You are investing $X immediately in a stock that you will keep for 12 years. At

Question

You are investing $X immediately in a stock that you will keep for 12 years. At the end of 12 years, the stock will be worth $13,947 with a probability of 0.43 and worth $17,350 with a probability of 0.57. When you sell the stock, you will need to pay taxes on the profit earned from selling the stock (i.e., taxes on the difference between the selling and buying prices of the stock). The tax rate will be 7% with a probability of 0.95 or 14% with a probability of 0.05. Your MARR is 5.2%. You will only invest in the stock if your expected net present worth is larger than 0. Find the largest possible value of X.

Explanation / Answer

Expected stock price at the end of 12 years=13947*0.43+17350*0.57=15886.71

Expected tax rate=7%*0.95+14%*0.05=7.35%

Final amount after tax=15886.71-(15886.71-X)*7.35%=14719.04+0.0735X

So, NPV=-X+(14719.04+0.0735X)/1.052^12

NPV must be greater than 0

=>-X+(14719.04+0.0735X)/1.052^12>0

=>X*(1.052^12-0.0735)<14719.04

=>X<14719.04/(1.052^12-0.0735)

=>X<8344.897

So, largest possible value of X is $8344

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