Explanation The depreciation in ADS for first and seventh year can be calculated using the following formula: Depreciation = 1 2 × ( Cost basis Total life time ) (1) Substitute the respective values in Equation (1) to calculate the depreciation in the first year and the last year. Depreciation = 1 2 ( 30 , 000 6 ) = 0.5 ( 5 , 000 ) = 2 , 500 The depreciation in the first year and the seventh year is $2,500. The depreciation in Alternate Depreciation System between first and seventh year can be calculated by using the following formula: Depreciation = ( Cost basis Total life time ) (1.A) Substitute the respective values in Equation (1.A) to calculate the depreciation in the first year. Depreciation = ( 30 , 000 6 ) = 5 , 000 The depreciation in the second year to sixth year is $5,000. Before tax cash flow is denoted by BTCF which is the net annual revenue. Taxable income (TI) can be calculated by using the following formula. TI i = BTCF i − Depreciation i (2) Substitute the respective values in Equation (2) to calculate the taxable income. TI i = 0 − 2 , 500 = − 2 , 500 Taxable income in the year 1 is -$2,500. Tax payment (TP) can be calculated as follows. TP i = TI i × ( − Tax rate ) (3) Substitute the respective values in Equation (3) to calculate the tax payment. TP 1 = − 2 , 500 × ( − 0 .25 ) = 625 Taxable income in the year 1 is 625. After tax cash flow (ATCF) can be calculated as follows. ATCF i = BTCF i + TP i (4) Substitute the respective values in Equation (4) to calculate the ATCF for the first year. ATCF 1 = 0 + 625 = 625 ATCF in the year 1 is $625. Table 1 shows the value of ATCF fro purchase option that obtained by using Equations (1), (1.A), (2), (3) and (4). The last year BTCF is included the selling price value or salvage value. Table 1 Year BTCF Depreciation TI Tax amount ATCF 0 –30,000 - - 1 0 2,500 –2,500 625 625 2 0 5,000 –5,000 1,250 1,250 3 0 5,000 –5,000 1,250 1,250 4 –10,000 5,000 –15,000 3,750 -6,250 5 0 5,000 –5,000 1,250 1,250 6 0 5,000 –5,000 1,250 1,250 7 0 2,500 –2,500 625 625 8 0 0 0 0 0 Time period is denoted by n and the interest is denoted by i

17th Edition

ISBN: 9780134870069

Author: William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher: PEARSON

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Chapter 7, Problem 38P

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Select the alternative based on the ATCF.

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Chapter 7, Problem 37P

Chapter 7, Problem 39P

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Chapter 7 Solutions

Engineering Economy (17th Edition)

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