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MNET 414: 2009 FallHome work # 6 solutionState tax 150,000x.096 14, 400Federal taxable income 150,000-14,400 135,600Federal tax rate for the income level from table 12.2 22,250 39% above 100,000Federal tax 22,250 (135,600-100,000)x0.39 36,134Total tax 14,400 36,134 50,534Combined incremental tax rate 0.096 0.39(1-0.096) 44.86%1/5
SOYD depreciation for an year t [# of remaining yr. including yr. t/SOYD]*(P-S) (n-t 1)/[n(n 1)/2]*(P-S)SOYD constant for 8 yrs. 8*9/2 36Thus for depreciation in year 1 8*(120000-12000)/36 8*3000 24,000depreciation in year 2 7*(120000-12000)/36 7*3000 21,000depreciation in year 3 6*(120000-12000)/36 6*3000 18,000depreciation in year 4 5*(120000-12000)/36 5*3000 15,000And so, on.Before and after tax cash flow is shown below.YrBTCFDEPTaxableincomeTax 1470011700870017700Note that in the year 8, in BTCF the salvage value is added to the benefit. However, thisis not taxable, since the book value and salvage value are the same.Now we apply present worth analysis to determine if the after tax cash flow is earning6% interest.NPW NPB-NPC 26,700(P/A,6%,8)-3000(P/G,6%,8) 12000(P/F,6%,8)-120,000 26,700(6.21)-3000(19.841) 12000(.6274)-120,000 - 6187.20Since NPW is a negative number, they will not obtain a 6% after tax rate of return.2/5
DDB depreciation (2/N)*BV, In this case N 4 years., thus DDB (2/4)*BV 0.5BVCalculation of Depreciation is shown below. Also, the depreciation in the year 4 is sameas the salvage value. Hence, after 4 years, no depreciation has been charged.Note that the salvage value is included to the sixth year BTCF.Also, note the salvage value is not taxable as it is not different than the 625062506250TaxableincomeTax 11650The ATCF, does not show any series. To find after tax IRRNPC NPB100000 39200(P/F,i,1) 27700(P/F,i,2) 24650(P/F,i,3) 24475(P/F,i,4) 5400(P/F,i,5) 11650(P/F,i,6)Plugging i 10%:39200(P/F,10%,1) 27700(P/F,10%,2) 24650(P/F,10%,3) 24475(P/F,10%,4) 5400(P/F,10%,5) 11650(P/F,10%,6) 39200*.9091 27700*.8264 24650*.7513 24475*.683 5400*.6209 11650*.5645 103693.253/5
Plugging i 12%:39200(P/F,12%,1) 27700(P/F,12%,2) 24650(P/F,12%,3) 24475(P/F,12%,4) 5400(P/F,12%,5) 11650(P/F,12%,6) 39200*.8929 27700*.7972 24650*.7118 24475*.6355 5400*.5674 11650*.5066 99149.70Interpolating:12 i12 10 (100000 99149.70) (103693.25 99149. 70)12 i2 850.3 4543.552 850.3i 12 h equipment has 5 year depreciable life (Table 11-2)Yearly MACRS depreciations percentages for 5 year property (based on the first cost) areobtained from Table 11-3, and the cash flow tables are as 02880MACRS%depTaxableincomeTax 80-8000-8000800080000027202720-2720-272000Before tax IRRIf all before tax cash flows are added that is-50000 2000 8000 17600 13760 5760 2880 04/5ATCF-50000472010720148801104057602880
That means cost and benefits are equal, thus IRR 0After tax IRRWe see that in year 1 &2 they save taxes 2,720 in each year, and in year 3&4 they paytaxes 2,720. Thus the total tax effect is zero, and hence after tax IRR 0Food processing equipment belongs to 3 year property class (Table 11-2)Yearly MACRS depreciations percentages for 3 year property (based on the first cost) areobtained from Table 11-3, and the cash flow tables are as %depTaxableincomeTax 8133924562818541*In the 4th year, there is a salvage value of 5000. Since MACRS depreciationdepreciates the full first cost, this 5000 is added to the taxable income of 4th year.ATCF’s NPW at 10% isNPW NPB-NPC 8133*(P/F,10%,1) 9245*(P/F,10%,2) 6281*(P/F,10%,3) 8541*(P/F,10%,4)-25000 8133*(.9091) 9245*(.8264) 6281*(.7513) 8541*(.683)-25000 586.20Since NPW is positive they will earn more than 10% after tax.5/5
Before and after tax cash flow is shown below. Yr BTCF DEP Taxable income Tax @ 46% ATCF 0 -120000 -120000 1 29000 24000 5000 -2300 26700 . obtained from Table 11-3, and the cash flow tables are as following. Yr BTCF MACRS% dep Taxable income Tax @ 40% ATCF 0 -25000 -25000 1 8000 33.33 8332.5 -332.5 133 8133 .
