Question

Emperor's Clothes Fashions can invest $5 million in a new plant for producing invisible makeup. The plant has an expected life of 5 years, and expected sales are 6 million jars of makeup a year. Fixed costs are $2.1 million a year, and variable costs are $1.10 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 $1.40 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 $1.6 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.) NPV a. million NPV b. million NPV million C. d. Price per jar

Answer 1

Given 5 Million $ Plant Cost Life 5 years Expected Sales 6 Million Units Fixed Cost 2.1 Million $ 1.10 $ Variable Cost Price/unit 2.40$ 40% Tax rate opportunity cost 12% Solution: Calculate Depriciation Depriciation Cost Life 5 5 1 Part a: NPV Calculation of Annual operating Cash Flow and NPV Unit Profit/U Profit CFADT CFAT Year Dep. FC PVE NCF CFSP CFC PV -5 -5 1 -5 0 3.410714 3.82 1 6 1.3 7.8 1 2.1 4.7 3 4 0.893 2 6 1.3 7.8 1 2.1 4.7 4 3.82 0.797 3.045281 0.712 2.719001 6 1.3 7.8 2.1 4.7 4. 3.82 7.8 2.427679 4 6 1.3 1 2.1 4.7 3 4. 3.82 0.636 7.8 1 2.1 4.7 4 3.82 0.567 2.167571 5 6 1.3 NPV 8.77 Where, Profit/Unit Selling Price per unit - Variable Cost per unit Profit No. of units x Profit /Unit Depreciation (Dep.) Fictional Cash Flow (Used on for Tax Calulation) FC Annual fixed cost NCF (Net Cash Flow) CFADT (Cash flow after Dep. & Tax) Profit- Dep. - FC NCF X (1- Tax Rate) CFAT Depreciation CFAT (Cash flow after Tax) Cash Flow due to Sale / Purchase of Asset CFSP= CFAT CFSP CFC (Annual operating cash flow) Hence, NPV is $8.77 Million. Part b: NPV if variable cost is $1.40 Calculation of Annual operating Cash Flow and NPV Unit Profit/U CFADT CFAT Profit Dep FC NCF CFSP CFC PVF PV Year 0 -5 -5 1 -5 1.00 2.446429 1 6 6 1 2.1 2.9 2 3 2.74 0.893 2.184311 6 2.1 2.9 2 2.74 0.797 6 1.00 6 1.00 6 1 2.1 2.9 2 2.74 0.712 1.950278 1.74132 4 6 1.00 6 1 2.1 2.9 2 3 2,74 0.636 5 6 1.00 6 1. 2.1 2.9 2 2.74 0.567 1.55475 NPV 4.88

Where, Profit/Unit Selling Price per unit - Variable Cost per unit Profit No. of units X Profit / Unit Depreciation (Dep.) Fictional Cash Flow (Used on for Tax Calulation) FC Annual fixed cost Profit Dep. - FC NCF (Net Cash Flow) CFADT (Cash flow after Dep. & Tax) = CFAT (Cash flow after Tax) NCF X (1-Tax Rate) CFAT Depreciation Cash Flow due to Sale / Purchase of Asset CFSP= CFC (Annual operating cash flow) CFAT CFSP Hence, NPV is $4.88 Million. Part c: NPV if fixed cost is $1.6 million per year Calculation of Annual operating Cash Flow and NPV Year Unit Profit/U Profit Dep CFADT CFAT NCF FC CFSP CFC PVF PV 0 -5 -5 1 -5 0.893 3.678571 1.3 5.2 7.8 1.6 4.12 1 6 3 4 0.797 2 6 1.3 7.8 1 1.6 5.2 4 4.12 3.284439 0.712 2.932535 0.636 2.618334 0.567 2.337799 6 1.3 7.8 1.6 5.2 3 4.12 5.2 4 6 1.3 7.8 1 1.6 4 4.12 4.12 7.8 1 1.6 5.2 4 5 6 1,3 NPV 9.85 Where, Profit/Unit Selling Price per unit - Variable Cost per unit Profit No. of units X Profit / Unit Depreciation (Dep.) Fictional Cash Flow (Used on for Tax Calulation) Annual fixed cost FC NCF (Net Cash Flow) Profit - Dep. - FC NCF X (1- Tax Rate) CFAT Depreciation CFADT (Cash flow after Dep. & Tax) CFAT (Cash flow after Tax) Cash Flow due to Sale / Purchase of Asset CFSP= CFAT CFSP CFC (Annual operating cash flow) Hence, NPV is $9.85 Million. Part d: At which price/jar NPV equal zero Lets assume Price as 1.5 and calculate NPV CFADT CFAT Dep Profit/U Profit Year Unit FC NCF CFSP CFC PVF PV -5 -5 1 -5 1 6 0.40 2.4 1 2.1 -0.7 0 1 0.58 0.893 0.517857 0.797 0.462372 0.712 0.412833 2.1 0.58 2 6 0.40 2.4 1 -0.7 0 -0.7 2.4 2.1 0 1 0.58 6 0.40 6 2.4 1 2.1 -0.7 0 1 0.58 0.636 0.3686 0.40 6 0.40 2.4 1 2.1 -0.7 0 1 0.58 0.567 0.329108 NPV -2.91

Where, Profit/Unit Selling Price per unit - Variable Cost per unit Profit No. of units X Profit / Unit Depreciation (Dep.) = Fictional Cash Flow (Used on for Tax Calulation) Annual fixed cost FC NCF (Net Cash Flow) Profit- Dep. - FC CFADT (Cash flow after Dep. & Tax) NCF X (1- Tax Rate) CFAT Depreciation CFAT (Cash flow after Tax) Cash Flow due to Sale / Purchase of Asset CFAT CFSP CFSP= CFC (Annual operating cash flow) Now we have following details Case Price NPV 1 2.4 8.77 2 1.5 -2.91 Using Interpolation, we get Price Price2 0 NPV2 X Price 1 Price 2 NPV1 - NPV2 1.5 2.91 X 0.9 11.68 1.5 0.2242 + 1.72 Hence, at Price at $1.72 per jar, NPV equals 0. Note: There may be difference in NPV at price $1.72 per jar due to rounding off