Question 2 (Linear Programming) - . The government of Ghana has available GH¢1 billion earmarked for financing the Free SHS next year. Instead of letting this money sit in a bank account for a paltry 6% risk free interest rate, it has decided to invest half of the money in four stocks on the Ghana Stock Exchange (GSE). The four stock options the government is considering and the relevant financial data are as follows: Stock A В C D Price Per Share (in GH¢) 100 50 80 40 Annual Return (in GH¢) 18 6. 8. 8. Possible Loss Per Share (in GH¢) 10 6. 6. However, the annual return is only a forecast (provided by experts at the ministry of finance), and could be worse or better - a risk that the government has been advised to be worry of in order not to jeopardize the finances of the Free SHS program. For example, though a share of stock A could yield a return amount of GH¢18, it is also likely it could lead to a loss of GH¢10. In order to minimize the risk (i.e. losses) associated with investing on the GSE, the Finance Ministry has advised the government to adhere to the following guidelines: (1) The total forecasted annual return for the four stocks must be at least 9% of the total amount invested to justify the investment. Also, total possible losses must not exceed 8% of the total amount invested. (2) The amount invested in stock A and Stock C must not exceed GH¢200 million since when one performs better (worse) the other also performs better (worse). Likewise, the amount invested in Stock B and D must not exceed GH¢350 million for the same reason as that of Stock A and C. (3) Although Stock A carries a risk of a loss of GH¢10, the government is willing to buy at least 500,000 shares given the high return of GH¢18 per share. a. Formulate a linear program to determine the number of shares of each stock the government should buy in order to minimize the risk involve. Note that the government is not obliged to spend all the money intended for investment.
Question 2 (Linear Programming) - . The government of Ghana has available GH¢1 billion earmarked for financing the Free SHS next year. Instead of letting this money sit in a bank account for a paltry 6% risk free interest rate, it has decided to invest half of the money in four stocks on the Ghana Stock Exchange (GSE). The four stock options the government is considering and the relevant financial data are as follows: Stock A В C D Price Per Share (in GH¢) 100 50 80 40 Annual Return (in GH¢) 18 6. 8. 8. Possible Loss Per Share (in GH¢) 10 6. 6. However, the annual return is only a forecast (provided by experts at the ministry of finance), and could be worse or better - a risk that the government has been advised to be worry of in order not to jeopardize the finances of the Free SHS program. For example, though a share of stock A could yield a return amount of GH¢18, it is also likely it could lead to a loss of GH¢10. In order to minimize the risk (i.e. losses) associated with investing on the GSE, the Finance Ministry has advised the government to adhere to the following guidelines: (1) The total forecasted annual return for the four stocks must be at least 9% of the total amount invested to justify the investment. Also, total possible losses must not exceed 8% of the total amount invested. (2) The amount invested in stock A and Stock C must not exceed GH¢200 million since when one performs better (worse) the other also performs better (worse). Likewise, the amount invested in Stock B and D must not exceed GH¢350 million for the same reason as that of Stock A and C. (3) Although Stock A carries a risk of a loss of GH¢10, the government is willing to buy at least 500,000 shares given the high return of GH¢18 per share. a. Formulate a linear program to determine the number of shares of each stock the government should buy in order to minimize the risk involve. Note that the government is not obliged to spend all the money intended for investment.
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Transcribed Image Text:Question 2 (Linear Programming) -:
The government of Ghana has available GH¢1 billion earmarked for financing the Free SHS next
year. Instead of letting this money sit in a bank account for a paltry 6% risk free interest rate, it has
decided to invest half of the money in four stocks on the Ghana Stock Exchange (GSE). The four
stock options the government is considering and the relevant financial data are as follows:
Stock
A
В
C
D
Price Per Share (in GH¢)
100
50
80
40
Annual Return (in GH¢)
18
6.
8
8.
Possible Loss Per Share (in GH¢)
10
6.
6.
5
However, the annual return is only a forecast (provided by experts at the ministry of finance), and
could be worse or better – a risk that the government has been advised to be worry of in order not to
jeopardize the finances of the Free SHS program. For example, though a share of stock A could yield
a return amount of GH¢18, it is also likely it could lead to a loss of GH¢10.
In order to minimize the risk (i.e. losses) associated with investing on the GSE, the Finance Ministry
has advised the government to adhere to the following guidelines:
(1) The total forecasted annual return for the four stocks must be at least 9% of the total amount
invested to justify the investment. Also, total possible losses must not exceed 8% of the total
amount invested.
(2) The amount invested in stock A and Stock C must not exceed GH¢200 million since when one
performs better (worse) the other also performs better (worse). Likewise, the amount invested in
Stock B and D must not exceed GH¢350 million for the same reason as that of Stock A and C.
(3) Although Stock A carries a risk of a loss of GH¢10, the government is willing to buy at least
500,000 shares given the high return of GH¢18 per share.
a. Formulate a linear program to determine the number of shares of each stock the government
should buy in order to minimize the risk involve. Note that the government is not obliged to spend
all the money intended for investment.
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