Question

Emperor’s Clothes Fashions can invest $4 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 5 million jars of makeup a year. Fixed costs are $2.7 million a year, and variable costs are $1.20 per jar. The product will be priced at $2.40 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 $1.30 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 $2.6 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

a)NPV =Total PV of Inflows -Initial outflow

Initial Investment =$4,000,000 SLM Depreciation =Cost of Asset/Useful Life of Asset that is $4,000,000/5=$800,000 per year Sales =$5,000,000*$2.4=$12,000,000 Variable Cost =$1.2*5,000,000=$6,000,000

after tax cashflow =Increase in sales -Increase in variable cost -Fixed cost -depreciation-tax add back depreciation

After tax Cashflow =Sales $12,000,000 Less variable costs $6,000,000 Less Fixed Costs $2,700,000 =$3,300,000 Less depreciation =$800,000 =$2,500,000 Less tax @40%=$1,000,000 Net effect after tax =$1,500,000 Add back Depreciation $800,000 we get $2,300,000 as after tax cashflow.Discounting it at 12% for 5 years PVAF =3.6048 Total PV =3.6048*$2,300,000=$8,291,040 NPV =$8,291,040-$4,000,000=$4,291,040

b)if variable costs become $1.3 Sales =$5,000,000*$2.4=$12,000,000 Variable Cost =$1.3*5,000,000=$6,500,000

After tax Cashflow =Sales $12,000,000 Less variable costs $6,500,000 Less Fixed Costs $2,700,000 =$2,800,000 Less depreciation =$800,000 =$2,000,000 Less tax @40%=$800,000 Net effect after tax =$1,200,000 Add back Depreciation $800,000 we get $2,00,000 as after tax cashflow.Discounting it at 12% for 5 years PVAF =3.6048 Total PV =3.6048*$2,000,000=$7,209,600 NPV =$7,209,600-$4,000,000=$3,209,600

c)if fixed costs are $2,600,000 Sales =$5,000,000*$2.4=$12,000,000 Variable Cost =$1.2*5,000,000=$6,000,000

After tax Cashflow =Sales $12,000,000 Less variable costs $6,000,000 Less Fixed Costs $2,600,000 =$3,400,000 Less depreciation =$800,000 =$2,600,000 Less tax @40%=$1,040,000 Net effect after tax =$1,560,000 Add back Depreciation $800,000 we get $2,360,000 as after tax cashflow.Discounting it at 12% for 5 years PVAF =3.6048 Total PV =3.6048*$2,360,000=$8,507,328 NPV =$8,507,328-$4,000,000=$4,507,328

d)price per jar at which NPV =0

Let x be the After tax cashflow So total Pv of inflows =3.6048x-$4,000,000=0 solving we get x =$1,109,631.60

Deducting depreciation we get $309,631.60 dividing by(1-.4) we get before tax cashflow as $516,052.6

Let x be the selling price per unit we get the equation $5,000,000x -$6,000,000 -$2,700,000-$800,000 =$516,052.6

Solving we get x =$2.00.Hence $2.00 is the selling price at which NPV =0

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