IE 343 Section 2 - Final Exam

Transcription

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. 1

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? 2

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 40 th 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) 3

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) 4

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) 5

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) 6

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

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) 8

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 $200 (in base yearzero dollars, b=0) market value at the end of the 3 rd year. For simplicity, these cash flows both net annual revenues and market value are estimated to increase at the general price inflation rate f = 10% per year. This equipment will be depreciated under the MACRS (ADS) method over a recovery period of 3 years. The effective income tax rate (t) is 40%. The selected study period is 3 years. Useful Formulas:,,,,,,,, (a) Please fill in the blanks in Actual Dollars (A$). (10 Points) EOY BTCF(A$) Depr(A$) TI(A$) Tax(A$) ATCF(A$)

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) 10

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 3 rd 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:,,,,,, 11

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, $3, $3, $3, $3, (b) Please calculate the Equivalent Uniform Annual Cost (EUAC) for the challenger based on the ATCF in part (a). (4 Points) 12

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 $5, $5, $5, $1, (d) Please calculate the Equivalent Uniform Annual Cost (EUAC) for the defender based on the ATCF in part (c). (4 Points) 13

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) 14

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) N+2.. 2N+1 15

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17 Formulas: Find F given P: Find P given F: Formulas and Tables Find F given A: N (1 i) 1 F A i Find P given A: Find P given G: P G 1 (1 i) N 1 N i i(1 i) N (1 i) N Find A given G: A G 1 i N (1 i) N 1 Find F given G: N 1 (1 i) 1 G NG F G N ( F / A, i%, N) i i i i Present Equivalent Value P of the Geometric Gradient Series: or equivalently r Compute effective rate when interest compounds more frequently: i 1 1 M Compute effective interest rate when interest compounds continuously: Geometric Series Summation Formula: k 17

18 Depreciation using SL method: d k B SV N N Depreciation using DB method: d B R R k 1 k (1 ) ( ) ; BV (1 ) k k B R Depreciation of SL when using DB with switchover to SL: d GDS depreciation: dk rk B [Gain(loss)on disposal] N MV N BV N k (SL) BVk SV 1 N ( k 1) N i m, i r, and f : i r im f ; 1 im (1 f )(1 ir ) ; im ir f ir ( f ) 1 f i us, i fm, and fe : ; ; Total Marginal Cost: EUAC: EUAC k k j 1 TC j (P /F,i%,j) A/P,i%,k 18

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22 GDS Recovery Rates 22