Engineering is $$$. A dollar today is worth more than a dollar tomorrow: Compound Interest. P 0 = principal 0 time units into the future (i.e., today) P n = principal n time units into the future. where r is the annual interest rate. A Dutchman Peter Inuit bought Manhattan from the
P0 = principal 0 time units into the future (i.e., today)
Pn = principal n time units into the future
where r is the annual
Canarsie Indians for $23 in 1626. Who got robbed. . .?
Assuming funds were invested at 6% compounded monthly
since 1626. The investment today would be worth
$23*(1+.06/12)(12*(2010-1626)) = $220 *109
where r is the annual interest rate
US treasury bills sold at “discount”, so that when the bill matures, you receive face value.
If you buy a one-year $10,000 bill with an interest rate of 3%, how much should you expect to pay for it?
Invest $10,000 in company stock. Ten years later, you sell
the stock for $20,000. What was your effective annual rate of
once per year
q times per year
Example: Honda Pilot EX AWD price = $33,595
(Chicago, 2006 figures)
Purchase with 20% down and a 36 month loan @6.75%
down payment = $ 6,719
monthly payment = $ 825
spent after 36 mo = $36,419
residual value = $23,701
total cost = $12,718
Lease for 36 months
down payment = $ 2,000
monthly payment = $ 359
spent after 36 mo = $14,565
residual value = $0
total cost = $14,565
over n time periods
Future value of an annuity:
where Pn = the value of the annuity after n payments of P
Multiply both sides by (1+r) to obtain
Subtract the first equation from the second to obtain
Annuity example: Each year for 20 years you deposit $1000 into an annuity at an interest rate of 5%. What will be its value in 20 years?
Annuity example: You win $1M in a lottery which pays you in 20 annual installments of $50K? What’s it worth $$ today, i.e., what is its present value? Assume 5% interest.
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:
Cost of capital
Analysis of comparative advantage
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.