Emperor’s Clothes Fashions can invest $6 million in a new plant for producing in

Question

Emperor’s Clothes Fashions can invest $6 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 7 million jars of makeup a year. Fixed costs are $2.5 million a year, and variable costs are $2.4 per jar. The product will be priced at $3.5 per jar. The plant will be depreciated straight-line over 5 years to a salvage value of zero. The opportunity cost of capital is 12%, and the tax rate is 40%.

What is project NPV under these base-case assumptions?

What is NPV if variable costs turn out to be $2.7 per jar?

What is NPV if fixed costs turn out to be $2.2 million per year?

At what price per jar would project NPV equal zero?

Explanation / Answer

Case 1:

Profit each year = 3.5 * 7000000 - 2.4*7000000 - 2500000 = 5,200,000

So cash flows are populated in an excel sheet as follows

NPV can be calculated as follows

NPV =NPV(12%,G3:G7)+G2 = 6,977,194.33

Case 2:

Profit each year = 3.5 * 7000000 - 2.7*7000000 - 2500000 = 3,100,000

So cash flows are populated in an excel sheet as follows

NPV can be calculated as follows

NPV =NPV(12%,G3:G7)+G2 = 2,435,176.31

Case 3:

Profit each year = 3.5 * 7000000 - 2.4*7000000 - 2200000 = 5,500,000

So cash flows are populated in an excel sheet as follows

NPV can be calculated as follows

NPV =NPV(12%,G3:G7)+G2 = 7,626,054.04

Case 4:

Using permutation and combinations, we can find this in excel as $3.039

Year Cash flow Tax Rate After tax Cash Flow Machine Depreciation value Depreciation Tax Shield Total net cash flows 0         (6,000,000.00) 40%          (6,000,000.00)                          -                              -           (6,000,000.00) 1            520,000.00 40%            312,000.00        1,200,000.00            480,000.00            3,600,000.00 2            520,000.00 40%            312,000.00        1,200,000.00            480,000.00            3,600,000.00 3            520,000.00 40%            312,000.00        1,200,000.00            480,000.00            3,600,000.00 4            520,000.00 40%            312,000.00        1,200,000.00            480,000.00            3,600,000.00 5            520,000.00 40%            312,000.00        1,200,000.00            480,000.00            3,600,000.00

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