You are investing $6,500 immediately in a stock that you will keep for 10 years.

Question

You are investing $6,500 immediately in a stock that you will keep for 10 years. At the end of 10 years, the stock will be worth $14,433 with a probability of 0.56 and worth $17,322 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 7% with a probability of 0.80 or 15% with a probability of 0.20. Your MARR is 6% What is the variance and standard deviation of the net present worth from investing in the stock?

Explanation / Answer

The amount invested in stock = $6,500

Case# Probability Value

1 0.56 $14,433

2 0.44 $17,322

The expected return from stock is $14,433 with 0.56 probability and $17,322 with 0.44 probability is

E(R) = 14,433*0.56 + 17322*0.44 = 8082.48 + 7621.68 = 15703.96

Similarly, Expected Tax Rate = 0.80*0.07+ 0.20*0.15 = 0.086 = 8.6%

FV of initial investment of $6,500 after 10 years with 6% interest rate = 6,500*(1.06)^10 = 11,640.51

After Tax Return on Case #1

(14,433 - 11,640.51) = 2792.49*(1-0.086) = 2552.33 + 11,640.51 = 14192.84

After Tax Return on Case #2

(17,322 - 11,640.51) = 5681.49*(1-0.086) = 5192.88 + 11,640.51 = 16833.39

Case# Probability After Tax Return

1 0.56 14192.84

2 0.44 16833.39

Case# Probability      Difference Expected Net Worth       Squared

1 0.56 (14192.84 - 11,640.51) = 2552.33                     6514388.42

2 0.44 (16833.39- 11,640.51) = 5192.88                      26966002.69

Variance = 0.56*6514388.42+ 0.44*26966002.69= 15513098.7

Standard Deviation = Square Root of Variance = 3938.66

PV of SD = 3938.66/1.06^10 = 2199.32 - Discounted using 6% MARR for 10 years

Variance = Square of SD = 4837040.01

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