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NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
1
IE 343 Section 2 - Final Exam
Dec 12, 2011
Closed book, closed notes.
120 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 or values are provided for you to use in questions that require numerical
answers. For problems requiring expressions as answers, carry your solution to the point where
the equation for each problem is specified. For example,
1,000 (P/A, 4%, 5) + 2,500 (P/F, 4%, 5) – 4,000
Final exam has 2 Parts 7 problems totally 108 points.
Part I: 6 regular problems for 100 points
Part II: 1 bonus problem for 8 points
Note: If you complete the course evaluation and submit the printout before the final exam, you
will get 2 extra points.
You are suggested to do Part I first. Part II bonus problem is optional.
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
2
Prat I: 6 Regular Problems, 100 Points
Question 1 (6 Points)
You have two alternatives to manufacture a product.
Alternative 1: The first alternative requires a fixed cost of $100 for the purchase of hand tools
and a variable cost of $2 per unit.
Alternative 2: The second alternative uses an automated process that has a fixed cost of $250 and
a variable cost of $1 per unit.
Assuming an annual production rate of 50 units, how long will it take (in years) to reach the
breakeven point, i.e., the point at which you are indifferent between the two alternatives?
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
3
Question 2 (12 Points)
Suppose you took out a bank loan of $25,000 at an annual interest rate of 12% compounded
monthly. The loan is repayable over a period of 5 years.
(a) What is the effective annual interest rate? (4 Points)
(b) What is your monthly payment? Please refer to the interest rate tables for numerical
answers. (4 Points)
(c) Monthly payments are made at the end of every month. After making 40 such payments,
you could pay a lump sum now (right after the 40th
payment) to close out the loan. How
much do you need to pay? Please refer to the interest rate tables for numerical answers.
(4 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
4
Question 3 (22 Points)
Your company is considering the purchase of a machine for its production line. Data for two
possible machines are provided in the table below. The company’s MARR is 10% per year.
Machine A Machine B
Initial cost $1,000 $2,000
Useful life 6 12
Annual expenses $100 $200
Annual revenues $400 $350 in the first year, then
increasing by $50 every year
Market value (end of useful life) $400 $800
Useful Formulas:
, , ,
,
, ,
, ,
(a) Please draw the cash flow diagram for Machine A from the company’s perspective?
(4 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
5
(b) Please calculate the AW of Machine A based on your cash flow diagram in part (a)?
(5 Points)
(c) Please draw the cash flow diagram for Machine B from the company’s perspective?
(5 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
6
(d) Please calculate the AW of Machine B based on your cash flow diagram in part (c)?
(6 Points)
(e) If the study period is 12 years and the repeatability assumption holds, which machine will
you select? (2 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
7
Question 4 (17 Points)
An asset (Defender) purchased 5 years ago for $75,000 can be sold today for $15,000. Operating
expenses will be $10,000 this year, but these will increase by $1,500 per year. It is estimated the
asset’s market value will decrease by $1,000 per year over the next 3 years. The company’s
MARR is 10%.
Useful Formulas:
, ,
, ,
(a) Please fill in the blanks? (9 Points)
Year j MVj Ej
MV
Loss(j)
Cost of
Capital
i=10%
Total
Marginal
Cost(TCj) TCj(P/F,i%,j) ΣTCj(P/F,i%,j) EUACj
0 .
1 14000 10000 1000 1500 12500 11364 11364 .
2 13000 11500 . . . . . .
3 12000 13000 1000 1300 15300 11495 34346 .
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
8
(b) What is the economic life of the defender? (2 Points)
(c) If the challenger has the minimum EUAC = 14000, when is the best time to replace the
defender with the challenger? (6 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
9
Question 5 (17 Points)
The cost of a new and more efficient electrical circuit switching equipment is $900. It is
estimated (in base year-zero dollars, b=0) that the equipment will produce net annual revenues
by $400 (in base year-zero dollars, b=0) per year for 3 years and will have a $200 (in base year-
zero dollars, b=0) market value at the end of the 3rd
year. For simplicity, these cash flows both
net annual revenues and market value are estimated to increase at the general price inflation rate f
= 10% per year. This equipment will be depreciated under the MACRS (ADS) method over a
recovery period of 3 years. The effective income tax rate (t) is 40%. The selected study period is
3 years.
