Salvage Value: $30 $100 $50 $50
Useful Life: 5 Year 5 Year 5 Year 5 Year
(a) Are the four design alternatives D1, D2, D3, D4 investment alternatives or cost
alternatives? Please explain why? (3 Points)
Solution:
(a) Investment alternative, because there are annual revenues.
(b) We claim that the design alternative D4 can be directly eliminated from the analysis.
Why? Please explain the reason. (4 Points)
Solution:
(b) D4 has higher initial investment than D3 ($200 > $150), but D4 has lower net annual
revenues less expenses than D3 ($45 < $55). D3 and D4 have the same Salvage Value
$50, So D3 is a strictly better alternative than D4. So D4 can be directly eliminated.
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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(c) You are calculating the IRR of D1. You get PW(15%) = 15.5, and PW(25%) = -9.5 by
trial and error. What is the approximated IRR using linear interpolation? Based on this
approximated IRR, is D1 profitable? Explain the reason why? (8 Points)
Solution:
(c) By linear interpolation:
D1 is profitable.
Circle exactly one solution for part (d) to (h) (20 Points)
After eliminating D4, we can perform the incremental analysis procedure using IRR. The
table we get is as follows,
Increment Considered △(D1 – DN) ____(d)____ ____(f)____
△Capital Investment $100 $50 $150
△Annual Revenues Less Expenses $30 $25 $20
△Salvage Value $30 $20 $50
Useful life(Years) 5 5 5
IRR△ 21.2% 45.01% 0.00%
Is increment justified by IRR△? Yes Yes No
Which alternative will you select? D1 ____(e)____ ____(g)____
(d) △(D1 – D3) / △(D2 – D3) / △(D3 – DN) / △(D3 – D1)
Solution:
(d) △(D3 – D1)
(e) D1 / D2 / D3 / DN
Solution:
(e) D3
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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(f) △(D2 – D3) / △(D3 – D2) / △(D3 – DN) / △(D3 – D1)
Solution:
(f) △(D2 – D3)
(g) D1 / D2 / D3 / DN
Solution:
(g) D3
(h) Which design alternative is the best?
D1 / D2 / D3 / D4
Solution:
(h) D3
Question 2 (20 Points)
Two mutually exclusive alternatives are being considered for the environmental protection
equipment at a petroleum refinery. One of these alternatives must be selected. The estimated case
flows for each alternative are follows:
Alternative A Alternative B
Capital investment $6,000 $5,000
Annual expenses $2,000 $2,500
Salvage value at end of useful life $1,000 $500
Useful life 4 years 8 years
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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(a) Which environmental protection equipment alternative should be selected? The firm’s
MARR is 10% per year. Assume the equipment will be needed indefinitely. (10 Points)
Solution:
(a) Since the equipment will be needed indefinitely, the repeatability assumption holds.
AW(A) = -6000(A/P,0.1,4)-2000+1000(A/F,0.1,4) = -6000*0.3155-2000+1000*0.2155 =
-3677.5
AW(B) = -5000(A/P,0.1,8)-2500+500(A/F,0.1,8) = -5000*0.1874-2500+500*0.0874 =
-3393.3
Select Alternative B, since AW(B) = -3393.3 > AW(A) = -3677.5
(b) Assume the study period is shortened to four years. The firm’s MARR is 10% per year.
The market value of Alternative B at the end of year four is estimated to be $3,000. Use
the imputed market value technique to determine which alternative you would
recommend. (10 Points)
Solution:
(b) AW(A) = -3677.5
AW(B) = -5000(A/P,0.1,4)-2500+3000(A/F,0.1,4) = -5000*0.3155-2500+3000*0.2155 =
-3431
Select Alternative B, since AW(B) = -3431 > AW(A) = -3677.5
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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Question 3 (21 Points)
Suppose that an asset with a cost basis of $60,000 is expected to produce net revenues of
$30,000 per year during the four year period, and its terminal market value is negligible. The
effective income tax rate is 40% and the after-tax MARR is 10% per year. The asset is being
depreciated under the Straight Line method over a period of three years.
EOY (A)
BTCF
(B)
Depreciation
(C)=(A)–(B)
Taxable Income
(D)= –t(C)
Income Taxes
(E)=(A)+(D)
ATCF
(a) What is the depreciation deduction d2 for year 2? (3 Points)
Solution:
(a) Since Straight Line method is applied, the depreciation deduction is the same every year,
d2 = d = $60,000 / 3 = $20,000
(b) Complete the table below with information given above. (12 Points)
EOY BTCF Depr TI Tax ATCF
0 -$60,000 -$60,000
1 $30,000 . . . .
2 $30,000 . . . .
3 $30,000 . . . .
4 $30,000 . . .
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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Solution:
(b) .
