Question

"You are investing $X immediately in a stock that you will keep for 15 years. At the end of 15 years, the stock will be worth $19,147 with a probability of 0.56 and worth $22,193 with a probability of 0.44. 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 10% with a probability of 0.83 or 20% with a probability of 0.17. Your MARR is 4.6%. You will only invest in the stock if your expected net present worth is larger than 0. Find the largest possible value of X."

Answer 1

Let the value of X be A.

Purchase price of X immediately = A

Value of stock at the end of 15th year = $19147*0.56 + 22193*0.44 = 10722.32 + 9764.92 = $20487.24

Effective tax rate after 15 years on profit earned on sale of shares = 10%*0.83 + 20%*0.17 = 8.3% + 3.4% = 11.7%

Tax amount to be paid on sale of shares = ($20487.24 - A)*11.7% = $2397 - 0.117 A

Net amount received on sale of shares after 15 years = $20487.24 - ($2397 - 0.117 A) = $20487.24 - $2397 + 0.117A = $18090.24 + 0.117A

Value of shares at the end of 15 years to earn 4.6% MARR = A*(1.046)^15 = 1.9632 A

So,

1.9632 A = $18090.24 + 0.117 A

1.9632 A - 0.117 A = $18090.24

1.8462 A = $18090.24

A = $18090.24/1.8462 = $9798.635 i.e. $9800 (approximately)

Largest possible value of X is $9800