MSE 604_HW7

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Dec 6, 2023

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California State University, Northridge MSE604 ENGINEERING ECONOMIC ANALYSIS Semester: Fall 2023 Professor: Ahmad Sarfaraz Submitted By: Bhushan Chaudhari Falguni Pande Tejal Nikam Mayur Ahire

7-12. A bowling alley costs $500,000 and has an estimated life of 10 years (SV10 = $20,000). a. Determine the depreciation for years one through 10 using: (i) the straight-line method; (ii) the 200% declining balance method; and (iii) the MACRS method (ADR guideline period = 10 years). A table containing some of the depreciation values is provided below. Please complete the table. (7.3, 7.4) b. Compute the present worth of depreciation at EOY zero for each of the three depreciation methods. The MARR is 10% per year. c. If a large present worth in Part (b) is desirable, what do you conclude regarding which method is most desirable Solution: Given Costs = $500,000 Salvage Value = $20,000 N = 10 years a. 1. Depreciation by straight-line method: = (500,000 - 20,000) / 10 = $48,000 2. By 200% Declining Balance Method: = 500,000 (1-R) K-1 • (R) R = 2 / 10 = 0.2

3. By MARCS Method: = 500,000 • dK EOY Straight-line Method Declining Balance Method MARCS Method 1 $48,000 $100,000 $71,450 2 $48,000 $80,000 $122,450 3 $48,000 $64,000 $87,450 4 $48,000 $51,200 $62,450 5 $48,000 $40,960 $44,650 6 $48,000 $32,768 $44,600 7 $48,000 $26,214 $44,650 8 $48,000 $20,972 $22,300 9 $48,000 $16,777 $0 10 $48,000 $13,422 $0 b. Present Worth MARR = 10% / year 1. Straight line Method PW(10%) = $48,000 (P/A, 10%, 10) = $294,941 2. Declining Balance Method PW(10%) = ∑ 10 i=1 dK (P/F, 10%, K) = $319,534

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3. MARCS (10%) PW(10%) = ∑ 10 i=1 dK (P/F, 10%, K) = $360,720 c. The present value is maximum for the MARCS depreciation method. Therefore, it is most appropriate from the income tax point of view. 7-25. Two different copying machines are being considered in your company. The Mortar copier would be purchased while the Xrocks copier would be leased. The company will replace any copier selected at this time after three years (i.e., the planning horizon for this evaluation is three years). The MACRS depreciation recovery period for office equipment is seven years. Assume an income tax rate of 40% and an after-tax MARR of 18% per year. Using the data in the table below, which machine would you recommend? (7.9) Solution: Year Investment Expenses Depreciation Bond Taxable Income ATCF Value Income Tax (40%) 0 -19,000 0 0 19,000 0 0 -19,000 1 0 -800 -2,715 16,285 -3,515 879 79 2 0 -800 -4,653 11,632 -5,453 1,363 563 3 8,000 -800 -1,662 9,970 -4,432 1,108 8,308 Present Worth PW (18%) = -$12,033.35

For X rocks: Present Worth PW (18%) = -9,000 (1-0.25) (P/A, 18%, 3) = -9,000 (1-0.25) (2.1743) = -14,677 As we can see, the lowest Present Worth value is for Mortar purchase. So, we consider this. 7-39. Two fixtures are being considered for a particular job in a manufacturing firm. The pertinent data for their comparison are summarized in Table P7-39. The effective federal and state income tax rate is 25%. Depreciation recapture is also taxed at 25%. If the after-tax MARR is 8% per year, which of the two fixtures should be recommended? State any important assumptions you make in your analysis. (7.9) Solution: Assumption – repeatability Fixture X EOY (A) BTCF (B) Depr. (C)=(A)-(B) TI (D)=-t(C) T(50%) (E)=(A)+(D ) ATCF 0 -30000 -- -- -- -30000 1-5 -3000 6000 -9000 4500 1500

