Problem

Currently we own 100 shares each of stocks 1 through 10. The original price we paid for th...

Currently we own 100 shares each of stocks 1 through 10. The original price we paid for these stocks, today’s price, and the expected price in one year for each stock is shown in Table 76.

We need money today and are going to sell some of our stocks. The tax rate on capital gains is 30%. If we sell 50 shares of stock 1, then we must pay tax of .3 • 50(30 – 20) − $150. We must also pay transaction costs of 1% on each transaction. Thus, our sale of 50 shares of stock 1 would incur transaction costs of .01 • 50 • 30 = $15. After taxes and transection costs, we must be left with $30.000 from our stock sales. Our goal is to maximize the expected (before-tax) value in one year of our remaining stock. What stocks should we sell? Assume it is all right to sell a fractional share of stock.

table 76

 

Price ($)

Stock

Share Owned

Purchase

Current

In One Year

1

100

20

30

36

2

100

25

34

39

3

100

30

43

42

4

100

35

47

45

5

100

40

49

51

6

100

45

53

55

7

100

50

60

63

8

100

55

62

64

9

100

60

64

66

10

100

65

66

70

Tax rate (%)

0.3

 

 

 

Transaction cost (%)

0.01

 

 

 

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