Finance:
Net Present Value
8.1
ECON 201
Summer 2009
1
Firm’s Financing Decision
• Firm’s desire to expand and purchase new
capital stock can be financed by:
– Loan (repay with interest)
• Borrow $X from a lending institution (bank)
– Issue bonds (debt)
• Promise to pay back bond holders later for
obtaining $X today
– Sell stock (corporate holdings, stock splits)
• Decrease stock price in the short-run
– Venture Capital
2
Benefit/Cost Analysis
• Basic Issue in Business or Personal Finance
Decisions
– How to evaluate projects/investment opportunities
that have a flow of benefits and costs over time
• Approach
– Stream of benefits and costs are discounted over
time (Net Present Value)
• Accounts for opportunity costs of money
– Time rate of preference
3
Why Firms Seek Funds
• The most common reason for firms to
seek funds (financial capital) is to pay for
plant and equipment (physical capital).
4
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.
5
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.
6
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
7
Time Value of Money
• Money today is more valuable than the
same amount of money at some point in
the future.
– If you have money today, you could deposit it
in a bank and earn interest.
8
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.
9
Present and Future Value
(cont’d)
• The future value (FV) of money is what
an amount of money will be worth at some
point in the future.
10
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)
11
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
12
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
13
Evaluating Projects
• Expansion project
– Requires an initial investment, Io
– Yields a flow of benefits over time, Bt
n
Bn
Bt
B1
NPV   I o  B0 
 ... 


I


o
t
(1  r )
(1  r )t
t  0 (1  r )
14
Net Present Value
• Firms focus on the net present value
(NPV) of an asset when making
investment decisions.
– NPV = PV of the asset minus the PV of the
expenditures on the asset.
• If NPV > 0 then the investment is profitable.
– All else equal, the sooner the benefits are received
and the lower the interest rate, the higher the NPV.
15
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.
16
Interest and the Demand for
Capital
• The interest rate represents the
opportunity cost of purchasing capital.
Therefore, as the interest rate increases,
the quantity of capital demanded will fall.
17
Figure 14.1 The Demand Curve
for Physical Capital
18
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
19
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
20