CDAE Class 07 Sept. 18 Last class: Result of Quiz 1 2. Review of economic and business concepts Today: 2. Review of economic and business concepts Next class: 2. Review of economic and business concepts Quiz 2 Important dates: Problem set 1: due Thursday, Sept. 20 Project 1: due Thursday, Sept. 27 (Download files from

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?

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 -- 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 Mortgage related concepts: -- Interest rate and “points” -- Mortgage insurance -- Closing costs -- “Home equity loan” vs. “home equity line of credit” -- Property tax -- What does “no closing cost” mean? -- Added to the money you will borrow (PVAn) -- Pay a higher interest rate

More applications of the TVM Examples of mortgage problems: Mr. Lang plans to purchase a house at $300,000 with 20% down payment and a 30-year mortgage with a fixed rate of 6.125% -- What will be a monthly payment? -- What will be the loan balance in the end of the 1 st year? -- What will be the loan balance in the end of the 10 th year? A good website to get answers for such questions:

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?

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?

2.5. Marginal analysis Basic concepts Major steps of using quantitative methods Methods of expressing economic relations Total, average and marginal relations How to derive derivatives? Profit maximization Average cost minimization

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.

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 = Q Q 2 where Q is the level of output

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

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

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.

Total, average and marginal relations (3) An example Q MAQ MA