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# Copy of selected topics engineering economics

sunum

by

Tweet## Hamid Akinfolarin

on 6 May 2013#### Transcript of Copy of selected topics engineering economics

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Images from Shutterstock.com Hope You Found This Quite Informative Thank You Hamid A. Akinfolarin Brings together and merges the objective, relevant data, feasible alternatives, and selection criterion.

In order to produce a scaled physical representation or mathematical equation for testing Construct model and predict alternative outcomes Relevant data to goal is gathered and feasible system alternatives are synthesized with economic requirements serving as a criterion. Assemble relevant data

&

feasible alternatives Identify,

Research,

Explore,

Investigate

Objectives & potential opportunities. Recognize problem and define goal 1. Recognize problem and define goal

2. Assemble relevant data & feasible alternatives

3. Construct model and predict alternative outcomes

4. Choose the best alternative and audit the result The Decision-Making Process WHY DO ENGINEERS

NEED TO LEARN ABOUT

ECONOMICS? Should I buy or lease my next car? For Example.. Is it cost-effective for the city to construct a new stadium for major sport events? For Example.. Which engineering projects should have a higher priority? Has the industrial engineer shown which factory improvement projects should be funded with the available dollars? For Example.. Which engineering projects are worthwhile? Has a mining or petroleum engineer shown that the mineral or oil deposit is worth developing? For Example.. THE IMPORTANT THING: MAKING DESICIONS! What Is... WHAT IS ENGINEERING?

WHAT IS ENGINEERING?

WHAT IS ECONOMY?

WHAT IS ENGINEERING ECONOMY? INTRODUCTION TO ENGINEERING ECONOMY Politics

Law

Science

Logistic

And so on... Industry

Education

Business

Health

Sports

History We can see Engineering Economy in: Making the exact desicion

considering all

system alternatives. 4. Decision Step Solution

P: money at the beginning of the period

i: interest rate in the period

m: the number of period in the year

nominal interest rate = 10 %

interest rate for 6 months (i) = 10/4 = 2.5 %

Money at the and of the period= P(1+i)M

=1000 (1+0.025)4 = 1103.812 $

Effective interest rate= (1+i) M-1

(1+0.025)4-1=%10.38 Solution

r = 0.21 per year

m = 12 months per year

i = [ 1 + (.21 / 12) ] 12 - 1

i = [1 + 0.0175 ] 12 - 1

i = (1.0175)12 - 1 = 1.2314 - 1

i = 0.2314 = 23.14% Solution

P = $1,000, i = 5%, n = 3 years

F =? at the end of year 3

F = P (1 + i) N

F= 1000 $ (1+0.05)3

F= 1157,625 $ Time value of money equivalences not calculated values of the purchasing power of money, calculated by numerical values. Time value of money equivalences, requires calculations based on the power of the earning money.

This connection is related to interested rate by mathematically. When the capital is 1000 $ and annual interest rate is %10, if there is paying interest for per 3 months, how much money will be earned? Example 4 : This is the interest rate, which is calculated without taking into account the impact of accumulation throughout the year Nominal Interest A credit card company charges 21% interest per year, compounded monthly. What effective annual interest rate does the company charge? Example 3 : This is the annual interest rate is calculated based on the cumulative effects throughout the year.

The Formula of the Effective Interest Rate (r):

r = (1+ i)^m – 1

Here, “i” is the effective interest rate. Therefore, i = i/m, where m is the number of period in that year Effective Interest 321 Credit Union loaned money to an engineer. The loan is for $1,000 for 3 years at 5% per year. How much money will the engineer repay at the end of 3 years?

P = $1,000

i = 5%

n = 3 years

F =? at the end of year 3 Example 2: Compound interest interested in principal sum, interested rate ,and money which is earned interest. It has also parabolic graphic .

Given a present dollar amount P, interest rate i% per year, compounded annually, and a future amount F that occurs N years after the present, then the relationship between these terms is: F = P (1 + i) N Compound Interest Suppose that an annual interest rate of 5% represents the time value of money. If $1000 is invested today at this interest rate, how much will it be worth one year from now?

The value one year from now = $1000 + (5%)($1000) = $1050 Example 1 : Simple interest interested in principal sum and interested rate, but it is not related to money which is earned interest. It has also arithmetical graphic .

The following single payment equation applies to simple interest: F = P (1 + iN) Simple Interest Simple Interest

Compound Interest

Effective Interest

Nominal Interest Diversity of Interest For instance; $909.1 now is the same as, or equivalent to, $1,000 a year from now, if interest is 10 percent per year,

compounded annually. Money is not constant value, so it changes due to time and usage. Money usually loses purchasing value with time. Equivalence of Cash Flow If two things produce same affect as a result, they are said to be equivalent. Equivalence The operation of evaluating a present sum of money some time in the future called a capitalization.

