# 1.AAI, Inc., forecasts unit sales for a potential new product as follows:Year Units of Output95,000107,000110,000The initial investment in Net Working Capital (NWC) is \$1,500,000. At the end of the project, theinvestment in NWC is expected to be fully recovered. Total fixed costs are \$1,750,000 each year,variable costs are \$280 per unit, and the units are sold at \$330 each. The new equipment is expected tocost S4,400,000 and will be depreciated using the 3-year MACRS depreciation schedules (relevantdepreciation rates are 33% in year 1, 45% in year 2, 15% in year 3 and 7% in year 4). At the end ofthree years the equipment can be sold for \$100,000. If the new project is taken, there will be a negativeeffect on the firm's existing products - cash flow from the firm's existing products will decrease by88,000 on a post-tax basis in years 1, 2, and 3. The tax rate s 40% and AAI Inc's cost ofcapital is 12%Compute the (i) payback period, (ii) NPV, (iii) IRR, and (iv) profitability index of the project.

Question
Step 1

Please see the table below. Since all the steps are sequential, I have converted the same into a tabular form.

Please be guided by the sign [+] / [-] against each variable in the first column.This will help you understand whether a particular variable has been added or subtracted.

All the four subparts have been solved at appropriate place in the table itself.

Step 2
 Year, N Linkage 0 1 2 3 Purchase cost of new equipment A 4,400,000 Investment in working capital B 1,500,000 Total Initial Investment C = A + B 5,900,000 Depreciation schedule D 33% 45% 15% Depreciation E = D x A 1,452,000 1,980,000 660,000 Accumulated Depreciation F = Sum of E 1,452,000 3,432,000 4,092,000 Tax Basis (Asset balance) G = A - F 4,400,000 2,948,000 968,000 308,000 Units of Output H 95,000 107,000 110,000 Sale Price per unit I 330 330 330 Variable cost per unit J 280 280 280 Annual Operating Cash flows Revenue K = H x I 31,350,000 35,310,000 36,300,000 [-] Variable Costs L = H x J 26,600,000 29,960,000 30,800,000 [-] Fixed Costs M 1,750,000 1,750,000 1,750,000 [-] Depreciation E (as above) 1,452,000 1,980,000 660,000 EBIT N = K-L-M-E 1,548,000 1,620,000 3,090,000 [-] Taxes O = 40% x N 619,200 648,000 1,236,000 NOPAT P =N - O 928,800 972,000 1,854,000 [-] Post tax reduction in existing cash flows P' 88,000 88,000 88,000 Annual Operating Cash flows Q = P + E - P' 2,292,800 2,864,000 2,426,000 Sale value of the machine R 100,000 Gain / (Loss) on sale S = R - G (208,000) Tax on gain / loss T = S x 40% (83,200) Terminal Cash flows Post tax salvage value U = R - T 183,200 Release of working capital B (as above) 1,500,000 Terminal Cash flows V = U + B 1,683,200 Net Cash flows W = -C + Q + V (5,900,000) 2,292,800 2,864,000 4,109,200 Cumulative cash flows Sum of W (5,900,000) (3,607,200) (743,200) 3,366,000 Part (i) Payback Period 2.18 =2+743,200/4,109200 Cost of Capital X 12% Discount Factor Y = (1 + X)-N 1.0000 0.8929 0.7972 0.7118 PV of cash flow Z = W x Y (5,900,000) 2,047,143 2,283,163 2,924,847 Part (ii) NPV AA = Sum of Z 1,355,154 Part (iii) IRR 24% =IRR(-5900000,2292800,2864000,4109200) Part (iv) Profitability Index (AA + C) / C 1.23
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