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The purpose of this report is to calculate and discuss several financial mathematics aspects. The aspects to be analyzed include; investment appraisal, Economic Order Quantity, simple linear regression, interest rates and linear programming. These concepts are vital as they inform decision making such as which project to invest in, how many quantities to reorder, the correlation between variables and which products to produce.

Bank of England Case Study

The acquisition value of the house is £ 487,500. According to the current conditions, Jeff's monthly mortgage payment will be £ 1689. However, if the Bank of England increases its interest rate by a percentage point in each quarter, the mortgage will become more expensive and Jeff will have to make higher monthly repayments. Therefore, if the mortgage rate increases to 10.65%, he will no longer be able to make repayment as the monthly payments will increase to £ 4327. The period relates to the second quarter of 2017.

The maximum monthly repayment he can afford is £ 3200. Jeff can be able to shorten the repayment period if he pays the maximum monthly amounts he can afford in the prevailing market conditions (Meeker and Escobar 180). The value of the house is £ 650,000. However, the acquisition rate is 75% of the house. As such, Jeff can be able to clear the mortgage in12 years and 8 months which is almost half the mortgage period. The £ 3200 is double what he is paying in the current case.

Linear Programming

The decision variables in the equation are the demand for individual products (Dantzig 89). The constraints are the number of hours in the forming, machining, assembly and testing. The objective is to maximize profit which is the difference between sales and cost. Sales is the product of demand and the selling price (Schabenberger and Gotway 19). The cost is the product of cost per hour, number of hours on each process and the demand.

The maximum profit that the company would earn of its opened it product lines is £ 138,872. According to the output, the firm will only sell premium and the demand will be 1347 units. The total sales will be £ 336,538 and the total cost will be £ 197,716. The firm should use 4038 forming hours, 17,500 machining hours, 4712 assembly hours and 3366 testing hours due to the time constraint.

If the demand of the premium product changes to 1000, the output will be as follows. According to the output, the firm will only sell premium and the demand will be 1347 units. The total sales will be £ 336,538 and the total cost will be £ 197,716. The firm should use 4038 forming hours, 17,500 machining hours, 4712 assembly hours and 3366 testing hours due to the time constraint.

If the machining hours are increased to 20000, the output will be as follows. According to the output, the firm will only sell premium and the demand will be 1500 units. The profit will be £ 154,688. The total sales will be £ 375,000 and the total cost will be £ 220,312. The firm should use 4500 forming hours, 19,500 machining hours, 5250 assembly hours and 3750 testing hours due to the time constraint. As such, increasing the machining hours increases the profit by £ 15,865. Therefore, for the entity to maximize profits, it should only sell the premium products because it has a high-profit margin. The machine hours should be increased to 20000 to enhance profit maximization.

Regression Analysis

According to the output, the F critical is 3.6 and the F statistics is 3.1 Therefore, we accept the null hypothesis that there is no significant difference between the two subjects. The correlation coefficient is measured by R squared (Chatterjee and Hadi 189). It shows the extent to which the dependent variable is explained by the independent variable. According to the output, 43.34% of the exam results in QM can be explained by the study hours. However, 56.7% of the results can be explained by other factors outside the model such as the attitude of the student towards the exam.

The output on acting shows that 60.5% of the exam results can be attributed to study hours. However, 39.5% of the results can be attributed to other factors outside the model. Therefore, study hours have a higher impact on the acting subject. The results are significant. The coefficient of determination for QM is 0.65 while that of the studying hours is 0.77. As such, the values are close to 1 which measures the goodness of fit.

The output below relates to QM students who studied for more than 20 hours. However, the p-value and t-statistics are not yielded. Therefore, we can conclude that the regression model is still poor. The intercept is zero. However, I don’t believe that the same results would be replicated when data for students that actually sat the exam is collected because the correlation in the current model is spurious (Draper and Smith 176). However, real and verifiable data will yield a better regression model and output.

