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CDAE 266 - Class 07 Sept. 19 Last class: Result of Quiz 1

CDAE 266 - Class 07 Sept. 19 Last class: Result of Quiz 1 2. Review of economic and business concepts Today: 2. Review of economic and business concepts Class exercise 2 Project 1 Next class: 2. Review of economic and business concepts

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CDAE 266 - Class 07 Sept. 19 Last class: Result of Quiz 1

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  1. CDAE 266 - Class 07 Sept. 19 Last class: Result of Quiz 1 2. Review of economic and business concepts Today: 2. Review of economic and business concepts Class exercise 2 Project 1 Next class: 2. Review of economic and business concepts Quiz 2 (time value of money) Reading: Time value of money (handout)

  2. CDAE 266 - Class 07 Sept. 19 Important dates: Problem set 1: due today Quiz 2 (time value of money), Thursday, Sept. 21 Project 1 report due Thursday, Sept. 28

  3. 2. Review of Economics Concepts 2.1. Overview of an economy 2.2. Ten principles of economics 2.3. Theory of the firm 2.4. Time value of money 2.5. Marginal analysis 2.6. Break-even analysis

  4. 2.4. Time value of money 2.4.1. What is the time value of money? 2.4.2. How to calculate the TVM? 2.4.3. Future value and compounding 2.4.4. Present value and discounting 2.4.5. Future value of an annuity 2.4.6. Present value of an annuity 2.4.7. Compounding & discounting periods 2.4.8. Perpetuities 2.4.9. How to calculate the TVM using Excel?

  5. 2.3.7. Compounding & discounting periods -- General assumption: interest is paid once a year (compounded annually): e.g., PV = $100, r = 12% per year FV1 = 100 (1+0.12) = 112

  6. 2.3.7. Compounding & discounting periods -- Suppose interest is paid twice a year (compounded semiannually): e.g., PV = $100, r = 12% per year (6% per 6-month). In the end of the 6th month: FV6 months = 100 (1+0.06) = $106 In the end of the first year: FV12 months = 106 (1+0.06) = $112.36

  7. 2.3.7. Compounding & discounting periods -- What is the “effective annual interest rate”? Effective annual interest rate = Annual interest income / PV e.g., an account with an annual interest rate of 12% and the interest is paid twice a year (compounded semiannually): Effective annual interest rate = 12.36 / 100 = 12.36% -- What is the effective annual interest rate if the annual interest rate is 12% and interest is paid quarterly (every three months)?

  8. 2.3.7. Compounding & discounting periods -- Procedures -- Choose a PV -- Calculate the FV in the end of the first period -- Calculate the FV in the end of the next period -- Calculate the FV in the end of the next period … -- Calculate the annual interest income = FV in the end of the year - PV -- Calculate the effective annual interest = (Annual interest income / PV) -- How to choose the present value?

  9. 2.3.7. Compounding & discounting periods -- A general formula of calculating the effective annual interest rate: Annual interest rate = r Number of times interest is paid per year = m Interest rate per period = r / m FV in the end of the first year FV 12 months = PV [1 + (r/m)]m PV can be any number but $100 is a good choice Annual interest income = FV12 months – PV Effective annual interest rate = (FV12 months – PV)/PV You can also use Table A to get the FV 12 months FV12 months = PV * Factor A (Use “m as the number of periods and r/m as the interest rate” to get Factor A from Table A)

  10. 2.3.8. Perpetuities (1) What is a perpetuity? An equal payment in the end of each period for an infinite number of periods. (2) PV of a perpetuity e.g., are you willing to pay $20,000 today and receive $1,150 in the end of each year in the next 100 years if the estimated annual interest rate is 6%? PVAp = A / r = 1150 / 0.06 = $19,167

  11. 2.3.9. How to calculate the TVM using Excel? -- How to get the program? (available in the class website) -- How to use the program? (1) Future value and compounding (2) Present value and discounting (3) Present value of an annuity (4) Future value of an annuity

  12. 2.3.9. How to calculate the TVM using Excel? -- How to get TVM factors from the computer grogram when they are not available in the TVM tables?

  13. More applications of the TVM Mortgage problem: Mrs. G. would like to purchase a house at $420,000 but she first wants to know the monthly mortgage payment. If the fixed annual rate for a 30 year mortgage is 6.72% with 20% down payment, what will be the monthly mortgage payment? Amount of loan = sale price – down payment = 336,000 Number of payments = 360 (months) Monthly interest rate = 6.72 / 12 = 0.56% per month PVA360 = 336,000 = A x Factor D How to get the factor from the Excel program? What will be the monthly mortgage payment?

  14. More applications of the TVM Value of a small business: Suppose a small business has been estimated to make a net profit of $20,000 per year in the next five years and the business can be sold at $95,000 in the end of the fifth year. What is the present value of this business if the annual interest rate is 5%?

  15. More applications of the TVM How to compare two or more projects: Suppose there are two projects with the same capital investment: the first one promises a profit of $10,000 in each of the next four years, and the second project promises a profit of $8,000 in each of the next six years. If the interest (discount) rate is 8%, what is your choice?

  16. What is the “effective annual interest rate” if the annual interest rate is 8% and interest is paid every six months? 2. What is the “effective annual interest rate” if the annual interest rate is 8% and interest is paid quarterly (every three months)? Class Exercise 2(Tuesday, Sept. 19)

  17. 1. Groups: 2-4 students in each group 2. Format requirements for project reports (available in the class website) 3. How will I grade your project reports? Group projects

  18. -- What is the business problem? -- What information do we have? --How to analyze the problem? -- How to write your business memo? Project 1

  19. 2. Review of Economics Concepts 2.1. Overview of an economy 2.2. Ten principles of economics 2.3. Theory of the firm 2.4. Time value of money 2.5. Marginal analysis 2.6. Break-even analysis

  20. 2.5. Marginal analysis 2.5.1. Basic concepts 2.5.2. Major steps of using quantitative methods 2.5.3. Methods of expressing economic relations 2.5.4. Total, average and marginal relations 2.5.5. How to derive derivatives? 2.5.6. Profit maximization 2.5.7. Average cost minimization

  21. 2.5.1. Basic concepts (1) Decision making: The process of deriving the best possible solution to a given problem. (2) Optimal decision: The action that produces the results most consistent with the decision objective or objectives.

  22. 2.5.2. Major steps of using quantitative methods: (1) The economic relations must be expressed in a form suitable for analysis. (2) Various techniques are used to determine the optimal solution. An example: Profit = -100 + 2 Q - 0.01 Q2 where Q is the level of output

  23. 2.5.3. Major ways to present economic relations: (1) Graphs (2) Tables (3) Functions (4) Computer programs

  24. 2.5.4. Total, average and marginal relations (1) General notations: P = price of a product (output) Q = quantity of a product (output) TR = P Q = Total revenue FC = total fixed costs VC = total variable costs TC = FC + VC = total costs AC = TC / Q = average cost  = TR - TC = total profit A =  / Q = average profit

  25. 2.5.4. Total, average and marginal relations (2) Marginal concepts: Marginal revenue (MR) = the change in total revenue (TR) when output quantity (Q) changes by one unit. Marginal cost (MC) = the change in total costs (TC) when output quantity (Q) changes by one unit. Marginal profit (M) = the change in total profit () when output quantity (Q) changes by one unit.

  26. 2.5.4. Total, average and marginal relations (3) An example Q  M A 0 0 --- --- 1 19 19 19 2 52 33 26 3 93 41 31 4 136 43 34 5 175 39 35 6 210 35 35 7 217 7 31 8 208 -9 26

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