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Welcome. Use of mathematical tools in business. Prepared for. Farzana Lalarukh Assistant professor, Department of Finance Faculty of Business Studies University of Dhaka. We are. Agenda. Measuring GDP in the product approach using matrix.

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  1. Welcome Use of mathematical tools in business

  2. Prepared for Farzana Lalarukh Assistant professor, Department of Finance Faculty of Business Studies University of Dhaka

  3. We are

  4. Agenda

  5. Measuring GDP in the product approach using matrix • GDP is the market value of all final goods and services made within the borders of a country in a year. GDP can be determined in three ways, • the product (or output) approach, • the income approach, and • The expenditure approach.

  6. Assumptions • There are only two firms in Bangladesh • A firm consists of three lands • Paddy and wheat are produced by two firms

  7. Production in each land Firm-1 Firm-2

  8. Measuring procedure • Total production from all firms is calculated • GDP=Total production Market Price

  9. Summation Total Production

  10. So the GDP is 40+60+64=164 taka

  11. Case Analysis Using Inverse Matrix To produce PRAN MANGO JUICE it is necessary to use 8 units of vitamin A, 14 units of vitamin B, and 13 units of vitamin C. One tube of mixture P contains 1 unit of A, 2 units of B and 3 units of C. One tube of mixture Q contains 2 units of A, 3 units of B, and 2 units of C. One tube of mixture R contains one unit of A, 2 units of B, and 2 units of C. How many tubes of each type of mixture should be used to produce the juice?

  12. Tabulate the data as follows

  13. Let x tubes of P, y tubes of Q and Z tubes of R be used to produce the juice. Then x+2y+z=8 2x+3y+2z=14 3x+2y+2z=13

  14. Writing the equations in the matrix form

  15. We can solve the problem by the inverse of a matrix Let A = Here the determinant of A │A│ = = 2=4-5 = 1

  16. M = = Here the minor matrix,

  17. Here Adjoint Matrix, A = A-1 = .AdjA =

  18. Putting the value in the equation × = = =

  19. Hence 1 tube of mixture P, 2 tubes of mixture Q, 3 tubes of mixture R , should be used to produce the juice.

  20. Hence 1 tube of mixture P, 2 tubes of mixture Q, 3 tubes of mixture R , should be used to produce the juice.

  21. What is Cost Function Cost function is a mathematical system relating a firms total cost to its output. TOTAL COST= (VARIAVLE COST x OUTPUT) (+) FIXED COST It is also a relationship between activity and its cost.

  22. Who use it Manufacturer company, Service company such as gas, electricity, Oil company, Many other small organizations.

  23. Case analysis General Electronics Company(GEC) charges its customers according to their usage of electricity and follows a fixed cost of 3.35 taka and 3.380 paisa per unit for the first 350 unit,5.634 paisa per unit in excess of 350. The requirements are finding out cost function, graph, total and average cost of using 200 units.

  24. Case analysis (cont’d) For first 350 units In excess of 350 units C(350)=3.35+0.0338(350) C=15.18 SO, C(k)=15.18+0.5634(k-350) C(k)=3.35+0.0338k Total cost of using 200units: C(200)=3.35+0.0338(200) =10.11 taka Average cost= =0.05055

  25. Graph

  26. Break even analysis • Break even point is the point where total revenue is equal to the total cost, that is, profit=0

  27. Case analysis-2 SoundTech, a manufacturer of compact disc (CDs) has • a fixed cost of 1000 Taka • variable cost of 7 Taka • Selling price is 12 Taka per CD. • A) find the revenue, cost and profit function? a)R(q) =12Q C(q) =7Q+10000 P(q) =12Q-(7Q+10000) = 5Q-10000 • b) What is the profit if 2800 CDs are made and sold? b)P(2800) =5(2800)-10000 =4000

  28. c) What is the profit if 1000 CDs are made and sold? c) P(1000) =5(1000)-10000 = -5000 • d) At What no. Of CDs made and sold will manufacturer break even? d) Break even point: 5Q-10000=0 Q=2000 CDs • e) At what sales volume (revenue) will break even occurs? e) Break even dollar volume of sales: R(2000) =12(2000) = 24000 Taka

  29. Graph

  30. Time value of money • Present value is the current worth of a future sum of money given a specified rate of return. • Future value is the value of an asset or cash at a specified date in the future.

  31. Annuity • An annuity is an amount of money that occurs (received or paid) in equal amounts at equally spaced time intervals. • These occur so frequently in business that special calculation methods are generally used.

  32. Example of present value • Sanjib is planning to buy a car next year that will cost taka 40,000 at that time. If the interest rate is 13% how much should he set aside now and to deposit in a bank in order to pay for the purchase? • So he should set aside now and to deposit in a bank taka 35,398.23 in order to pay for the purchase.

  33. Example of Future Value • Shamim places taka 10,000 in a savings account @ 13% interest compounded annually. How much will he get at the end of 5 years? • He will get taka 11592.74 at the end of 5 years.

  34. Parts of an Annuity End of Period 2 (Ordinary Annuity) End of Period 1 End of Period 3 0 1 2 3 $100 $100 $100 Equal Cash Flows Each 1 Period Apart Today

  35. Parts of an Annuity Beginning of Period 2 (Annuity Due) Beginning of Period 1 Beginning of Period 3 0 1 2 3 $100 $100 $100 Equal Cash Flows Each 1 Period Apart Today

  36. Present Value of Annuity • Selim took a loan of taka 15,00,000 from Brac Bank at 15% interest to be repaid in equal yearly installment over next 20 years. • What will be his annual payment at the beginning of each year? • What will be his annual payment at the end of each year?

  37. Findings Matrix is used to calculate large amount of data in a simple and smarter way. Cost function and break even point analysis help to find marginal cost, marginal revenue and optimum level of production. Interest on loan/deposit, amount of annuity etc are easily calculated by using time value of money concept.

  38. ANY QUEARY?

  39. THANKS TO ALL

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