# Question

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, which might be off by 10 percent (either above or below), associated with this new product are as follows:

Unit price: .......... $125

Variable costs: ....... $75

Fixed costs: ........ $250,000 per year

Expected sales: ........ 10,000 per year

Because this is a new product line, you are not confident in your estimates and would like to know how well you will fare if your estimates on the items listed above are 10 percent higher or 10 percent lower than expected. Assume that this new product line will require an initial outlay of $1 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 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 10 percent above expected, variable costs 10 percent less than expected, fixed costs 10 percent less than expected, and expected sales 10 percent more than expected). Calculate the project’s NPV under the “worst-case scenario.”

Unit price: .......... $125

Variable costs: ....... $75

Fixed costs: ........ $250,000 per year

Expected sales: ........ 10,000 per year

Because this is a new product line, you are not confident in your estimates and would like to know how well you will fare if your estimates on the items listed above are 10 percent higher or 10 percent lower than expected. Assume that this new product line will require an initial outlay of $1 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 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 10 percent above expected, variable costs 10 percent less than expected, fixed costs 10 percent less than expected, and expected sales 10 percent more than expected). Calculate the project’s NPV under the “worst-case scenario.”

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