6 -3000 0 -3000 1500 -1500 6 (Market value) 6000 -- 6000 (Depreciation Recapture) -3000 3000 Therefore, AW x (8%) = -$4,989 Fixture Y EOY (A) BTCF (B) Depr (C)=(A)-(B) TI (D)=-t(C) T(40%) (E)=(A)+(D) ATCF 0 -40000 -- -- -- -40000 1 -2500 8000 -10500 5250 2750 2 -2500 12800 -15300 7650 5150 3 -2500 7680 -10180 5090 2590

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4 -2500 4608 -7108 3554 1054 5 -2500 4608 -7108 3554 1054 6 -2500 2304 -4804 2402 -98 7 -2500 0 -2500 1250 -1250 8 -2500 0 -2500 1250 -1250 8 4000 (Market value) -- 4000 -2000 2000 Therefore, AW B (8%) = -$5,199 Hence, according to the AW value Fixture X should be selected.

7-41. Two alternative machines will produce the same product, but one is capable of higher- quality work, which can be expected to return greater revenue. The following are relevant data: Machine A EOY (A) BTCF (B) Depr (C) = (A) - (B) TI (D) = -t(C) T(40%) (E) = (A) + (D) ATCF 0 -$20,000 - - - -$20,000 1-12 $12,000 1,333.33 $10,666.67 -$4,266.67 $7,733.33 12 $4,000 - 0 0 $4,000 AW(A) = -$20,000(A/P, 10%, 12) + $7,733.33 + $4,000(A/F, 10%, 12) = (-20000)(0.1468) + 7733.33 + (4000)(0.0468) = $4,984.53 Machine B EOY (A) BTCF (B) Depr (C) = (A) - (B) TI (D) = -t(C) T(40%) (E) = (A) + (D) ATCF 0 -$30,000 - - - -$30,000 1-8 -$18,000 $3,750 -$14,250 -$5,700 -$12,300 AW(B) = -$30,000(A/P, 10%, 8) + $12,300

= (-30000)(0.1874) + 12300 = $6,678 Since the AW value for machine B is larger than that for machine A, we select machine B. 7-44. A biotech company has an effective income tax rate of 40%. Recaptured depreciation is also taxed at the rate of 40%. The company must choose one of the following mutually exclusive cryogenic freezers for its tissue samples. The after-tax MARR is 12% per year. Which freezer should be selected based on after-tax present worth? (7.10) Freezer 1 EOY (A) BTCF (B) Depr (C) = (A) - (B) TI (D) = -t(C) T(40%) (E) = (A) + (D) ATCF Total ATCF 0 -$11,000 - - - -$11,000 -$11,000 1 $3,000 $3,000 0 0 $3,000 $3,000 2 $3,000 $3,000 0 0 $3,000 $3,000 3 $3,000 $3,000 0 0 $3,000 $3,000 4 $3,000 - $3,000 -$1,200 $1,800 $1,800 5a $3,000 - $3,000 -$1,200 $1,800 $3,800 5b $2,000 - 0 0 $2,000

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 PW(12%) = -$494.35 Freezer 2 EOY (A) BTCF (B) Depr (C) = (A) - (B) TI (D) = -t(C) T(40%) (E) = (A) + (D) ATCF Total ATCF 0 -$33,000 - - - -$33,000 -$33,000 1 $9,000 $10,998.9 -$1,998.9 $799.56 $9,799.56 $9,799.56 2 $9,000 $14,668.50 -$5,668.50 $2,2267.4 $11,267.4 $11,267.4 3 $9,000 $4,887.3 $4,112.7 -$1,645.08 $7,354.92 $7,354.92 4 $9,000 $2,445.3 $6,554.7 -$2,621.88 $6,378.12 $6,378.12 5a $9,000 - $9,000 -$3,600 $5,400 $6,600 5b $2,000 - $2,000 -$800 $1,200  PW(12%) = -$2,234.58 Hence, Freezer 1 should be selected.

MSE 604_HW7

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