Unit price: $124 Variable costs: $72 Fixed costs: $248,000 per year Expected sal

Question

Unit price: $124 Variable costs: $72 Fixed costs: $248,000 per year Expected sales: 10,800 per year (Scenario analysis) Family Security- is considering introducing tiny GPS trackers that can be inserted in the sole of a child's shoe, which would then allow for the tracking of that child if he or she was ever lost or abducted. The estimates, that might be off by 11 percent (either above or below), associated with this new product are shown here: 0 . Since this is a new product line, you are not confident in your estimates and would Hike to know how well you will fare if your estimates on the items listed above are 11 percent higher or 11 percent lower than expected. Assume that this new product line waffle require an initial of day of SI. 12 million, with no working capital investment, and will last for 10 years, being depreciated down to zero using straight-line depreciation. In addition, the firm's required rate of return or cost of capital is 10.2 percent, and the firm's marginal tax rate is 34 percent. Calculate the project's NPV under the "best-case scenario" (that is, use the high estimates-unit price 11 percent above expected, variable costs 11 percent less than expected, fixed costs 11 percent less than expected, and expected sales 11 percent more than expected). Calculate the project's NPV under the "worst-case scenario."

Explanation / Answer

Time line 0 1 2 3 4 5 6 7 8 9 10 Equipment cost -1120000 +Increase in working capital 0 =Initial Investment outlay -1120000 Sales 1.11*No. of units*(selling price*1.11) 1650028.32 1650028 1650028 1650028 1650028 1650028 1650028 1650028 1650028 1650028 -Variable cost =1.11*sales*.89*variable cost -768191.04 -768191 -768191 -768191 -768191 -768191 -768191 -768191 -768191 -768191 Net sales of project 881837.28 881837.3 881837.3 881837.3 881837.3 881837.3 881837.3 881837.3 881837.3 881837.3 -Fixed cost -220720 -220720 -220720 -220720 -220720 -220720 -220720 -220720 -220720 -220720 -Depreciation (cost of equipment and plant)/7 -112000 -112000 -112000 -112000 -112000 -112000 -112000 -112000 -112000 -112000 = 549117.28 549117.3 549117.3 549117.3 549117.3 549117.3 549117.3 549117.3 549117.3 549117.3 -taxes =(net sales - fixed cost - depreciation)*(1-tax) 362417.405 362417.4 362417.4 362417.4 362417.4 362417.4 362417.4 362417.4 362417.4 362417.4 +Depreciation 112000 112000 112000 112000 112000 112000 112000 112000 112000 112000 =after tax perating cash flow 474417.405 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 Reversal of Increase in working capital 0 = Terminal year after tax non operating CF 0 Total Cash flow -1120000 474417.405 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 474417.4 Cost of capital = 10% 10.20% Discount factor = (1 + cost of capital) ^ corresponding period 1 1.102 1.214404 1.338273 1.474777 1.625204 1.790975 1.973655 2.174967 2.396814 2.641289 Discounted cashflow = total cash flow/discount factor -1120000 430505.812 390658.6 354499.7 321687.5 291912.5 264893.3 240375.1 218126.2 197936.7 179615.9 NPV= Sum of discounted cash flow = 1770211 Worst case Time line 0 1 2 3 4 5 6 7 8 9 10 Equipment cost -1120000 +Increase in working capital 0 =Initial Investment outlay -1120000 Sales .89*No. of units*(selling price*.89) 1060780.32 1060780 1060780 1060780 1060780 1060780 1060780 1060780 1060780 1060780 -Variable cost =.89*sales*1.11*variable cost -768191.04 -768191 -768191 -768191 -768191 -768191 -768191 -768191 -768191 -768191 Net sales of project 292589.28 292589.3 292589.3 292589.3 292589.3 292589.3 292589.3 292589.3 292589.3 292589.3 -Fixed cost -275280 -275280 -275280 -275280 -275280 -275280 -275280 -275280 -275280 -275280 -Depreciation (cost of equipment and plant)/7 -112000 -112000 -112000 -112000 -112000 -112000 -112000 -112000 -112000 -112000 = -94690.72 -94690.7 -94690.7 -94690.7 -94690.7 -94690.7 -94690.7 -94690.7 -94690.7 -94690.7 -taxes =(net sales - fixed cost - depreciation)*(1-tax) -62495.875 -62495.9 -62495.9 -62495.9 -62495.9 -62495.9 -62495.9 -62495.9 -62495.9 -62495.9 +Depreciation 112000 112000 112000 112000 112000 112000 112000 112000 112000 112000 =after tax perating cash flow 49504.1248 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 Reversal of Increase in working capital 0 = Terminal year after tax non operating CF 0 Total Cash flow -1120000 49504.1248 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 49504.12 Cost of capital = 10% 10.20% Discount factor = (1 + cost of capital) ^ corresponding period 1 1.102 1.214404 1.338273 1.474777 1.625204 1.790975 1.973655 2.174967 2.396814 2.641289 Discounted cashflow = total cash flow/discount factor -1120000 44922.0733 40764.13 36991.05 33567.19 30460.25 27640.88 25082.47 22760.86 20654.14 18742.41 NPV= Sum of discounted cash flow = -818415

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