1. CDAE 266 - Class 06 Sept. 14 Last class: Result of class exercise 1 2. Review of economic and business concepts Problem set 1 Quiz 1 Today: Result of Quiz 1 2. Review of economic and business concepts Class exercise 2 Next class: 2. Review of economic and business concepts Project 1

2. CDAE 266 - Class 06 Sept. 14 Reading: Time value of money (handout) Important dates: Problem set 1: due Tuesday, Sept. 19 Project 1 report due Thursday, Sept. 28

3. Result of Quiz 1 N = 51Range = 4 –- 10Average = 9.25 1. Three major reasons for the U.S. to have so many small businesses 2. Future value:PV, n and r  FVn = PV * Factor A 3. Present value:FVn, n and r  PV = FVn * Factor B 4. Future value of annuity: A, n and r  FVAn = A * Factor C 5. Present value of annuity: PVAn, n and r  A = PVAn / Factor D

4. 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

5. 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?

6. 2.3.7. Compounding & discounting periods -- General assumption: interest is paid once a year (compounded annually): e.g., PV = $100, r = 12% per year FV 1 = 100 (1+0.12) = 112

7. 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: FV 6 months = 100 (1+0.06) = $106 In the end of the first year: FV 12 months = 106 (1+0.06) = $112.36

8. 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)?

9. 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 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?

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%? PVA p = A / r = 1150 / 0.06 = $19,167

11. 2.3.9. How to calculate the TVM using Excel? -- How to get the program? -- It has been emailed to you -- Bring a disk to class if you could not open the attached file -- 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. 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 PVA 360 = 336,000 = A x Factor D How to get the factor from the Excel program? What will be the monthly mortgage payment?

13. More applications of the TVM Mortgage related concepts: -- Interest rate and “points” -- Fixed rate vs. flexible rate -- Mortgage insurance -- Closing costs -- Property tax -- What does “no closing cost” mean?

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. More applications of the TVM – Problem set 1

17. Class Exercise 2 ( Thursday, Sept. 14 ) 1.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)?