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

CDAE 266 - Class 07Sept. 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)

CDAE 266 - Class 07Sept. 19

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

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 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?

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

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

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)?

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?

2.3.7. Compounding & discounting periods -- A general formula of calculating the

effective annual interest rate: Annual interest rate = rNumber of times interest is paid per year = m Interest rate per period = r / mFV 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 choiceAnnual interest income = FV12 months – PVEffective annual interest rate = (FV12 months – PV)/PVYou 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)

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


-- 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


-- How to get TVM factors from the computer grogram when they are

not available in the TVM tables?

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?


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%?


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?

Class Exercise 2 (Tuesday, Sept. 19)

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)?

Group projects

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?

Project 1

-- What is the business problem?

-- What information do we have?

-- How to analyze the problem?

-- How to write your business memo?

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

2.5. 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

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.

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

2.5.3. Major ways to present economic relations:

(1) Graphs

(2) Tables

(3) Functions

(4) Computer programs


(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

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.


(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

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

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