1. You have just won another secret lottery that will provide you ten payments of $10,000 with the first payment being made six months from today and subsequent payments occurring semi-annually. For your analysis, assume a stated annual interest rate of 8%. Please carefully show the work you undertake as you do the right thing to determine today's value of your lottery winnings. For your work there is no need to consider any tax or inflation implications. Simply evaluate the cash flow and provide me with a present value outcome.

2. What is the value today if you win a lottery that will pay you eight payments of $20,000 with the first payment beginning today and subsequent payments occurring annually that would increase by 2%. With an interest rate of 4%, what would be the value today of this eight payment lottery?

3. The Diamond Calculators for Finance (DCF) Company was one of the companies formed a number of years ago by Jeff "Spot" Diamond. The company, while not known by all MBA students, has discovered a profitable niche market by renting out HP12c calculators on a semester or year long basis to MBA students who do not want to incur the cost of buying the calculator as suggested by their unreasonable finance professors who most students assume own stock in HP. In the past, the DCF Company has suffered from cost inefficiencies in its inventory management system. As a result, "Spot" is considering the purchase of a $240,000 computer-based inventory management equipment system that utilizes some robotic components. If purchased, the equipment will be depreciated fully to zero via straight line depreciation over its 4 year life. At the end of its useful life, the company expects the equipment will be able to be sold for $20,000. Prior to consideration of tax impacts, the system will save the DCF Company $70,000 in on-going operating costs. This expected $70,000 in cost savings excludes any impact of the equipment depreciation expense on free cash flow. In addition to reducing operating costs, the new inventory management equipment system would allow DCF to carry less total inventory. This ability to carry less inventory would reduce the amount of net working capital by the amount of $50,000 throughout the life of the new inventory management equipment and this reduction would be immediate. Of course, at the end of the equipment's 4-year life, the amount of net working capital needed for the business would return to the same level that was necessary prior to the purchase and implementation of the inventory management system. ` Assuming an interest rate of 8% for evaluating this project and assuming the DCF Company is profitable and pays a 30% tax rate on profits and a 20% tax rate on capital gains, should "Spot" Diamond go ahead with the purchase? Please calculate the NPV of the computer-based inventory management equipment system and give me your recommendation regarding its purchase. Be sure to clearly illustrate your thinking and work.

4.- A bicycle manufacturer currently produces 300,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $2 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $250,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require additional working capital of $50,000 but argues that this sum can be ignored since it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $20,000. If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?

5.-You have found three investment choices for a one-year deposit: 10% APR compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.)

6.- In an MBA class that graduated a few years ago there was a student, Jeff "Spot" Diamond, who came up with a number of business ideas related to improving the life of his fellow classmates. One of the ideas Spot considered required him to buy a piece of equipment at an immediate cost of $3,750. The asset would have a two-year life and be responsible for generating a positive cash flow of $2,000 at the end of the first year and a positive cash flow of $3,000 at the end of the second year. For his analysis, Spot determined that the appropriate interest rate for evaluation of the purchase decision was 15%. For this problem right now let's make it a pure finance question without any concerns about any possibly confusing accounting issues. That is, let's assume the equipment has zero salvage value, zero disposal cost, and that Spot's company existed in a world without taxes. Don't worry, we will make our world more realistic in a bit by bringing in more accounting. a. Calculate the Internal Rate of Return (IRR) for this investment. Please show your finance and mathematical work in driving yourself to an answer. Calculating IRR by simply using your financial calculator or spreadsheet program is not sufficient. You are going to have to go back to your ability to do some math from your early years in school. Be sure to show that work. [0.50 points] b. Based upon your answer in a. above, indicate whether the piece of equipment should be purchased. Please be sure to explain your answer fully. To do that you should clearly explain in a couple of well-written sentences why buying or not buying this piece of equipment for $3,750 is a good decision to make relative to your calculated IRR.

7.- You are considering moving your money to new bank offering a one-year CD that pays an 8% APR with monthly compounding. Your current bank's manager offers to match the rate you have been offered. The account at your current bank would pay interest every six months. How much interest will you need to earn every six months to match the CD?