IE 343 Section 2 - Final ExamIE 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

NAME (Printed): _________________,________________ (Last) (First)

Purdue University Fall 2011 – IE 343 – Section 2 Instructor: Tian Ni Final Exam, Dec. 12, 2011

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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.



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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?



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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)



4


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)



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(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)



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(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)



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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 .



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(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)



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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 . . . .



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(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)



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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:

, ,

, ,

, ,



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(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)



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(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)



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(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)



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Part II, Bonus Problem, 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=



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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:



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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



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GDS Recovery Rates

IE 343 Section 2 - Final ExamIE 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

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