Fundamentals of Algorithms : mathematical induction sample

May 12th, 2015
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1. Prove by mathematical induction that the sum of the first N natural numbers is N* (N+ 1)/2. Base case, n = 1 1* (1 + 1) / 2 = 1 Inductive hypothesis, n = k

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Capital Budgeting ScenarioCapital Budgeting ScenarioProposal A: New FactoryA company wants to build a new factory for increased capacity. Using the net present value (NPV) method of capital budgeting, determine the proposals appropriateness and economic viability with the following information:Building a new factory will increase capacity by 30%.The current capacity is \$10 million of sales with a 5% profit margin. The factory costs \$10 million to build.The new capacity will meet the companys needs for 10 years. The factory is worth \$14 million over 10 years.On the current proposal for building the new factory below will explain the analysis needed for the projection of the incremental cash flows that will be used for the NPV analysis. Building of a new factory will increase the capacity by 30% which is 3 million a year. With the estimate of profit margin

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