CDAE Class 06 Sept. 13 Last class: 2. Review of economic and business concepts Quiz 1 Today: Result of Quiz 1 2. Review of economic and business concepts Next class: 2. Review of economic and business concepts Important dates: Problem set 1: due Tuesday, Sept. 18 Project 1: due Tuesday, Sept. 25 (Download files from

Result of Quiz 1 N = 59Range = 2.5 – 10 Average = Three major reasons for the U.S. to have so many small businesses 2. Four-step decision-making process 3. PV, r and n  FVn = PV * Factor A Table A 4. FVn, r and n  PV = FVn * Factor B Table B 5. A, r and n  FVAn Table C 6. PV, FVn and n  r Table A or Table B 7. FVAn, r and n  ATable C FVAn = A * Factor C  A = FVAn / Factor C See Class Exercise 2 on Sept. 6

Class Exercise 2 (Thursday, Sept. 6) Mrs. Sullivan would like to save money to replace her car in 5 years from today by depositing the same amount of money in the end of each year over the next 5 years. If the estimated cost for a new car in 5 years from today is $25,000 and the interest rate is 6% per year, how much does she need to deposit each year?

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

2.4. Time value of money What is the time value of money? How to calculate the TVM? Future value and compounding Present value and discounting Future value of an annuity Present value of an annuity Compounding & discounting periods Perpetuities How to calculate the TVM using Excel?

Present value of an annuity -- Formula -- Table D: PVA n = A * Factor D -- Example question: Suppose that you are the winner of a lottery ticket and you will receive $5,000 in the end of each year over the next 3 years. What is the present value of the ticket if the annual interest (discount) rate will be fixed at 6% in the next 3 years.

Take-home practice problems 1. What is the present value (PV) of $1500 to be received in 7 years from today if the annual discount rate is 5%? 2. A small business has just borrowed $30,000 from a local bank and the money must be paid back by 6 equal end-of-year payments over the next 6 years, what will be the annual payment if the annual interest rate is 7%?

General procedures of solving a TVM problem Step 1. List the information you have Step 2. Determine what we are looking for Step 3. Decide which formula or Table to use Step 4. Do the calculation Step 5. Answer the question For example: 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%?

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 FV 2 = 112 (1+0.12) =

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

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 = / 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)?

Compounding & discounting periods -- Procedures of calculating the “effective annual interest rate -- Choose a PV (e.g., $100) -- Calculate the FV in one year from today Method 1: Period-by-period calculation Method 2: Using Table A -- Calculate the annual interest income = FV in one year - PV -- Calculate the effective annual interest = (Annual interest income / PV) -- How to choose the present value?

Class Exercise 3 ( Thursday, Sept. 13 ) 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)?

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

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 We can not get this factor from Table D because n=360 and r=0.56% and we will introduce a worksheet in Excel to calculate the monthly mortgage payment.

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) Future value of an annuity (4) Present value of an annuity

More applications of the TVM Problem set 1 Project 1

Group projects 1. Groups: 2-4 students in each group (organize your own group by Tuesday, Sept. 18) 2. Format requirements for project reports (available in the class website) 3. How will I grade your project reports?

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