EOY BTCF Depr TI Tax ATCF
0
-$60,000
-$60,000
1
$30,000
$20,000
$10,000
-$4,000
$26,000
2
$30,000
$20,000
$10,000
-$4,000
$26,000
3
$30,000
$20,000
$10,000
-$4,000
$26,000
4
$30,000
$30,000
-$12,000
$18,000
(c) Are you willing to invest this asset if the income tax is considered? (6 Points)
Solution:
(c) PW = -60,000 + 26,000 (P/A,10%, 3) + 18,000(P/F,10%,4) = -60,000 + 26,000*2.4869 +
18,000*0.6830 = 16,953 > 0
So I will invest this asset.
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
Version A 8
Part II, 1 Problem, 24 Points: New Problem
Question 4 (24 Points)
XYZ Corp. is considering buying a computer workstation for $1,000. The equipment is in the
3-year MACRS (GDS) property class and is expected to reduce net operating expenses by $500
every year. The company’s effective income tax rate is 40%. Assume that the after-tax MARR is
10% per year and the study period is 4 years.
EOY (A)
BTCF
(B)
Depreciation
(C)=(A)–(B)
Taxable Income
(D)= –t(C)
Income Taxes
(E)=(A)+(D)
ATCF
(a) What are the depreciation deductions d2 and d3 for year 2 and 3? (4 Points)
EOY BTCF Depr
0 -$1,000
1 $500 d1 = $333.3
2 $500 d2 = .
3 $500 d3 = .
4 $500 d4 = $74.1
Solution:
(a) Under 3-year MACRS GDS r1 = 0.3333, r2 = 0.4445, r3 = 0.1481, r4 = 0.0741
EOY BTCF Depr
0 -$1,000
1 $500 d1 = $333.3
2 $500 d2 = $444.5 .
3 $500 d3 = $148.1 .
4 $500 d4 = $74.1
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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(b) If you can sell the asset at end of year 2 for $500, what is your capital gain (loss) on this
disposal? What is the tax liability (or tax credit) on this disposal? (10 Points)
Solution:
(b) If the asset is sold at end of year 2, half-year convention will be applied to the depreciation
deduction in year 2. Now d2 = $444.5/2 = $222.25
BV2 = $1,000 - $333.3 - $222.25 = $444.45
Capital gain (loss) = MV2 – BV2 = $500 - $444.45 = $55.55
Tax liability = 0.4(Capital gain) = 0.4 ($55.55) = $22.22
(c) If you can sell the asset at the end of year 2 for $500, please complete the table below.
(10 Points)
EOY BTCF Depr TI Tax ATCF
0 -$1,000 -$1,000
1 $500 . . . .
2 $500 . . . .
2 $500 . . .
Solution:
(c) .
EOY BTCF Depr TI Tax ATCF
0 -$1,000 -$1,000
1 $500 $333.3 $166.7 -$66.68 $433.32
2 $500 $222.25 $277.75 -$110.1 $388.9
2 $500 $55.55 -$22.22 $477.78
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
Version A 10
Part III, 1 Bonus Problem, 5 Points
Question 5 – Extension of Question 4 (5 Points)
XYZ Corp. is considering buying a computer workstation for $1,000. The equipment is in the
5-year MACRS (ADS) property class and is expected to reduce net operating expenses by $500
every year. The company’s effective income tax rate is 40%. Assume that the after-tax MARR is
10% per year and the study period is 4 years. The market value of the computer workstation at
the end of year 4 is considered to be negligible.
Please complete the table below.
EOY BTCF Depr TI Tax ATCF
0 -$1,000 -$1,000
1 $500 . . . .
2 $500 . . . .
3 $500 . . . .
4 $500 . . . .
4 $0 . . .
Solution:
For 5-year MACRS (ADS) property class, we need 6 years to fully depreciate the computer
workstation. Study period is 4 years and the market value of the computer workstation is
negligible after 4 years, which means there’s an early disposal in year 4. Then half year
convention should be applied to the 4th
year. For MACRS (ADS), straight line method with
half year convention to the 1st year is applied, so d1=1000/5/2=100, d2=d3=1000/5=200,
d4=1000/5/2=100
BV4 = 1000-d1-d2-d3-d4 = 1000-100-200-200-100 = 400
MV4 = 0
Capital gain (loss) = MV4 – BV4 = 0 – 400 = -400
Tax credit = -0.4 * (-400) = 160
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
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EOY BTCF Depr TI Tax ATCF
0 -$1,000 -$1,000
1 $500 $100 $400 -$160 $340
2 $500 $200 $300 -$120 $380
3 $500 $200 $300 -$120 $380
4 $500 $100 $400 -$160 $340
4 $0 -$400 $160 $160
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
Version A 12
Formulas and Tables
Find F given P:
Find P given F:
Imputed Market Value:
Capital Investment, : Salvage Value, : Useful life, : Study Period
Depreciation using SL method:
;
Depreciation using DB method:
; ;
Depreciation of SL when using DB with switchover to SL:
GDS or ADS depreciation: k kd r B
Taxable Income (TI) = Gross income - all expenses (except capital investments) - depreciation
deductions.
[Gain(loss)ondisposal]N MVN BVN
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Spring 2012 – IE 343 – Section 1 Instructor: Tian Ni Midterm Exam #2, April 6, 2012
Version A 13