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# Emperor's Clothes Fashions can invest \$5 million in a new plant for producing invisible makeup. What is NPV? What is NPV if variable costs turn out to be \$1.20 per jar? What is NPV if fixed costs turn out to be \$1.5 million per year?

Emperor's Clothes Fashions can invest \$5 million in a new plant for producing invisible makeup. The plant has an expected life of 15 years, and expected sales are 6 million jars of makeup a year. Fixed costs are \$2 million a year, and variable costs are \$1 per jar. The product will be priced at \$2 per jar. The plant will be depreciated straight-line over 5 years to salvage value of zero. The opportunity cost of capital is 10%, and the tax rate is 40%.
(a) What is the project's NPV under these base-case assumptions?
(b) What is NPV if variable costs turn out to be \$1.20 per jar?
(c) What is NPV if fixed costs turn out to be \$1.5 million per year?
(d) At what price per jar would the project's NPV equal zero?

Note the answers should be:
a) 5.6 million
b) 2.9 million
c) 6.8 million
d) \$1.59 per jar

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#### Solution Preview

Actually the plant life is 5 years as its depreciated in 5 years to nil. Thus the project life is 5 years.

a. What is project NPV under these base-case assumptions?
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Revenue \$12,000,000 \$12,000,000 \$12,000,000 \$12,000,000 \$12,000,000
Less Expense \$8,000,000 \$8,000,000 \$8,000,000 \$8,000,000 \$8,000,000
Less Depreciation \$1,000,000 \$1,000,000 \$1,000,000 \$1,000,000 \$1,000,000
Profit before Tax \$3,000,000 \$3,000,000 \$3,000,000 \$3,000,000 \$3,000,000
Less Taxes \$1,200,000 \$1,200,000 \$1,200,000 \$1,200,000 \$1,200,000
Profit after Tax \$1,800,000 \$1,800,000 \$1,800,000 \$1,800,000 \$1,800,000
Add Depreciation \$1,000,000 \$1,000,000 \$1,000,000 \$1,000,000 \$1,000,000

Cash flow \$2,800,000 \$2,800,000 \$2,800,000 \$2,800,000 \$2,800,000
Capital Outlay -5000000
Net Cash flows -5000000 \$2,800,000 \$2,800,000 \$2,800,000 \$2,800,000 \$2,800,000

Cost of capital 10%
NPV \$5,614,202.95 or 5.6 mn

NPV is positive and ...

#### Solution Summary

Computations done for you in Excel (attached). No references.

\$2.19