ECON 201
Lecture 4-5(a)
1-30-2009
Finance:
Net Present Value
& Benefit/Cost Analysis
Evaluating Projects
• Expansion project
– Requires an initial investment, Io
– Yields a flow of benefits and costs over time: Bt, Ct
Bn  Cn
Bt  Ct
B1  C1
NPV  I o  B0  Co 
 ... 
 I o  
n
t
(1  r )
(1  r )
t 0 (1  r )
n
The Net Benefits from an
Investment
• The net benefit of an investment
project is the difference between
the revenue generated by the project and
the project’s cost, including opportunity
cost.
Interest
• Interest is an important part of the
investment decision for two reasons:
– First, interest must be paid to borrow funds.
– Second, interest is the opportunity
cost of using money to pay for an investment
project.
• Money used to purchase capital could have been
deposited in a bank to earn interest.
Interest (cont’d)
• Lenders charge interest:
– To compensate themselves for not being able
to use their own money to buy the things they
want
– To compensate themselves for the risk they
assume when they make a loan
– Because rising prices will reduce the
purchasing power of the money when it
is repaid
Present and Future Value
• The present value (PV) of money
received in the future is equal to its value
today.
– In other words, it is the maximum amount that
someone would pay today to receive the
money in the future.
Present and Future Value
(cont’d)
• The relationship between present and
future value can be shown by the following
equations:
FV  PV (1 Interest Rate)
PV  FV (1 Interest Rate)
Present and Future Value
(cont’d)
• Examples:
Suppose the interest rate is 5%.
– What is the future value of $10,000 one year
from now?
• FV = $10,000 x (1 +.05) = $10,500
– What is the present value of $10,000 received
one year from now?
• PV = $10,000 / (1 +.05) = $9,524
Present and Future Value
(cont’d)
• Discounting refers to the method used to
calculate the present value of a stream of
payments over time.
– Example: Suppose a firm expects to earn $10,000 of
revenue in each of the next 2 years.
•
•
•
PV in Year 1  $10,000 (1 .05)  $9,524
PV in Year 2  $10,000 (1 .05)2  $9,070
Total Value  $9,524  $9,070  $18,594
Net Present Value (cont’d)
• Example: Suppose a firm is considering
investing $8,000 in new equipment. As a result
of the new equipment, the firm expects to earn
revenues of $10,000 in each of
the next 2 years.
NPV   $8,000  $10,000 / (1 .05)  $10,000 / (1 .05)2
  $8,000  $9,524  $9,070  $10,594
• Since NPV is positive, the firm should undertake
the investment.
Other Applications
• How do we determine the value of the firm
– Flow of revenues and costs
– Bt = “expected” revenue stream
– Ct = “expected” expenses
n
Bn  Cn
Bt  Ct
B1  C1
NPV   I o  B0  Co 
 ... 
  Io  
n
t
(1  r )
(1  r )
t  0 (1  r )
• Stock price
– NPV/(#shares)
Closer to Home
• Mortgage Payments
n
Pi
Amount borrowed  
rannual
i 1
(1 
)
12
Washington State Lottery
• Jackpot Analysis For Washington MEGA
Millions
Draw Date: Tuesday, March 11, 2008
• Jackpot is worth $47,000,000
• Payment Options
– Annuity
• 26 Annual Payments of $1,807,692
– Lump Sum
•
$29,200,000
Lump Sum or Annuity?
annual
NPV @ 5%
1,802,692 $25,914,031.54
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
1,802,692
46,869,992
Lump sum
29,200,000