Quantitative Methods for Business: Euromotors Limited - Case Study Example

CASE STUDY: EUROMOTORS LIMITED Name: Tutor: Course: Date: Executive summary Clyde EXR car dealership is a prospective business venture that Euromotors wishes to undertake. This will be an addition to the car dealership of other niche motor vehicles such as the Trionfo P13 sports car that Euromotors deals with. However, to determine whether the Clyde EXR car dealership will be profitable, appropriate break even analysis and other essential benefit-cost analysis would be essential. The break even analysis showed that for Euromotors to break even, they would need to sell at least fourteen Clyde EXRs every month. The annuities evaluation and net present value analysis also showed that a cash offer of $39,200 for the Trionfo P13 would be profitable since the value was greater than the net present value compounded monthly at 4.5% interest rate. Furthermore, the linear programming used to determine optimum inputs for the servicing department established that three major services, two minor services and ten tyre replacement would maximize profits generated from the servicing department. Introduction Benefit-cost analysis of prospective business deals of a business organization are of great importance because they help evaluate and determine the impact of the prospective business engagements on the profitability of the organization. Euromotors wishes to evaluate a prospective car dealership for the sale of Clyde EXR. The evaluation of the annuities and the net present value of car dealership of the fleet of cars it currently sells will also be established. This includes the establishment of optimum inputs and resources in the servicing department that is required to maximize profits. Break even analysis The retail selling price of products is usually inclusive of the 10% GST amount. The retail price at which Euromotors plan to sell the Clyde EXR is $28,499. However, this figure includes the 10% GST amount of $2,590.80. Therefore, the retail price of the Clyde EXR exclusive of the 10% GST amount is $25,908.20. The total variable cost exclusive of the 10% GST is $23,918.20. This total variable cost includes the cost that Euromotors will pay to Clyde International for the Clyde EXR and the checking cost of the Clyde EXR upon delivery. Therefore, the contribution margin for the Clyde EXR is $1,990. The salary of the sales person to be hired is $9,500 per month, while two mechanics to handle the servicing of the Clyde EXR are each going to be paid a salary of $7,000 per month. The cost of stocking the Clyde EXR spare parts is estimated at $3,000 per month and the cost of maintaining the servicing skills of the two mechanics is approximated to be $300 per month. Therefore, the total fixed cost for the dealership of the Clyde EXR is estimated to be $26,800 per month. Consequently, using the total fixed cost and contribution margin the break even quantity can be established. Therefore, to break even, Euromotors would need to sell at least fourteen Clyde EXRs per month. This implies that sales of only twelve Clyde EXRs per month as expected by Euromotors would result in a net loss of $2,920 per month. Annuities and Net Present Value (NPV) The retail selling price of Trionfo P13 sports car at Euromotors is $39,999. However, for installment payment of the car, the allowable deposit for is $3,999 and the balance of $36,000 is to be paid over a period of three years using monthly installments at 3% per annum interest rate compounded monthly. This implies that at the given interest rate, the monthly installment which is payable to Euromotors for the Trionfo P13 sports car is $1,046.90. However, if the balance for the Trionfo P13 sports car of $36,000 is to be paid on an interest free basis, over the three year period, the customer would be required to pay a monthly installment of $1,000 to completely pay the amount required. Therefore, the monthly installment with a 3% per annum interest rate compounded monthly is higher than the monthly installment on an interest free basis. The present value of the monthly repayments received by Euromotors, at the cost of capital of 4.5% per annum compounded monthly, over a period of three years, is $35,193. 60. This is the present value only for the $1,046.90 monthly repayments not inclusive of the initial deposit. Therefore, the total present value of all the payments received by Euromotors inclusive of the initial deposit is $39,192.60. This implies that if a customer offers a cash price of $39,200, Euromotors should accept the offer for the Trionfo P13. This is because the cash offer for the Trionfo P13 sports car is more than the total present value of the car. Gloria Jones is a prospective customer at Euromotors who is willing to buy the Trionfo P13. However, she wants to pay $1,000 upfront as deposit, while she hopes to pay the balance using irregular monthly payments for a period of six months. Therefore, at the end of the six months, Gloria will have paid a total of $40,000 using her proposed plan. However, at the 4.5% per annum cost of capital compounded monthly, the net present value of Gloria’s payments is $39,428.60. This implies that Gloria Jones is offering too much for the Trionfo P13, because her proposed offer is higher than the net present value. Linear programming To maximize profits generated from the service department the number of major services, minor services and tyre replacement that would optimize the profits have to be established. The three decision variables that Euromotors need to consider when balancing the extra capacity available in the servicing department include the major servicing, minor servicing and tyre replacement. A major service generates a profit of $50, while a minor service generates a profit margin of $10. On the other hand, replacing a pair of tyre generates a profit of $20. In addition, the major service, minor service and tyre replacement each require four hours, one hour and one hour of bay time respectively, while six hours, one hour and one hour of mechanic time is needed for the major service, minor service and tyre replacement respectively. However, there are constraints which have to be considered when determining the number of major services, minor services and tyre replacements that would maximize the profits. These include the available bay hours, mechanic hours and storage capacity. The amount of bay time available per day amounts to 24 hours, while the available of mechanic hours is 30 hours. The storage capacity available per day can accommodate only 10 pairs of tyres. Consequently, to maximize the profits generated from the additional services using the constraint resources, Euromotors would need to provide three major services, two minor services and ten tyre replacements where each tyre replacement involves a pair of tyres. Using these optimum inputs derived from the linear programming, the optimum profit generated from the service department from major services, minor services and tyre replacement is $370. The sensitivity analysis indicates that the Lagrange multiplier corresponding to tyre replacement is 10. This means that one extra pair of tyre replacement per day would generate an additional profit of $10. Therefore, if the storage capacity is increased to accommodate five extra pair of tyres the profits generated from the servicing department would increase by $50. However, if the profit margin generated from a minor service changes to $16, the total profits generated would increase to $424. However, with this new profit for the minor service, the optimum number of tyre replacement required to maximize profits remains unchanged at 10 pairs, while no major service would need to be done so as to maximize the profits generated from the servicing department. List of Appendices Appendix 1: Break even analysis Appendix 2: Annuities and NPV Appendix 3: Linear programming a) The decision variables for the linear model include; X1 = Major Service X2 = Minor Service X3 = Tyre replacement b) Objective function Profits = 50 X1 + 10 X2 + 20 X3 c) The constraints for the decision model include; 4X1 + X2 + X3 ≤ 24 6X1 + X2 + X3 ≤ 30 X3 ≤ 10 d) The answer report; The sensitivity report e) The optimum available resources that would maximize the profits include; X1 = 3 major services X2 = 2 minor services X3 = 10 tyre replacements f) When the profit generated from a minor service is increased to $16, the answer report for the optimum solutions is as indicated in the answer report below; Read More