Engineering is $$$

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Engineering is
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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
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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
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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?
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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?
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Compound interestdifferent forms
Interest compounded once per year
Interest compounded q times per year
Interest compounded continuously
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DJIA 1900-2010
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Lease vs. Buy?
Example Honda Pilot EX AWD price
33,595 (Chicago, 2006 figures)
Purchase with 20 down and a 36 month loan
_at_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
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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 (1r) to obtain
Subtract the first equation from the second to
obtain
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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?
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Annuity example You win 1M in a lottery which
pays you in 20 annual installments of 50K?
Whats it worth today, i.e., what is its
present value? Assume 5 interest.
but,
So,
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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 Analysis of comparative advantage

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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.