Question 1: You wish to start a project. Your initial investment is $100000. You generate 0 cash flows for the first 2 years but generate $16000 in year 3 and increase by 15% every year till year 7, after which time they decline by 2% until year 9. You expect 0 growth in cash flows beyond year 9, but expect to generate constant cash flows into the foreseeable future. If capital cost is 8% per year, find the NPV
ANSWER: Net Present Value=$168609.42

Question 2: You want to buy new machine and replace the existing machine, which you have used for the past 3 years. New machine costs $75000 and will be useful for 5 years after which can be sold to fetch salvage value of $9000. New machine will be depreciated straight-line to 0 over 5 years. Old machine was bought for $70000 and also depreciates straight-line to 0 over 5 years. Old machine can be sold today for $30000 but if you wait for 5 years, it will only worth $6500.
New machine is efficient. Annual savings in operating costs are $12000. Your net working capital requirement will decline annually by $4000. Tax rate is 35% and capital cost rate is 12%. Find the NPV
ANSWER: Net Present Value(replacing)=$9598.75

Please show me detailed step-by-step solutions. Thanks.

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  1. An excel spreadsheet is very handy for these types of analyses. I'll do the first one, which should give you a process for working the second.

    First calculate the net present value for the cash flows for years 0 to 10.
    0 = -100000/(1.08^0) = -100000
    1 = 0
    2 = 0
    3 = 16000/(1.08^3) =
    4 = (16000*1.15)/(1.08^4)
    9 = 26875.93/(1.08^9)
    10 = 26875.93/(1.08^10)

    Now then year 10's PV flows forever, but declining by 8% per year. With this infinite expansion, the multiplier is simply 1/.08 = 12.5

    So, years 11 and beyond = (PV in year 10)*12.5

    Sum the PV's for years 0 to 11+ and you should get 168609.42

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