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4) a) You decide that your family would be comfortable living on an annual income of $150,000, growing at 4% per year. Youd also like to continue generating this cash flow for your descendants, forever. With interest rates of 8%, how much wealth would you need today to provide this income starting with S150,000 one year from now? b) Suppose all income is taxed at 20%. How would this (if at all) change your answer to a)? Assume that you still feel 4% growth and $150,000 (after-tax) income is sufficient. Show a calculation and briefly explain.

Please Refrain from using Excel Thanks!

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Answer #1
4)
a) It is a growing perpetuity. The PV (wealth needed today) of the growing perpetuity is given by
PV = CF/(r-g), where CF = Cash flow = interest rate, g = growth rate in CF
= 150000/(0.08-0.04) = $ 37,50,000
b) Interest rate after tax = 8%*(1-20%) = 6.4%
PV (wealth needed today) 150000/(0.064-0.04) = $ 62,50,000
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