How much will 100 today be worth in 5 years? Capitalization A cash flow diagram allows you to graphically depict the timing of the cash flows as well as their nature as either inflows or outflows. CASH FLOW DIAGRAMS So What Is

ANNUAL CASH FLOW STATEMENT Cash flow is the movement of money into or out of a business, project, or financial product. TERMS THAT WE WILL USE FINDING SOLUTIONS

i:Interest Rate

n: The number of interest periods

PV or P: The present value of money

FV or F:The future value of money

A: term ongoing series of regular payments, end of period

EUAC:Equivalent uniform annual cost PV < 0

This project does not provide enough financial benefits to justify investment, since alternative investments are available that will earn i% (that is the meaning of

"opportunity cost")

The project will need additional, possibly non-cash benefits to be justified Meaning of PV of a Time Stream of

Cash Flows PV > 0

This project is better than making an investment at i% per year for the life of the project

This project is worth further consideration Meaning of PV of a Time Stream of

Cash Flows Present value is a future amount of money that has been discounted to reflect its current value, as if it existed today.

The present value is always less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money. The opposite operation, evaluating the present value of a future amount of money, is called discounting.

How much will 100 received in 5 years be worth today? Discounting PRESENT WORTH ANALYSIS There are three types of cash flow statements: As an analytical tool, the statement of cash flows is useful in determining the short-term viability of a company, particularly its ability to pay bills. What is cash flow? ANNUAL CASHFLOWS

&

PRESENT WORTH ANALYSIS How Cash Flow Statements are useful? "Annual income twenty pounds, annual expenditure nineteen six, result happiness. Annual income twenty pounds, annual expenditure twenty pound ought and six, result misery,"

Mr. Micawber

(in the novel of Charles Dickens “David Copperfield”)

Mr. Micawber got it and that was in 1849… The annual cash flow statement sums to the actual change in cash during the year. We use them to,

Report operating cash flow as well as other cash flow information.

Provide important information to investors and creditors. Operational cash flows Investment cash flows Financing cash flows Choose the best alternative and audit the result

Final step after choosing best possible alternative an audit of results is done as a comparison of what happened against the predictions. Engineering Economic Analysis

Full transcriptImages from Shutterstock.com Hope You Found This Quite Informative Thank You Hamid A. Akinfolarin Brings together and merges the objective, relevant data, feasible alternatives, and selection criterion.

In order to produce a scaled physical representation or mathematical equation for testing Construct model and predict alternative outcomes Relevant data to goal is gathered and feasible system alternatives are synthesized with economic requirements serving as a criterion. Assemble relevant data

&

feasible alternatives Identify,

Research,

Explore,

Investigate

Objectives & potential opportunities. Recognize problem and define goal 1. Recognize problem and define goal

2. Assemble relevant data & feasible alternatives

3. Construct model and predict alternative outcomes

4. Choose the best alternative and audit the result The Decision-Making Process WHY DO ENGINEERS

NEED TO LEARN ABOUT

ECONOMICS? Should I buy or lease my next car? For Example.. Is it cost-effective for the city to construct a new stadium for major sport events? For Example.. Which engineering projects should have a higher priority? Has the industrial engineer shown which factory improvement projects should be funded with the available dollars? For Example.. Which engineering projects are worthwhile? Has a mining or petroleum engineer shown that the mineral or oil deposit is worth developing? For Example.. THE IMPORTANT THING: MAKING DESICIONS! What Is... WHAT IS ENGINEERING?

WHAT IS ENGINEERING?

WHAT IS ECONOMY?

WHAT IS ENGINEERING ECONOMY? INTRODUCTION TO ENGINEERING ECONOMY Politics

Law

Science

Logistic

And so on... Industry

Education

Business

Health

Sports

History We can see Engineering Economy in: Making the exact desicion

considering all

system alternatives. 4. Decision Step Solution

P: money at the beginning of the period

i: interest rate in the period

m: the number of period in the year

nominal interest rate = 10 %

interest rate for 6 months (i) = 10/4 = 2.5 %

Money at the and of the period= P(1+i)M

=1000 (1+0.025)4 = 1103.812 $

Effective interest rate= (1+i) M-1

(1+0.025)4-1=%10.38 Solution

r = 0.21 per year

m = 12 months per year

i = [ 1 + (.21 / 12) ] 12 - 1

i = [1 + 0.0175 ] 12 - 1

i = (1.0175)12 - 1 = 1.2314 - 1

i = 0.2314 = 23.14% Solution

P = $1,000, i = 5%, n = 3 years

F =? at the end of year 3

F = P (1 + i) N

F= 1000 $ (1+0.05)3

F= 1157,625 $ Time value of money equivalences not calculated values of the purchasing power of money, calculated by numerical values. Time value of money equivalences, requires calculations based on the power of the earning money.

