Engineering is \$\$\$

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# Engineering is \$\$\$ - PowerPoint PPT Presentation

Engineering is \$\$\$ A dollar today is worth more than a dollar tomorrow: Compound Interest P 0 = principal 0 time units into the future (i.e., today) P n = principal n time units into the future where r is the annual interest rate A Dutchman Peter Inuit bought Manhattan from the

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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 annual

interest rate

A Dutchman Peter Inuit bought Manhattan from the

Canarsie Indians for \$23 in 1626. Who got robbed. . .?

Assuming funds were invested at 6% compounded monthly

since 1626. The investment today would be worth

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

A dollar today is worth more than a dollar tomorrow:

Present Value:

where r is the annual interest rate

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:

Invest \$10,000 in company stock. Ten years later, you sell

the stock for \$20,000. What was your effective annual rate of

return?

Compound interest—different forms

Interest compounded

once per year

Interest compounded

q times per year

Interest compounded

continuously

Example: Honda Pilot EX AWD price = \$33,595

(Chicago, 2006 figures)

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

down payment = \$ 6,719

monthly payment = \$ 825

spent after 36 mo = \$36,419

residual value = \$23,701

total cost = \$12,718

Lease for 36 months

down payment = \$ 2,000

monthly payment = \$ 359

spent after 36 mo = \$14,565

residual value = \$0

total cost = \$14,565

Annuities: Equal payments paid (or received)

over n time periods

Future value of an annuity:

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

Multiply both sides by (1+r) to obtain

Subtract the first equation from the second to obtain

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?

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.

but,

So,

Opportunity Cost

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.

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

Payback Period

The length of time required to recover

the 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.