Financial Mathematics and Business Statistics - Assignment Example

Financial Mathematics and Business Statistics: work Question Decision making in businesses is constant problem that managersmust devise ways of handling. Decision-making may require complex approach; in fact, there are several approaches available for manager to use in devising appropriate judgement when addressing uncertainties that has probable likelihood. The problem requires ‘prior’ probability assessment (subjective probability) that forms the basis for further assessment like the construction of decision tree. In the case of Dreamcatcher, the first approach is to evaluate expected payoff from each of the project. Expected payoffs determine the amount each of the three scenarios (International expansion, domestic expansion, or no change) may give based on the probabilities. The scenario with the highest sum shows the best selection among the three. However, such an approach may not give a conclusive and decisive approach for consideration hence the need to construct reliability matrix based on the values obtain. Construction of the reliability matrix requires normalisation of the number so that probabilities add up to one. The reliability matrix helps in the construction of decision tree that makes recommendation and selection of the superior alternative possible. Construction of the Reliability matrix table Project / Scenario Pessimistic Values for Pessimistic   Average Values for Average   Optimistic Values for Optimistic SUM (expected payoffs) International Expansion 7,500 1875 13,800 7590 21,900 4380 13845 Domestic Expansion 8,600 2150 14,000 7700 19,500 3900 13750 No Change 11,000 2750 12,300 6765 16,700 3340 12855 Probability 25% 55% 20% Value for pessimistic (international expansion) = 0.25*7500 = 1875 (Domestic expansion) = 0.25*8600 = 2150 (No change) =0.25*11000 = 2750 Value for average (international expansion) = 0.55*13800 = 7590 (Domestic expansion) = 0.55*14000 = 7700 (No change) = 0.55*12300 = 6765 Value for Optimistic (international expansion) = 0.20*21900 = 4380 (Domestic expansion) = 0.20*19500 = 3900 (No change) = 0.20*16700 = 3340 Expected payoffs (Sum) = (Value for pessimistic + Value for average + Value for Optimistic) (International expansion) = 13845 (Domestic expansion) = 13750 (No change) = 12855 Project / Scenario Pessimistic Average Optimistic Expected Value International Expansion 7,500 13,800 21,900 13845 Domestic Expansion 8,600 14,000 19,500 13750 No Change 11,000 12,300 16,700 12855 Probability 25% 55% 20%   Maxima Regret Project/Scenario Pessimistic Average Optimistic International Expansion 7,500 13,800 21,900 Domestic Expansion 8,600 14,000 19,500 No Change 11,000 12,300 16,700 Project/Scenario Pessimistic Average Optimistic Maximum International Expansion 3,500 200 0 3,500 Domestic Expansion 1,100 0 2,400 2,400 No Change 0 200 5,200 5,200 Minimum 2,400 Normalisation of the values Normalisation of the values used for calculating the expected payoffs is important for making probabilities that sums up to 1 This was done by dividing the values gotten after multiplying individual probability by the value (e.g. international expansion for pessimistic value of 1875) was divided by the sum in that category (13845) to give 0.1354 as shown in the table below. All values followed a similar procedure The normalised values were used for the construction of the Reliability matrix table that helps in drawing the decision tree Construction of the Reliability matrix table Project / Scenario Pessimistic Average Optimistic International Expansion 0.135 0.548 0.316 Domestic Expansion 0.156 0.560 0.284 No Change 0.214 0.526 0.260 Figure 1: Decision tree model: showing the different options in the selection of the most appropriate project Discussion of the decision tree From the decision tree above, the average option for both international and domestic expansion gave higher values; however, the domestic average was slightly higher than that of the international expansion by (21450-21435 = 15). The difference is not significant. Besides, the pessimistic option for both domestic and international expansion were slightly different (15900-15720 = 180), again the domestic value was higher than the international expansion. The maximum difference was reported in the optimistic categories between the domestic and international expansions. The difference was 18225-17650, which gives 575. The twist is that international expansion was higher than the domestic expansion. Therefore, optimistic category is the only category that depicted significant difference between the international and domestic expansion. In fact, this category should form the basis for selecting the most appropriate model for implementation. Recommendation Selection of the international expansion based on optimistic variable because the difference between the two projects was quite significant as opposed to both average and pessimistic variables. Question 2 Linear equation method Let forming = x1 Machining = x2 Assembly = x3 Testing = x4 Maximise (Z) = 75x1 + 150x2 + 375X3 subject to 0.5x1 + 175x2 +0,25x3 +0.25x4 Read More

