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Financial Management Series

Number 3

Using Net Present Value

To Evaluate

The Value of Money Over

Time

Alan Probst

Local Government Specialist

Local Government CenterUW-Extension

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Financial Management

Fiscal Policy

Sound financial decision-makingresults from an informed fiscalpolicy and a solid understanding ofthe value of money and the

vehicles through which it ismanaged.

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Financial Management

Financial Decisions require consideration of:

Projected revenues over the period oftime being considered

Projected operating expenditures overthe period being considered

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Financial Management

(cont.)

The governmental bodys ability to

acquire financing, now and in the future

Present and future value of money

when applied to the project beingconsidered.

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Financial Decision-Making

When making financial decisions for a

governmental body, the same rational doesntnecessarily apply as is used in managing ones

own personal finances.

What looks like a common sense good idea at first

may turn out to be a bad financial decision whenworked through the formulas

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Financial Decision-Making

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

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Time Value of Money

Moneys value changes over time

A dollar today is worth more than a dollartomorrow

When time value is considered, the cost-

effectiveness of a project can change

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Todays 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 todays 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 andyou can only purchase 13.33 of that same item with our $20.00. Thus,todays money is worth more.

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Value of Money Over Time

Future Value

Measures what todays money would be worth at aspecified time in the future assuming a certaindiscount rate

Present ValueMeasures what money at a specified period of time inthe future would be worth if valued in terms of todaysmoney

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Discount Rate

The rate used in calculating the present value ofexpected yearly benefits and costs

Used to reflect the time value of money

The higher the discount rate, the lower the presentvalue of future cash flows

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Real vs Nominal

Discount Rates

A nominal discount rate that reflects

expected inflation should be used todiscount nominal benefits and costs

Market interest rates are nominal interest

rates

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Real vs. Nominal 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 bysubtracting expected inflation from a nominal

interest rate

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Real Discount Rate

(1+ Nominal Interest Rate) = (1 + Real

Interest Rate) * (1 + Inflation rate)

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Free Cash Flows

Free Cash Flowis a measure of cash

flow remaining after all

expenditures required to maintainthe operation

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Future VS Present Value Future Value = Present Value X (1+discountrate) 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

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Example

Future value of 100 of todays dollars in

five years.

100 X (1.0 + .04)5 = 121.67 where .04 is the

discount rate.

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Done on Excel:

=SUM(100*(1+0.04)^5)

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Example

Present Value of 100 dollars five years in

the future.

100 / (1.0 + .04)5 = $82.19

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On Excel:

=SUM(100/(1+0.04)^5)

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Would you rather pay $15,000 now

for a years worth of your

newborns education or $30,000

eighteen years from now?

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Present value of $30,000 eighteen

years into the future + 30000

divided by (1+.04)18 = $14,809

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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

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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 Valueis a criterion for deciding whether agovernment program can be justified on economic

principles.

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Net Present Value (NPV)

NPV is the future stream of benefits and costsconverted into equivalent values today

Programs with a positive NPV are generally costeffective

Programs with negative NPV are generally not cost

effective

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CalculatingNPV

Assign monetary values to benefits and costs

Discount future benefits and costs using anappropriate discount rate

Subtract the sum total of discounted costsfrom the sum total of discounted benefits

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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?

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Project Example

You cannot directly compare two different

years without discounting

2006 is Present Value

2007 is Future Value

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Project Example

You must find the PRESENT VALUE ofProject B in 2006 to compare

Since this is a government project, well use4.5% interest on a US Treasury Bond as theDiscount Rate

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Project Example

The PRESENT VALUE of Project B is

determined by:

$5,200 / (1+ 0.045) = $4,976

NPV = $4,976

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Project Example

After discounting, the present value of :

Project A = $5,000

Project B = $4,976

Choose Project A

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Real World Example

New County Historical Society & Museum Construction cost: $10,000,000

Visitor ticket: $15

Annual expected visitors 56,700

Expected growth of visitors 12% (for 10 year

horizon) Annual maintenance costs $10,000 w/7% growth

Annual repair expenses $5,000 w/7% growth

Discount rate 4.85% (10 yr TreasuryBond Rate)

Depreciation $285,714 w/5% growth Capital Expenditure $300,000

Inventory, etc. $5,000 w/5% growth

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Real World Example

For each year of payback of 10 year project: Projected revenuesannual maintenance and repair expenses =

Benefits

Add benefits + depreciation

Subtract capital expenditure for the year and change in working capitalto get Free Cash Flows

Free Cash Flows/(1+.0485) to the power of the year number (1-10) forPresent Value of Cash Flows (PVCF)

Total of ten years PVCF Cost of Construction = NPV

NPV this project is $249,758; generally cost effective

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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 sameformula, our NPV result is a negative ($2,698,349),

a major loss and commonly viewed as not cost-

effective

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Summary

As local officials and decision-makers, it isonly necessary to understand the conceptsso you can make informed decisions based

on data presented to you by your financialstaff or consultants, it is not necessary to beable to perform these calculations