7-32. your company is considering the introduction of a new product line. the in
ID: 1095417 • Letter: 7
Question
7-32. your company is considering the introduction of a new product line. the initial investment required for this project is $500,000, and annual maintenance costs are anticipated to be $35,000. annual operating cost will be in direct proportion to the level of production at $8.50 per unit, and each unit of product can be sold for $50.00. if the project has a life of 7 years, wht is the minimum annual production level for which this project is economically viable? work this problem on an after tax basis. assume 5-year SL depreciation (SV.5 = 0), MV.7 = 0, an effective income tax rate of 40%, and an after-tax MARR of 10% per year. (7.9)
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Explanation / Answer
let x be the annual production
depriciation per year = 35000/5 = 7000
cash flow per year(1-5)
= (50x -8.5x - 35000 - 7000) * (1-0.4) + 7000 * 0.4
= 24.9x - 22400
cash flow pr year (6,7)
= (50x -8.5x - 35000) * (1-0.4)
= 24.9x - 21000
NPV =0
-500000 + 24.9x - 22400 * [1-(1.15)^-5]/0.15 + 24.9x-21000 *{ [1-(1.15)^-7]/0.15 - [1-(1.15)^-5]/0.15 } =0
-500000 + 24.9x - 22400 * (3.352155098) + 24.9x-21000 *0.8082646358 =0
-500000 + 83.46866194 - 75088.2742 + 20.12578943 x - 16973.55735 =0
x = 6276 units ..ans
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