Engineering is $$$

A dollar today is worth more than a dollar tomorrow:Compound Interest

P0 = principal 0 time units into the future (i.e., today)Pn = principal n time units into the future

where r is the annualinterest rate

nn rPP 10

A dollar today is worth more than a dollar tomorrow:

Present Value:

where r is the annual interest rate

nn rPP 10

US treasury bills sold at “discount”, so that when the bill matures, you receive face value.If you buy a one-year $10,000 bill with an interest rate of 3%, how much should you expect to pay for it?

A dollar today is worth more than a dollar tomorrow:

Effective Interest:

1

1

0

nn

P

Pr

Invest $10,000 in company stock. Ten years later, you sellthe stock for $20,000. What was your effective annual rate ofreturn?

nn rPP 10

nq

n q

rPP

10

Interest compoundedonce per year

Interest compoundedq times per year

rn

nq

qn eP

q

rPP 00 1lim

Interest compoundedcontinuously

Compound interest—different forms

A Dutchman Peter Inuit bought Manhattan from theCanarsie Indians for $23 in 1626. Who got robbed. . .?

Assuming funds were invested at 6% compounded monthlysince 1626. The investment today would be worth

$23*(1+.06/12)(12*(2010-1626)) = $220 *109

nq

n q

rPP

10

DJIA 1900-2010

Lease vs. Buy?

Example: Honda Pilot EX AWD price = $33,595(Chicago, 2006 figures)

Purchase with 20% down and a 36 month loan @6.75%

down payment = $ 6,719monthly payment = $ 825spent after 36 mo = $36,419residual value = $23,701total cost = $12,718

Lease for 36 months

down payment = $ 2,000monthly payment = $ 359spent after 36 mo = $14,565residual value = $0total cost = $14,565

Annuities: Equal payments paid (or received)over n time periods

Future value of an annuity:

])1()1()1[( 121 rrrPP nnn

where Pn = the value of the annuity after n payments of P

Multiply both sides by (1+r) to obtain

])1()1()1[()1( 01 rrrPrP nnn

Subtract the first equation from the second to obtain

r

rPP

n

n

]1)1[(

Annuity example: Each year for 20 years you deposit $1000 into an annuity at an interest rate of 5%. What will be its value in 20 years?

33065$05.

]1)05.1[(*1000$

20

nA

r

rPP

n

n

]1)1[(

Annuity example: You win $1M in a lottery which pays you in 20 annual installments of $50K? What’s it worth $$ today, i.e., what is its present value? Assume 5% interest.

nn rPP 10but,

So, KKrr

rPP

n

n

623$)05.1(*05.

105.150$

)1(

]1)1[(20

20

0

Applications of Opportunity Cost

The concept of opportunity cost has a wide range of applications including:

Consumer choice Production possibilities Cost of capital Time management Career choice Analysis of comparative advantage

The opportunity cost of a decision is based on what must be given up (the next best alternative) as a result of the decision. Any decision that involves a choice between two or more options has an opportunity cost.

Opportunity Cost

The length of time required to recoverthe cost of an investment.

Shorter paybacks are better investments.

Problems with this metric:

1. It ignores any benefits that occur after the payback period and, therefore, does not measure profitability.

2. It ignores the time value of money.

Payback Period

Identity

• Your name– Single most important asset that you own– Permanent – it follows you through your life– Important in all societal interactions– Attached to every personal achievement and

failure

Ways to enhance this asset• Honesty

• Reliability

• Competence

• Truthfulness

• Consistency

• Fair Play

• Education

Things to tarnish this asset

• Dishonesty

• Cheating

• Trickery

• Criminal Activity

• Unethical Behavior

Social Security Number

• Second most important asset you own

• Permanent

• Important in almost all activities involving money– Taxes– Credit cards– Retirement Benefits– Medical Records

Where you live

• Used by insurance companies to determine rates

• Used by state governments to establish property tax rates

• Suggests social status

• Determines educational opportunities for public K-12 schools

Other Identity Influences• Who you know

• Where you went to school

Ethics

• Moral Principles or values• Code of Conduct• Recognition of “good” or “right” vs. “bad” or

“wrong”• System or code of morals for a religion, group or

profession• Personal code of conduct based on respect for one’s

self, others, and one’s surroundings• A set of principles and values that govern behavior to

accord with a notion of morality

Legal vs. Moral

• Laws attempt to define unambiguous, enforceable rules that parallel a culture’s morality

• Money muddies the waters of legal vs. moral.

Corporations/Companies• Identity independent of those who run the

company

• Trademarks, Intellectual property are corporate assets

• Unlike personal reputations, can erase problems by dissolving and reforming

• The bottom line – money

• Short term vs. long term views

You have borrowed a knife from a friend who, since has turned homicidal. He wants it returned. On the one hand you have a moral obligation to return what you have borrowed. On the other hand you have a moral obligation to protect those around you.

Dilemma posed by Plato in The Republic

As a medical representative for a friend who lays dying in the hospital, you are asked whether you want life support removed. Your friend could live indefinitely in a coma with support, but would die within 24 hours without it. Hospital costs are $1000/day. You know that both yourself and several other friends are named in his will.

An energy corporation must be responsive to its stockholders. Extracting coal using strip mining is clearly most profitable, but the terrain will be permanently compromised. Shaft mining is much less profitable, but will preserve the landscape.

A family is 6months behind in paying its rent (husband lost job, child became critically ill). Landlord has the legal right to evict.

An engineering firm has won an award to build a bridge to specification for a set price. Due to misestimating costs, if the firm builds the bridge as specified the company will go bankrupt. However, if the firm uses inferior materials and reduces the safety factor in the bridge design, it can make a profit.

An automobile manufacturer discovers a significant design flaw in a new model that, under the right circumstances, could cause the car to flip at high speed. But the chances are slim. Issuing a recall would be very expensive and would probably negatively affect future sales. Ignoring the flaw and hoping that resulting accidents could be blamed by driver error would save profits and the model line.