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 $2.40 per jar. The product will be priced at $3.50 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%.

a. What is project NPV under these base-case assumptions? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

b. What is NPV if variable costs turn out to be $2.70 per jar? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

c. What is NPV if fixed costs turn out to be $2.2 million per year? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

d. At what price per jar would project NPV equal zero? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Fixed cost : 2.5 Million

Variable cost : 2.40 per Jar

Price per Jar : 3.50

Life of machine 5 year

Opportunity cost 12%

Tax Rate 40%

Production and sales per year = 7 Million

Calculation of Profit per year :

Total Sales = 7 Million *3.50 = 24.50 Million

Total cost = Variable cost + Fixed Cost

= 2.40 *7 Million + 2.5 Million

= 19.30 Million

Depreciation = invest value/Life of machine

= 6 Million /5. = 1.20 Million

Profit = Total Sales - Total cost - Depreciation

= 24.50 Million - 19.30 Million - 1.20 Million

= 4.00 Million

Tax = 4 Million *40% = 1.60 Million

Cash flow = Profit + Depreciation - Tax

= 4+1.20-1.60

= 3.60 Million

Answe a) NPV = Cash flow * PVIFA (5, 12%) - cost of investment

= 3.60 *3.605 -6 =

= 6.98 Million

b) Profit on new variable cost

= Sales - Variable Cost- Fixed cost - Depreciation

= 24.50 - 2.70*7 - 2.50 - 1.20

= 1.90

Tax = 1.90*40% = 0.76

Cash flow = 1.90-0.76+1.20 = 2.34

NPV = 2.34*PVIFA (5,12%) - 6

= 2.34 * 3.605 -6

= 2.44 Million

C) Fixed Cost 2.20 Million

Profit = 24.50-16.80- 2.20 -1.20 = 4.30 Million

Tax = 4.30*40%=1.72 million

Cash flow= 4.30-1.72+1.20=3.78 Million

NPV = 3.78*3.605-6=7.63 Million

D) for NPV zero

Per year cash flow = Investment/ PViFA(5,12%)

= 6/3.605 = 1.664 Million

Profit after tax of the year = Cash flow - Tax of Depreciation

=1.664-(1.20*40%)

= 1.184 Million

Profit before tax= 1.184/60%=1.974 Million

Sale price = Profit + variable cost - Fixed cost

= 1.974 + 16.80+2.50

= 21.274 Million

Sale price per Jar = 21.274/7

= $ 3.04