Tax Homework. A B C Installed cost $10,000 $15,000 $20,000 Net Uniform annual before 3,000 6,000 10,000

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1 Tax Homework 1. A firm is considering three mutually exclusive alternatives as part of a production improvement program. Management requires that you must select one. The alternatives are: A B C Installed cost $10,000 $15,000 $20,000 Net Uniform annual before 3,000 6,000 10,000 tax income Useful Life and Tax Life in years Tax and Actual Salvage 10,000 3,000 0 Depreciation Method Straight Line Straight Line Double Rate Declining Balance Make your selection with an after tax analysis using a tax rate of 40%. Which alternative should be selected given that the after tax MARR is 12%? You can use any method for analysis. Solution: Compare with the NAW method. Alternative A: NAW = * *.6 = = Alternative B: After Tax Cash Flow = ( )*.4 = = 4400 NAW = * (A/P, 0.12, 6) = * = -( ) = = Alternative C: Depr 1 = 20000*2/3 = Depr 2 = ( )*2/3 = 13334/3 = 4444 Depr 3 = ( )*2/3 = 2222*2/3 = 4444/3 = 1481 BV 3 = = 742 After Tax CF Year 1: ( )*.4 = *.4 = = Year 2: ( )*.4 = *.4 = = Year 3: ( )*.4 = *.4 = = Year 3 Tax Savings on Disposal 742*.4 = October 11,

2 NPV = *(P/F,.12,1) *(P/F,.12,2) + ( )*(P/F,.12,3) NPV = * * * NPV = = = NAW = *(A/P,.12,3) = * = Choose A 2. We are considering the purchase of an asset for $90,000. The life used for tax purposes is three years. The tax salvage is zero. The tax rate for both ordinary income and capital gains is 30%. In the tables provided show the before and after tax cash flow. Leave blank any cells not required. a. Situation: We use straight line depreciation. We keep the asset for 5 years. We sell the asset for $40,000 at the end of the fifth year. The cost of operation in each year is $20,000. Year BTCF = 20 ATCF =14 The Depreciation per year is 90/3 = 30. For the first three years, the after tax cash flow is; ATCF = BTCF - Tax = (-20-30).3 = *.3 = = - 5. For the final two years the ATCF is ATCF = BTCF - Tax = (-20).3 = = -14 Considering salvage, the BV is zero at year 5. Then the after tax salvage is AT Salvage = SV - Tax = 40-40*.3 = = 28. b. Situation: We use double rate declining balance depreciation. We keep the asset for 2 years. We sell the asset for $40,000 at the end of the second year. The net revenue from operations in each year is $30,000. Year BTCF = 70 ATCF = 58 The Depreciation in the first year year is 90(2/3) = 60. October 11,

3 The Depreciation in the second year is 30(2/3) = 20 The book value at the end of year 2 is 10. For the first year, the after tax cash flow is: ATCF = BTCF - Tax = 30 - (30-60).3 = *.3 = 39. For the second year, the after tax cash flow is: ATCF = BTCF - Tax = 30 - (30-20).3 = 30-3 = 27. Considering salvage, the BV is 10 at year 2. Then the after tax salvage is AT Salvage = SV - Tax = 40 - (40-10)*.3 = 40-9 = a. Your company is purchasing a machine. The machine costs $20,000. The life of the machine is 5 years. The machine will be worthless at the end of the five years. You expect a savings in annual operating cost over the existing machine of $10,000. The machine is depreciated using the straight line method using a tax life of 5 years and zero salvage. You pay a tax rate of 40% on net taxable income. Find the after tax rate of return for the investment in this machine. The depreciation on the machine is $4000 per year. The taxable income is = 6000 per year. The tax is 6000*0.4 = 2400 per year. The after tax cash flow is 7600 per year. Find the after tax ROR NPW = (P/A, i, 5) = 0 or (P/A, i, 5) = /7600 = Looking in the table, the closest interest rate is about 25%. b. Consider again the situation of part a, but this time assume the actual salvage is $20,000 at the end of the five years (you get back all that you have invested). The government changes the tax law so that the tax on capital gains to 0%. All other data of part a is the same. In particular, the government still allows you to assume that the tax salvage is zero when determining the depreciation. What is the after tax rate of return for this investment? Since the entire investment is recovered after five years. The ROR is The after tax annual income/investment = 7600/20000 = 38%. 4. You are comparing two alternatives with an after tax analysis. The alternatives are identical in function so we do not consider incomes in our analysis. Assume the tax rates on ordinary income and capital gains are both 30%. Both alternatives are depreciated with the straight line method with a tax salvage of zero. We do, however, expect the actual salvage will be positive as shown in the table. Data for the two possibilities is shown in the table below. Select the best alternative using an after tax MARR of 10%. You may use any method of analysis. A B Initial Cost 50,000 90,000 Annual Operating Cost 15,000 10,000 October 11,

