Financial Mathematics and Business Statistics - Assignment Example

Financial Mathematics and Business Statistics and of the Question 1 i. Calculation (a) The Economic Order Quantity Annual Demand=500,000 units Ordering Cost per order, S= 40 sterling pounds Average carrying cost per unit, H = 110 pence or 1.10 pounds sterling Optimal Order Quantity, Q= (2DS/H) ^1/2 Q= (2*500,000*40/1.1)^1/2 Q= 6,030.22 units (b) The number of orders Per Year The number of orders per year= D/Q 500,000/6,030 83 orders per year (c) The Reorder Period Reorder period= Q/D 6,030.22/500,000*300 4 days Assumption= the business runs 360 days per year ii. Calculating Sensitivity (7.5%) Annual Demand=500,000 units Annual demand = 537,500 Annual Demand=462,500 Ordering Cost per order, S= 40 sterling pounds Order Cost per Order= 43 Order Cost per Order=37 Average carrying cost per unit, H = 110 pence or 1.10 pounds sterling Average carrying cost per unit = 1.1825 Average carrying cost per unit= 1.0175 The Upward Change on the Factors Optimal Order Quantity, Q= (2DS/H) ^1/2 Optimal Order Quantity, Q= (2*537,500*43/1.1825)^1/2 6,252 Number of Orders per Year D/Q=575,000/6,252= 92 orders The Re-Order Period Q/D= 6,252/575,000*360 = 4 days The Downward Change Optimal Order Quantity, Q= (2DS/H) ^1/2 Q= (2*462,500*37/1.0175)^1/2 5,800 Number of Orders per Year D/Q= 462,500/5800= 80 orders iii. Recommendation as to the number of units it should include in each order With respect to the assumption that the company would operate 360 days in a year; the company would ensure that the carrying and shortages costs are minimized by ordering 6,030.2 for every order. However, the company is expected to make 83 orders in year in order to fulfill its dream of meeting a demand of 500,000 every year. As a result, the company can be able to meet the demand of 500,000 units while ensuring the carrying and shortages costs are maintained at minimum possible level by purchasing a new order of 6030 after every four days. Nevertheless, the results made on the assumption that the company runs its business on a period of 360 days every year. Although the following factors hold true as far as the company operations are concerned, it is notable that other aspects, such as the rise or drop of the Economic Order Quantity models’ constituents. In the case of a 7.5% increase or decline of these factors would lead to a significant change of the optimal quantity, the reorder period and number of orders per year. For instance, a rise of 7.5% of the carrying costs, ordering cost and carrying cost would to an increase of 6,252 with respect to the optimal quantity; this results in 92 orders and re-order period of 4 days. On the other hand, a decrease of 7.5% with respect to the carrying cost, ordering cost and demand would lead to an optimal quantity of 5,800; this results in 82 orders. With respect to the above situation, it is wise to take into consideration the possibility of fluctuations regarding the demand. This denotes that an increase in the level of demand is likely not to be satisfied by a current quantity of 6030 for every order. It is important to consider increasing the level of units for every order given the fact that the market it not constant with respect to the level of demand among the consumers. The increases in the carrying costs are likely to be low in relation to the costs of shortages as far as both low and high demands are concerned. Question 2 (a) The Monthly Payment The Value of Mortgage to be Acquired= 75%/100%*500,000 pounds =375,000 sterling pounds Total Payment by Avery Bradley After 20 Years = 104.39%/100%* 375,000 pounds 391,462.50 pounds The Period of Payment 20 Years The Payment per year= 391,426.50 pounds/20 years 19, 573.125 pound s The Monthly Payment 19,573.125/12 1,631.09 pounds sterling (b) The Effect on Avery’s Monthly Payment for Each Quarter Percentage Point Increase in the Bank of England up to 4 percentage points Current Rate= HBSC’s Lifetime Tracker Standard Mortgage Rate= 4.39% Period (20*12) = 240 months 1. A 0.25% Increase = (4.39+0.25) = 4.64% [375,000*104.64%/100%]/240 =1635.78 pounds per month 2. A 0.5% Increase [375,000*1.0489]/240 =1638.91 3. A 0.75 Increase 375,000*1.0514/240 1642.81 4. A 2% Increase [375,000*1.0639]/240 1662.34 5. A 3% Increase [375,000*1.0739]/240 1677.96 pounds per month 6. 4% Increase [375,000*1.0839]/240 1693.59 Determining the Point at Which Avery would be Unable to Make the Monthly Payment 1. 8% Increase [375,000*1.1239]/240 =1,756.09 pounds 2. 