Homework 10 Solution

# Homework 10 Solution - Homework 10 Solution 1 ACME Widgets...

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Homework 10 Solution 1. ACME Widgets has just completed its new factory in Toluca, Mexico. During their first month of operation, they expect to make 10,000 widgets. That amount is expected to rise by 1500 widgets per month until the plant reaches its full capacity during Month 12. If ACME makes a profit of \$35 per widget and their time value of money is 12% per year compounded monthly, what is the value of their profits at the end of the factory’s first 12 months of operation? During Month 1, ACME makes 10,000 \$35=\$350,000. That amount rises by 1500 \$35=\$52,500 in each of the next 11 months (Months 2 through 12). This is an arithmetic gradient series with an equal- payment amount of \$350,000 per month and a gradient of \$52,500 per month. If we assume the 12% per year is the nominal rate (which is the standard assumption) then the interest rate per month is i = r / m = 12% / 12 = 1% per month Since we’ve been given monthly cash flows, we can use this effective monthly interest rate directly: 12.6825 68.2503 F \$350,000 F| A,1%,12 \$52,500 F| G,1%,12 \$8,022,020 2.

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