Useful Formulas:
, ,
, ,
, ,
, ,
(a) Please fill in the blanks in Actual Dollars (A$). (10 Points)
EOY BTCF(A$) Depr(A$) TI(A$) Tax(A$) ATCF(A$)
0 -900 -900
1 . . . . .
2 . . . . .
3 . . . . .
3 . . . .
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
10
(b) Assume the real MARR (after taxes) is 10% per year, compute the market MARR (after
taxes) per year? (3 Points)
(c) Is this capital investment justified? (4 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
11
Question 6 (26 Points)
The information for the defender and the challenger are given below:
Defender
Useful life Another 3 years
MARCS(GDS) with recovery period 7 years
Capital investment when purchased 5 years ago $10,000
Total annual expenses $5,000
Present MV $5,000
Estimated market value at the end of 3 additional years $1,000
Challenger
Useful life 3 years
Straight line depreciation method 3 years
Capital investment 15,000
Total annual expenses 3,000
Estimated MV at the end of 3rd
year 3,000
The after-tax MARR is 10%. Effective income tax rate is 40%. Study period is 3 years for both
defender and challenger.
Useful Formulas:
, ,
, ,
, ,
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
12
(a) Please fill in the blanks to calculate the ATCF for the challenger. (8 Points)
EOY BTCF Depr(SL) TI Tax(40%) ATCF
0 -$15,000 -$15,000
1 -$3,000 . . . .
2 -$3,000 . . . .
3 -$3,000 . . . .
3 $3,000 . . .
(b) Please calculate the Equivalent Uniform Annual Cost (EUAC) for the challenger based
on the ATCF in part (a) . (4 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
13
(c) Please fill in the blanks to calculate the ATCF for the defender. (8 Points)
EOY BTCF Depr(GDS) TI Tax(40%) ATCF
0 -$5,000 None . . .
1 -$5,000 . . . .
2 -$5,000 . . . .
3 -$5,000 . . . .
3 $1,000 . . .
(d) Please calculate the Equivalent Uniform Annual Cost (EUAC) for the defender based on
the ATCF in part (c). (4 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
14
(e) Based on the EUAC of the challenger you get in part (b) and the EUAC of the defender
you get in part(d), which alternative will you select under the study period 3 years?
1. Keep the defender for another 3 years
2. Replace the defender with the challenger immediately and then keep the challenger
for 3 years? (2 Points)
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
15
Part II, Bonus Problem, 8 Points
Question 7 (8 Points)
Write an expression to calculate the present equivalent value of the following infinitely
length alternating geometric gradient series. Assume is the cash flow at the end of year 1, is
the interest rate, is the constant increase or decrease percentage, . (Hint: You may need
the geometric series summation formula)
…………….. 9 8 7 6 0 1 2 3 4 5
……………..
2N+1
N=
2N+2
N=
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
16
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
17
Formulas and Tables
Formulas:
Find F given P:
Find P given F:
Find F given A: (1 ) 1Ni
F Ai
Find P given A:
Find P given G:
P G1
i
(1 i)N 1
i(1 i)N
N
(1 i)N
Find A given G:
A G1
i
N
(1 i)N 1
Find F given G: 1 (1 ) 1
( / , %, )Ni G NG
F G N F A i Ni i i i
Present Equivalent Value P of the Geometric Gradient Series:
or equivalently
Compute effective rate when interest compounds more frequently: 1 1
kr
iM
Compute effective interest rate when interest compounds continuously:
Geometric Series Summation Formula:
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
18
Depreciation using SL method: Nk
B SVd
N
Depreciation using DB method: 1(1 ) ( )k
kd B R R ; (1 )k
kBV B R
Depreciation of SL when using DB with switchover to SL:
GDS depreciation: k kd r B
[Gain(loss)ondisposal]N MVN BVN
im, ir, and f : f
fii mr
1; )1)(1(1 rm ifi ; )( fifii rrm
ius, ifm, and fe :
;
;
Total Marginal Cost:
EUAC:
EUACk TC j (P /F,i%, j)j1
k
A /P,i%,k
)1( (SL) 1
kN
SVBVd Nk
k
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
19
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
20
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
21
NAME (Printed): _________________,________________ (Last) (First)
Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011
22
GDS Recovery Rates