4 Tax Life and Actual Life 5 10 Actual Salvage 20,000 20,000 Total Costs B: = A: 2*( ) = 2* = Compute the after tax net annual cost for each alternative A: BTCF = -15,000, Taxable Income = = , Tax = ATCF = = Net Annual Cost = 50,000(A/P,.10, 5) (A/F,.10, 5) = 50,000* * = 13, = 18,396.8/yr B: BTCF = -10,000, Taxable Income = = *.3, Tax = ATCF = = Net Annual Cost = 100,000(A/P,.10, 10) (A/F,.10, 10) = 90,000* * = 14, = 18,065.2/yr Select B with the smallest net annual cost 5. Consider an asset that has an initial cost of $80,000, a tax life of 4 years, and a tax salvage of 0. The tax on ordinary income is 40%, and the tax rate on capital gains is 20%. a. Show in the table below the depreciation amounts for the first and second years. Year Straight line method (SL) Sum of years digits method (SYD) Double Rate Declining balance method (DRDB) October 11,

5 b. Over the entire life of the machine, which is the preferable method for depreciation: the straight line method or the sum of years digits method? Explain your conclusion. The sum of the years digits method is best, because it returns the capital earlier. The capital can then be reinvested. c. Say in the first year we had a net taxable income of $50,000 not considering depreciation. If we were using the sum of years digits method of depreciation, what is our after tax cash flow in the first year? Including Depreciation the Taxable income is = The tax is 18000*.4 = After tax cash flow = = 42800, d. Assume that you have used the straight line method for the first two years. Say we sell the machine at the end of year 2 for $30,000. What effect does the sale have on the capital gains taxes paid by the company? The book value after two years is $40,000. The sale results in a tax loss of $10,000. The capital gains tax is *0.2 = The loss results in a reduction on capital gains tax of $ You are comparing two alternatives with an after tax analysis. The alternatives are identical in function so we do not consider incomes in our analysis. Assume the tax rates on ordinary income and capital gains are both 30%. Both alternatives are depreciated with the straight line method with a tax salvage of zero. We do, however, expect the actual salvage will be positive as shown in the table. Data for the two possibilities is shown in the table below. Select the best alternative using an after tax MARR of 15%. You may use any method of analysis. A B Initial Cost 50, ,000 Annual Operating Cost 15,000 10,000 Tax Life and Actual Life 5 10 Actual Salvage 20,000 20,000 B: = A: 2*( ) = 2* = Compute the after tax net annual cost for each alternative A: BTCF = -15,000, Taxable Income = = , Tax = ATCF = = Net Annual Cost = 50,000(A/P,.15, 5) (A/F,.15, 5) October 11,

6 = 50,000* * = 14, = 20,338.8/yr B: BTCF = -10,000, Taxable Income = = , Tax = ATCF = = Net Annual Cost = 100,000(A/P,.15, 10) (A/F,.15, 10) = 100,000* * = 19, = 23,239.8/yr Select A with the smallest net annual cost 7. Find the after tax equivalent present worth of a process which requires an initial investment of $100,000, has a ten year economic life, has a salvage value of $30,000 at the end of its economic life, and has operating costs of $40,000 per year. Annual revenue attributable to the process is $60,000. The tax rate is 30%. The process is depreciated with the ACRS method using a 5 year tax life. The after tax minimum acceptable rate of return is 15%. Is this an acceptable investment? Periods BTCF Depr T.I Tax ATCF PW Salvage TotalDepr NPW You purchase a rental house for $50,000 on Jan. 1, The land is valued at $10,000 and the structure is valued at $40,000. You are required by the government to use the ACRS method for depreciation. This allows a depreciation in each year of 3.64% of the purchase cost of the structure. a. You sell the house on Dec. 31 of What is the book value of the property (land and structure) when you sell it? Also include the affect of the 1990 depreciation. The depreciation over the ten year period is 10*40000* = October 11,

7 The book value is then = b. In 1990 you sell the house for $70,000. What is the capital gain on which you must pay taxes? If your marginal tax rate is 31%, what tax must you pay on your gain? The capital gain is = Tax =.31*34560 = October 11,