This connection is related to interested rate by mathematically. When the capital is 1000 $ and annual interest rate is %10, if there is paying interest for per 3 months, how much money will be earned? Example 4 : This is the interest rate, which is calculated without taking into account the impact of accumulation throughout the year Nominal Interest A credit card company charges 21% interest per year, compounded monthly. What effective annual interest rate does the company charge? Example 3 : This is the annual interest rate is calculated based on the cumulative effects throughout the year.

The Formula of the Effective Interest Rate (r):

r = (1+ i)^m – 1

Here, “i” is the effective interest rate. Therefore, i = i/m, where m is the number of period in that year Effective Interest 321 Credit Union loaned money to an engineer. The loan is for $1,000 for 3 years at 5% per year. How much money will the engineer repay at the end of 3 years?

P = $1,000

i = 5%

n = 3 years

F =? at the end of year 3 Example 2: Compound interest interested in principal sum, interested rate ,and money which is earned interest. It has also parabolic graphic .

Given a present dollar amount P, interest rate i% per year, compounded annually, and a future amount F that occurs N years after the present, then the relationship between these terms is: F = P (1 + i) N Compound Interest Suppose that an annual interest rate of 5% represents the time value of money. If $1000 is invested today at this interest rate, how much will it be worth one year from now?

The value one year from now = $1000 + (5%)($1000) = $1050 Example 1 : Simple interest interested in principal sum and interested rate, but it is not related to money which is earned interest. It has also arithmetical graphic .

The following single payment equation applies to simple interest: F = P (1 + iN) Simple Interest Simple Interest

Compound Interest

Effective Interest

Nominal Interest Diversity of Interest For instance; $909.1 now is the same as, or equivalent to, $1,000 a year from now, if interest is 10 percent per year,

compounded annually. Money is not constant value, so it changes due to time and usage. Money usually loses purchasing value with time. Equivalence of Cash Flow If two things produce same affect as a result, they are said to be equivalent. Equivalence The operation of evaluating a present sum of money some time in the future called a capitalization.

How much will 100 today be worth in 5 years? Capitalization A cash flow diagram allows you to graphically depict the timing of the cash flows as well as their nature as either inflows or outflows. CASH FLOW DIAGRAMS So What Is

ANNUAL CASH FLOW STATEMENT Cash flow is the movement of money into or out of a business, project, or financial product. TERMS THAT WE WILL USE FINDING SOLUTIONS

i:Interest Rate

n: The number of interest periods

PV or P: The present value of money

FV or F:The future value of money

A: term ongoing series of regular payments, end of period

EUAC:Equivalent uniform annual cost PV < 0

This project does not provide enough financial benefits to justify investment, since alternative investments are available that will earn i% (that is the meaning of

"opportunity cost")

The project will need additional, possibly non-cash benefits to be justified Meaning of PV of a Time Stream of

Cash Flows PV > 0

This project is better than making an investment at i% per year for the life of the project

This project is worth further consideration Meaning of PV of a Time Stream of

Cash Flows Present value is a future amount of money that has been discounted to reflect its current value, as if it existed today.

The present value is always less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money. The opposite operation, evaluating the present value of a future amount of money, is called discounting.

How much will 100 received in 5 years be worth today? Discounting PRESENT WORTH ANALYSIS There are three types of cash flow statements: As an analytical tool, the statement of cash flows is useful in determining the short-term viability of a company, particularly its ability to pay bills. What is cash flow? ANNUAL CASHFLOWS

&

PRESENT WORTH ANALYSIS How Cash Flow Statements are useful? "Annual income twenty pounds, annual expenditure nineteen six, result happiness. Annual income twenty pounds, annual expenditure twenty pound ought and six, result misery,"

Mr. Micawber

(in the novel of Charles Dickens “David Copperfield”)

Mr. Micawber got it and that was in 1849… The annual cash flow statement sums to the actual change in cash during the year. We use them to,

Report operating cash flow as well as other cash flow information.

Provide important information to investors and creditors. Operational cash flows Investment cash flows Financing cash flows Choose the best alternative and audit the result

Final step after choosing best possible alternative an audit of results is done as a comparison of what happened against the predictions. Engineering Economic Analysis