15% Increase [375,000*1.1939]/240 1865.46 Find R= the optimal rate Avery can afford 2600= [375000*(1+R)]/240 R+1 =2600/375,000*240 R=1.664-1 R=0.664 =66.4% Avery cannot afford a rate beyond 66.4% per month (c) The Shortest Period Avery Could Take to Pay the Mortgage Based on the Maximum Affordable Monthly Payment Total Payment = 375000 pounds*104.39%/100% = 391,462.50 pounds The Maximum Amount Avery Can Afford Every Month = 2,600 pounds sterling The Length of Period for a total payment = 391,462.5/2600= 140 months Question 3 2 (a) An increase of 250 sterling pounds on the premium model would lead to a decrease in the premium’s profitability and, consequently, the total firm’s profitability. (b) If the maximum available direct material is increased by 50,000 units, the firm is likely to experience an increased level of profit due to an increase in the level of units produced. AS a result of the margin profit, the profit is likely to increase due to increased number of products. (c) An increase in the labor costs may lead to decreased margin profit for every product if the same work would be done by the workers. However, if productivity increases, the company is likely to experience a level of profit. 3. An increase in the level of labor cost is likely to motivate employees to work hard; this may lead to more output in a short period. On the other hand, it the workers do not increase their productivity, high level of labor costs would reduce the profit margin. Question 4 Year Country A (000) Country B (000) 0 (Initial Investment) 2,100 2,100 1 300 800 2 550 800 3 1250 800 4 2300 1,700 The present value is one of the concepts that are used to evaluate the value of two or more projects during a certain period of their operations; the present value of the projects are calculated by taking into consideration their level of cash flows over a certain period. The future cash flows are normally discounted at the current discount rate. Typically, the cost of capital, which incorporates the cost of equity and debt, denotes the discount rate that a company can use to discount its cash flows, as well as the initial investment (Ehrhardt and Brigham, 2013). Cost of Capital, r= 11.25% Present Value PV = Cash flow/ [1+r] ˆn Where n= number of periods The Present Value of the Firm in the Case of an Investment in Country A PV (A) = 2,100/1.1125^0+300/ (1.1125)^1+550/1.1125^2+1250/1.1125^3+2300/1.1125^4 = 2,100 +269.66+444.39+907.84+1501.51 =£5,223.40 The Present Value of the Firm in the Case of an Investment in Country B PV (B) = 2,100^1.1125^0 + 800^1.1125^1+800^1.1125^2 +800^1.1125^3 +1,700^1.1125^4 2100+719.10+646.38+581.02+1109.81 =£5,156.31 In order to compare the two investments, it was necessary to compute the present values of investments in both countries; the results are reflected in a period of four years. According to the above table, an investment in country B is more beneficial than an investment in country A. This is attributable to the fact that an investment in country results in a present value of 5,156.31 sterling pounds in country B while that of country A leads to a present value of 5,223 sterling pound. In this respect, the investor should choose to invest in country B. Question 5 1 The profit of the company’s branches is associated with a high level of variance; the high level of variation of the branches’ is reflected by a high level of standard deviation (13.23). The high level of the standard deviation indicates that the company’s branches are likely to experience a similar level of profit during their operations. 2 The average number of the product lines of the branches is significantly different from 78; the 20 branches are associated with an average of 100.5 product lines. An average of 100.5 product lines among the 20 branches lead to difference of 22.5 average number of product lines with respect to the average of 78. 3 When the companies branches are divided into two groups; the branches that earn more than 15,000 sterling pounds and less than that value, an individual would realize a significant difference with respect to their profits. For instance, the average profit for branches with more than a 15,000 profit are characterized by an average income of 28,617 while the branches with an income of less than 15,000 are associated with an average income of 4,491. The two group of branches lead to a difference of 24,126; this difference substantial given the fact that branches which have an income of more than 15,000 sterling pounds stand at 6 while the branches which are characterized by an average profit of 15,000 sterling pounds and below are fourteen. 4 According to the regression model, the branches with a profit of more 15,000 sterling pounds are associated with a high variance of 123; the figure denotes the tendency of these firms to deviate significantly from the mean. On the other hand , the variance of branches with less than 15,000 sterling pounds profit were characterized by a relatively low level of variance- 20.5; the figure implies the tendency of these firms to experience profits that do not vary significantly from the mean. A P(T Read More