Table 2. QM students who studied more than 20 hours. Adopted From Excel

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0

#N/A

#N/A

#N/A

#N/A

#N/A

#N/A

#N/A

49

1.35982

0.288471

4.713891

0.000332

0.741111

1.978528

0.741111

1.978528

Investment Appraisal

Investment appraisal involves using a range of methods in analyzing and determining the viability and profitability of investment projects (Baum and Crosby 118). The methods applied in this report are the Net Present Value and Internal Rate of Return. Net present value (NPV) is the total of the discounted cash inflows and outflows. The discount rate used is 11.25%, which is the cost of capital. If the net present value is positive, the project is acceptable. However, if it is negative, the investment is rejected. The internal rate of return is the discount rate when the net present value is zero. If the Internal rate of return is higher than the cost of funds, the investment is acceptable and vice versa.

According to the net present value, country A yields a positive NPV of £ 919.91. The project in country B yields a positive NPV of £ 859.61. As such, the NPV in both projects is positive. Therefore, the project in country A should be implemented because it has a higher net present value (Gotze and Schuster 256). According to the internal rate of return, country A yields 26% and country B 29%. The return on both projects is higher than the cost of funds. Therefore, the project in country B should be accepted and implemented because it has a higher internal rate of return. Allen PLC should change the investment if there is a change in the cost of funds in the near future. For instance, if the cost of capital increases to 17%, the net present value of country A will be £ 483.80 and country B will be £ 491.34. Therefore, the project should be implemented in country B in the event of an increase in the cost of funds.

Economic Order Quantity

The Economic Order Quantity (EOQ) is the reorder quantity that minimized both the carrying and procurement costs (Ott and Longnecker 200). At EOQ, the holding cost is equal to the ordering cost. It assumes that the annual demand, carrying cost, procurement cost and reorder period is known and constant. It ensures that the reorder is optimal and reduces the overall inventory costs.

Calculation using the provided figures yields and EOQ of 4264 units. If the annual demand increases by 7.5%, EOQ increases to 4421 units. If the ordering cost increases by 7.5%, EOQ is 4421 units. If the holding cost increases by 7.5%, EOQ is 4113 units. However, if all the factors increase by 7.5%, the EOQ is 4421 units. If the annual demand decreases by 7.5%, EOQ is 4101 units. If the ordering cost decreases by 7.5%, EOQ is 4101 units. If the holding cost decreases by 7.5%, EOQ is 4264 units. However, if all the factors decrease by 7.5%, the EOQ is 4101units. Therefore, the EOQ remains constant when the annual demand, ordering costs, and all factors change by the same margin.

The firm should reorder 4264 units when the annual demand is 250,000. If the demand increases by 7.5% the firm should reorder 4421 units. Ultimately, when the demand drops by 7.5%, the entity should reorder 4101 units which will lower both the holding and ordering costs.

Works Cited

Baum, Andrew E., and Neil Crosby. Property investment appraisal. John Wiley & Sons, 2014.

Chatterjee, Samprit, and Ali S. Hadi. Regression analysis by example. John Wiley & Sons, 2015.

Dantzig, George. Linear programming and extensions. Princeton university press, 2016.

Draper, Norman R., and Harry Smith. Applied regression analysis. Vol. 326. John Wiley & Sons, 2014.

Gotze, Uwe, Deryl Northcott, and Peter Schuster. INVESTMENT APPRAISAL. SPRINGER-VERLAG BERLIN AN, 2016.

Meeker, William Q., and Luis A. Escobar. Statistical methods for reliability data. John Wiley & Sons, 2014.

Ott, R. Lyman, and Micheal T. Longnecker. An introduction to statistical methods and data analysis. Nelson Education, 2015.

Schabenberger, Oliver, and Carol A. Gotway. Statistical methods for spatial data analysis. CRC Press, 2017.

September 25, 2023

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