Q1 Mickey Lawson
To address this issue, we need to compute the expected profit for each investment alternative option based on the stated probabilities for the economic circumstances, then evaluate the opportunity loss for each alternative, and lastly figure out which selection minimizes the predicted opportunity loss.
Solution a
To maximize expected profits, we compute the expected value (EV) for each choice alternative:
Formula
Expected Value (EV)= (Probability of Good Economy X Profit of Good Economy) + (Probability of Bad Economy X Profit of Bad Economy)
Stock Market:
EV = (0.5 X 80,000) + (0.5 X -20,000)
EV = 40,000 – 10,000
EV = 30,000
Bonds:
EV = (0.5 X 30,000) + (0.5 X 20,000)
EV = 15,000 + 10,000
EV = 25,000
CDS:
EV = (0.5 X 23,000) + (0.5 X 23,000)
EV = 11,500 + 11,500
EV = 23,000
Decision Alternative | Profit-Good Economy | Probability- Good Economy | Expected Value- Good Economy | Profit- Bad Economy | Probability- Bad Economy | Expected Value- Bad Economy | Expected Monetary Value- Each Investment Decision |
| a | b | c=aXb | d | e | f=dXe | g=c+f |
Stocks | 80,000 | 0.5 | 40,000 | (20,000) | 0.5 | (10,000) | 30,000 |
Bonds | 30,000 | 0.5 | 15,000 | 20,000 | 0.5 | 10,000 | 25,000 |
CDS | 23,000 | 0.5 | 11,500 | 23,000 | 0.5 | 11,500 | 23,000 |
Investing in the stock market, with an anticipated profit of 30,000, is the choice that would result in the highest possible projected gains.
Solution b
Finding the maximum profit for each economic condition is the first step in developing an opportunity loss table, from which the opportunity loss for each investment possibility may be determined.
So
Profit Maximized in Good Economy = 80,000 i.e Stocks
Profit Maximized in Bad Economy = 23,000 i.e CDS
Opportunity loss for each alternative is calculated as the difference between the maximum profit for that state of the economy and the profit realized by the alternative.
So
Stock Market:
Good Economy: 80,000 – 80,000 = 0
Poor Economy: 23,000 – (-20,000) = 43,000
Stock | Maximum profit-state economy | Maximum Profit from Alternative | |
Good Economy | 80,000 | 80,000 | – |
Bad Economy | 23,000 | (20,000) | 43,000 |
Bonds:
Good Economy: 80,000 – 30,000 = 50,000
Poor Economy: 23,000 – 20,000 = 3,000
Bonds | Maximum profit-state economy | Maximum Profit from Alternative | |
Good Economy | 80,000 | 30,000 | 50,000 |
Bad Economy | 23,000 | 20,000 | 3,000 |
CDS:
Good Economy: 80,000 – 23,000 = 57,000
Poor Economy: 23,000 – 23,000 = 0
CDS | Maximum profit-state economy | Maximum Profit from Alternative | |
Good Economy | 80,000 | 23,000 | 57,000 |
Bad Economy | 23,000 | 23,000 | – |
To minimize the expected opportunity loss, we calculate the expected opportunity loss (EOL) for each decision alternative:
Stock Market:
EOL = (0.5 X 0) + (0.5 X 43,000)
EOL = 0 + 21,500
EOL = 21,500
Bonds:
EOL = (0.5 X 50,000) + (0.5 X 3,000)
EOL = 25,000 + 1,500
EOL = 26,500
CDS:
EOL = (0.5 X 57,000) + (0.5 X 0)
EOL = 28,500 + 0
EOL = 28,500
Expected opportunity loss (EOL) for each decision alternative: | |||||||
Decision Alternative | Good Economy | Probability | EOL | Bad Economy | Probability | EOL | Total EOL |
Stock | – | 0.50 | – | 43,000 | 0.50 | 21,500 | 21,500 |
Bonds | 50,000 | 0.50 | 25,000 | 3,000 | 0.50 | 1,500 | 26,500 |
CDS | 57,000 | 0.50 | 28,500 | – | 0.50 | – | 28,500 |
The decision that would minimize the expected opportunity loss is investing in the Stock Market, with an EOL of 21,500.
Q2 A Company considering the purchase
Solution
- a) Payoff Matrix:
The payoff matrix for the three alternatives under the two market conditions
Payoff Matrix | ||
Decision alternative | Favourable Market | Unfavourable Market |
M1-Large Robots | 50,000 | (40,000) |
M2-Small Robots | 30,000 | (20,000) |
Do Nothing | – | – |
- b) Decision Tree Calculations:
To calculate the Expected Monetary Value for each alternative, we multiply the profit or loss by the probability of each market condition and sum the results.
Expected Monetary Value = (Probability of Favourable Market X Profit in Favourable Market) + (Probability of Unfavourable Market X Loss in Unfavourable Market)
M1- Large Rebots
Expected Monetary Value = (0.6 X $50,000) + (0.4 X -$40,000)
Expected Monetary Value = $30,000 – $16,000
Expected Monetary Value = $14,000
M2- Small Robots
Expected Monetary Value = (0.6 X $30,000) + (0.4 X -$20,000)
Expected Monetary Value = $18,000 – $8,000
Expected Monetary Value = $10,000
Do things
Expected Monetary Value = (0.6 X $0) + (0.4 X $0)
Expected Monetary Value = $0
Decision alternative | Favourable Market | Probability of Favourable Market | Expected Return | Unfavourable Market | Probability of Unfavourable Market | Expected Return | Expected Monetary Value |
M1-Large Robots | 50,000 | 0.6 | 30,000 | (40,000) | 0.4 | (16,000) | 14,000 |
M2-Small Robots | 30,000 | 0.6 | 18,000 | (20,000) | 0.4 | (8,000) | 10,000 |
Do Nothing | – | 0.6 | – | – | 0.4 | – | – |
Decision
The expected return on the decision to purchase M1 is the EMV we calculated, which is $14,000. This is the average profit expected from the decision to purchase M1, considering the probabilities of the market being favourable or unfavourable.
