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
Pn  P0 1  r 
n
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:
P0  Pn 1 r 
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?
n
A dollar today is worth more than a dollar tomorrow:
Effective Interest:
1
n
 Pn 
r     1
 P0 
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
Pn  P0 1  r 
n
 r
Pn  P0 1  
 q
nq
Interest compounded
continuously
nq
 r
Pn  P0 lim1    P0 e rn
q 
 q
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
monthly payment
spent after 36 mo
residual value
total cost
= $ 6,719
= $ 825
= $36,419
= $23,701
= $12,718
Lease for 36 months
down payment
monthly payment
spent after 36 mo
residual value
total cost
= $ 2,000
= $ 359
= $14,565
= $0
= $14,565
Annuities: Equal payments paid (or received)
over n time periods
Future value of an annuity:
Pn  P[(1  r )n1  (1  r )n2 (1  r )1 ]
where Pn = the value of the annuity after n payments of P
Multiply both sides by (1+r) to obtain
Pn (1  r)  P[(1  r)n  (1  r)n1 (1  r)0 ]
Subtract the first equation from the second to obtain
[(1  r ) n  1]
Pn  P
r
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?
[(1.05) 20  1]
An  $1000*
 $33065
.05
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.
[(1  r ) n  1]
Pn  P
r
but,
So,
Pn  P0 1  r 
n
[(1  r ) n  1]
1.0520  1
P0  P
 $50K
 $623K
n
20
r (1  r )
.05* (1.05)
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
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.