Financial Management Series
Number 3
Using Net Present Value
To Evaluate
The Value of Money Over
Time
Alan Probst
Local Government Specialist
Local Government Center
UW-Extension
Financial Management
Fiscal Policy
Sound financial decision-making
results from an informed fiscal
policy and a solid understanding of
the value of money and the
vehicles through which it is
managed.
Financial Management
Financial Decisions require consideration of:
• Projected revenues over the period of
time being considered
• Projected operating expenditures over
the period being considered
Financial Management
(cont.)
• The governmental body’s ability to
acquire financing, now and in the future
• Present and future value of money
when applied to the project being
considered.
Financial Decision-Making
When making financial decisions for a
governmental body, the same rational doesn’t
necessarily apply as is used in managing one’s
own personal finances.
What looks like a “common sense” good idea at
first may turn out to be a bad financial decision
when worked through the formulas
Financial Decision-Making
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Performing a Cost/Benefit Analysis is
essential to sound financial decision-making
A critical part of a Cost Benefit Analysis is
determining the value of money over time
Time Value of Money
•
Money’s value changes over time
•
A dollar today is worth more than a dollar
tomorrow
•
When time value is considered, the costeffectiveness of a project can change
Today’s dollar is worth more
because:
•
Interest rates
$100 you invest at a 4% interest rate today will be worth $104 in 1 year,
thus making today’s money worth more
•
Inflation
You purchase 20 items today at $1.00 each for $20.00
After one year, due to inflation, those same items cost $1.50 each and
you can only purchase 13.33 of that same item with our $20.00. Thus,
today’s money is worth more.
Value of Money Over Time
Future Value
Measures what today’s money would be worth at a
specified time in the future assuming a certain
discount rate
Present Value
Measures what money at a specified period of time in
the future would be worth if valued in terms of
today’s money
Discount Rate
•
The rate used in calculating the present value of
expected yearly benefits and costs
•
Used to reflect the time value of money
•
The higher the discount rate, the lower the present
value of future cash flows
Real vs Nominal
Discount Rates

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A nominal discount rate that reflects
expected inflation should be used to
discount nominal benefits and costs
Market interest rates are nominal interest
rates
Real vs. Nominal

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A real discount rate adjusted to eliminate the effect
of expected inflations should be used to discount
constant-dollar or real benefit benefits and costs
A real discount rate can be approximated by
subtracting expected inflation from a nominal
interest rate
Real Discount Rate
(1+ Nominal Interest Rate) = (1 + Real
Interest Rate) * (1 + Inflation rate)
Free Cash Flows
Free Cash Flow is a measure of cash
flow remaining after all
expenditures required to maintain
the operation
Future VS Present Value
•
Future Value = Present Value X (1+discount
rate) raised to a power of the number of
years
•
Present Value = Future Value/ (1+discount
rate) raised to a power of the number of
years
Example
Future value of 100 of today’s dollars in
five years.
100 X (1.0 + .04)5 = 121.67 where .04 is the
discount rate.
Done on Excel:
=SUM(100*(1+0.04)^5)
Example
Present Value of 100 dollars five years in
the future.
100 / (1.0 + .04)5 = $82.19
On Excel:
=SUM(100/(1+0.04)^5)
Would you rather pay $15,000 now
for a year’s worth of your
newborn’s education or $30,000
eighteen years from now?
Present value of $30,000 eighteen
years into the future + 30000
divided by (1+.04)18 = $14,809
So why is this important?
Understanding the time value of money can
help you identify misconceptions about real
costs and benefits of projects or courses of
action
So why is this important?
•
Future value, present value, and discount rates are used to
determine Net Present Value
•
Net Present Value is a component of Cost Benefit Analysis
•
Net Present Value is a criterion for deciding whether a
government program can be justified on economic
principles.
Net Present Value (NPV)
•
NPV is the future stream of benefits and costs
converted into equivalent values today
•
Programs with a positive NPV are generally cost
effective
•
Programs with negative NPV are generally not cost
effective
Calculating NPV
•
•
•
Assign monetary values to benefits and costs
Discount future benefits and costs using an
appropriate discount rate
Subtract the sum total of discounted costs
from the sum total of discounted benefits
Project Example

Project A produces $5,000 of revenue in 2006

Project B produces $5,200 of revenue in 2007

Which is the more fiscally sound project?
Project Example
•
You cannot directly compare two different
years without discounting
•
2006 is Present Value
•
2007 is Future Value
Project Example

You must find the PRESENT VALUE of
Project B in 2006 to compare

Since this is a government project, we’ll use
4.5% interest on a US Treasury Bond as the
Discount Rate
Project Example
•
The PRESENT VALUE of Project B is
determined by:
$5,200 / (1+ 0.045) = $4,976
NPV = $4,976
Project Example
After discounting, the present value of :
Project A
Project B
=
=
$5,000
$4,976
Choose Project A
Real World Example
New County Historical Society & Museum

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Construction cost:
Visitor ticket:
Annual expected visitors
Expected growth of visitors
Annual maintenance costs
Annual repair expenses
Discount rate
Depreciation
Capital Expenditure
Inventory, etc.
$10,000,000
$15
56,700
12% (for 10 year
horizon)
$10,000 w/7% growth
$5,000 w/7% growth
4.85% (10 yr Treasury
Bond Rate)
$285,714 w/5% growth
$300,000
$5,000 w/5% growth
Real World Example
For each year of payback of 10 year project:

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Projected revenues – annual maintenance and repair expenses =
Benefits
Add benefits + depreciation
Subtract capital expenditure for the year and change in working capital
to get Free Cash Flows
Free Cash Flows/(1+.0485) to the power of the year number (1-10) for
Present Value of Cash Flows (PVCF)
Total of ten year’s PVCF – Cost of Construction = NPV
NPV this project is $249,758; generally cost effective
Real World Example
HOWEVER, if you decrease the expected growth
rate in paying visitors from 12% to only 5% the
entire picture changes
With only a 5% expected increase, using the same
formula, our NPV result is a negative ($2,698,349),
a major loss and commonly viewed as not costeffective
Summary
As local officials and decision-makers, it is
only necessary to understand the concepts
so you can make informed decisions based
on data presented to you by your financial
staff or consultants, it is not necessary to be
able to perform these calculations