Offset mortgage helps in making the money work harder. It helps in reducing the mortgage balance that one is charged interest on, by doing so it reduces the mortgage terms or the payments made monthly for the mortgage. b. Identify the lowest rate the bank is currently charging for an Offset mortgage; and According to Barclays Bank (2015a), the initial interest rate charged is 1.79% (BBBR + 1.29%) variable for 2 years; followed by 3.99% (variable for the remaining period. The application fee for this product is 999.

One is only allowed to borrow 75% maximum of the value for the home, no early repayment charges. c. Identify the lowest rate, application fees (if applicable) and respective period the bank is charging for a fixed rate mortgage; According to Barclays Bank (2015b), the lowest initial fixed rate mortgage is at 1.55% fixed until 30th June 2017. The product is a two years fixed rate with the following interest rate at 3.99% variable for the remaining term, accompanied by 3.8% APR, 499, 85% is the maximum value of the home (minimum loan 5,000 and maximum loan 1M).

The product requires that the 3% of the balance be repaid until 30th June 2017. b) Calculate the amount you advise Adam and Eve to borrow and which size flat to buy, given their financial and professional situation; Application fee 999 Total Savings 45000 Assets 185000 Pending Mortgage 124000 Total value available 105001 Period (Years) 25 Amount compounded After 2 Years 108793.7 The Remaining amount for the 23 Years based on the rates 267553.1 376346.8 75% 100% (expected value of the house) Total amount borrowed for Mortgage 376346.8 501795.7 Based on the above analysis, the two couples can borrow a maximum of 376346.

80, which reflects 75% of the house value. It signifies that the house should not exceed 501795.70; therefore, the couple should select a 3-bedroom house whose value was £575,000 to maximise on the 75% mortgage available on the value of the house c) Using the two rate identified in a) calculate which is the best mortgage that Adam and Eve can take out (assume they take out the amount you recommended in b); Application 499 Total Savings 45000 Assets 185000 Pending Mortgage 124000 105501 Period Years 25 Amount After 1.

5 Years 107963.4 Remaining 23.5 Years 270756.3 378719.7 85% 100% Total Mortgage Available 376346.8 442760.9 The two products (offset mortgage and the fixed rate mortgage provided the same amount that the couples could borrow). However, the fixed rate mortgage reflects the amount as 85% of the house value as opposed to offset mortgage, which was 75%. Offset mortgage provides the. Therefore, the offset mortgage provided a better product for the couples. d) Whether that advice would change if interest rates went up or down by up to three percentage points.

The advice will shift the dynamics, for instance for the offset mortgage, an increase in percentage by 3 points will increase the amount the couples can borrow to 660210.90. The value is a 75% of the house valued at 880281.20. Therefore, an increase in percentage Question 4 a) Summarise the distribution of profits of the twenty branches and comment on the results? Summary of the profit distribution distribution of profits Profit (£000s) Mean 11.729 Standard Error 2.959079773 Median 6.8 Mode 0 Standard Deviation 13.

23340705 Sample Variance 175.1230621 Kurtosis 0.592914083 Skewness 1.236672727 Range 44.82 Minimum -2.69 Maximum 42.13 Sum 234.58 Count 20 Confidence Level (95.0%) 6.193425131 The standard deviation helps in assessing the variation between each value from the mean. The larger the standard the higher the spread-out between the sets of data analysed. The high standard deviation reported in the data summary signifies high degree of variability. The salaries are very diverse. Although the range is 44, which signifies the difference between the maximum and the minimum b) Is there evidence that the average number of lines stocked per store is significantly different from 78?

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