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Financial Management SeriesFinancial Management SeriesNumber 3Number 3Financial Management SeriesFinancial Management SeriesNumber 3Number 3

Using Net Present ValueUsing Net Present ValueTo EvaluateTo Evaluate

The Value of Money Over The Value of Money Over

TimeTimeAlan ProbstAlan ProbstLocal Government SpecialistLocal Government SpecialistLocal Government Center Local Government Center UWUW--ExtensionExtension

Using Net Present ValueUsing Net Present ValueTo EvaluateTo Evaluate

The Value of Money Over The Value of Money Over

TimeTimeAlan ProbstAlan ProbstLocal Government SpecialistLocal Government SpecialistLocal Government Center Local Government Center UWUW--ExtensionExtension

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Financial ManagementFinancial ManagementFinancial ManagementFinancial Management

Fiscal PolicyFiscal PolicySound financial decisionSound financial decision- -makingmaking

results from an informed fiscalresults from an informed fiscalpolicy and a solid understanding of policy and a solid understanding of the value of money and thethe value of money and thevehicles through which it isvehicles through which it ismanagedmanaged ..

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Financial ManagementFinancial ManagementFinancial ManagementFinancial Management

Financial Decisions require consideration of:Financial Decisions require consideration of:

Projected revenues over the period of Projected revenues over the period of time being consideredtime being considered

Projected operating expenditures over Projected operating expenditures over the period being consideredthe period being considered

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Financial ManagementFinancial Management(cont.)(cont.)

Financial ManagementFinancial Management(cont.)(cont.)

The governmental bodys ability toThe governmental bodys ability toacquire financing, now and in the futureacquire financing, now and in the future

Present and future value of moneyPresent and future value of moneywhen applied to the project beingwhen applied to the project beingconsidered.considered.

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Financial DecisionFinancial Decision- -MakingMaking

Performing a Cost/Benefit Analysis isPerforming a Cost/Benefit Analysis isessential to sound financial decisionessential to sound financial decision- -makingmaking

A critical part of a Cost Benefit Analysis is A critical part of a Cost Benefit Analysis isdetermining the value of money over timedetermining the value of money over time

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T ime Value of Money T ime Value of Money

Moneys value changes over timeMoneys value changes over time

A dollar today is worth more than a dollar A dollar today is worth more than a dollartomorrow tomorrow

When time value is considered, the cost When time value is considered, the cost- -effectiveness of a project can changeeffectiveness of a project can change

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T odays dollar is worth more T odays dollar is worth morebecause:because:

Interest ratesInterest rates$100 you invest at a 4% interest rate today will be worth $104 in 1 year,$100 you invest at a 4% interest rate today will be worth $104 in 1 year,thus making todays money worth morethus making todays money worth moreInflationInflation

You purchase 20 items today at $1.00 each for $20.00 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 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. T hus, you can only purchase 13.33 of that same item with our $20.00. T hus,todays money is worth more.todays money is worth more.

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Value of Money Over T ime Value of Money Over T ime

Future ValueFuture ValueMeasures what todays money would be worth at aMeasures what todays money would be worth at aspecified time in the future assuming a certainspecified time in the future assuming a certain

discount ratediscount rate

Present ValuePresent ValueMeasures what money at a specified period of time inMeasures what money at a specified period of time inthe future would be worth if valued in terms of todaysthe future would be worth if valued in terms of todaysmoneymoney

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Discount RateDiscount RateT he rate used in calculating the present value of T he rate used in calculating the present value of expected yearly benefits and costsexpected yearly benefits and costs

Used to reflect the time value of moneyUsed to reflect the time value of money

T he higher the discount rate, the lower the present T he higher the discount rate, the lower the present value of future cash flows value of future cash flows

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Real vs NominalReal vs NominalDiscount RatesDiscount Rates A nominal discount rate that reflects A nominal discount rate that reflects

expected inflation should be used toexpected inflation should be used todiscount nominal benefits and costsdiscount nominal benefits and costsMarket interest rates are nominal interestMarket interest rates are nominal interest

ratesrates

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Real vs. NominalReal vs. Nominal A real discount rate adjusted to eliminate the effect A real discount rate adjusted to eliminate the effectof expected inflations should be used to discountof expected inflations should be used to discountconstantconstant- -dollar or real benefit benefits and costsdollar or real benefit benefits and costs A real discount rate can be approximated by A real discount rate can be approximated bysubtracting expected inflation from a nominalsubtracting expected inflation from a nominalinterest rateinterest rate

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Real Discount RateReal Discount Rate

(1+ Nominal Interest Rate) = (1 + Real(1+ Nominal Interest Rate) = (1 + RealInterest Rate) * (1 + Inflation rate)Interest Rate) * (1 + Inflation rate)

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Free Cash FlowsFree Cash Flows

Free Cash Flow Free Cash Flow is a measure of cashis a measure of cashflow remaining after allflow remaining after allexpenditures required to maintainexpenditures required to maintainthe operationthe operation

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Future VS Present ValueFuture VS Present ValueFuture ValueFuture Value = Present Value X (1+discount= Present Value X (1+discountrate) raised to a power of the number of rate) raised to a power of the number of

years years

Present ValuePresent Value = Future Value/ (1+discount= Future Value/ (1+discountrate) raised to a power of the number of rate) raised to a power of the number of

years years

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E xampleE xample

Future value of 100 of todays dollars inFuture value of 100 of todays dollars infive years.five years.

100 X (1.0 + .04)100 X (1.0 + .04) 55 = 121.67 where .04 is the= 121.67 where .04 is thediscount rate.discount rate.

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Done on E xcel:Done on E xcel:

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

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E xampleE xample

Present Value of 100 dollars five years inPresent Value of 100 dollars five years inthe future.the future.

100 / (1.0 + .04)100 / (1.0 + .04) 55 = $82.19= $82.19

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On E xcel:On E xcel:

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

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Would you rather pay $15,000 now Would you rather pay $15,000 now

for a years worth of yourfor a years worth of yournewborns education or $30,000newborns education or $30,000eighteen years from now?eighteen years from now?

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Present value of $30,000 eighteenPresent value of $30,000 eighteen

years into the future + 30000 years into the future + 30000divided by (1+.04)divided by (1+.04) 18 = $18 = $14,80914,809

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So why is this important?So why is this important?

Understanding the time value of money canUnderstanding the time value of money can

help you identify misconceptions about realhelp you identify misconceptions about realcosts and benefits of projects or courses of costs and benefits of projects or courses of actionaction

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So why is this important?So why is this important?Future value, present value, and discount rates are used toFuture value, present value, and discount rates are used todeterminedetermine Net Present ValueNet Present Value

Net Present ValueNet Present Value is a component of Cost Benefit Analysisis a component of Cost Benefit Analysis

Net Present ValueNet Present Value is a criterion for deciding whether ais a criterion for deciding whether agovernment program can be justified on economicgovernment program can be justified on economic

principles. principles.

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Net Present Value (NPV)Net Present Value (NPV)NPV is the future stream of benefits and costsNPV is the future stream of benefits and costsconverted into equivalent values todayconverted into equivalent values today

Programs with a positive NPV are generally costPrograms with a positive NPV are generally costeffectiveeffective

Programs with negative NPV are generally not costPrograms with negative NPV are generally not costeffectiveeffective

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CalculatingCalculating NPV NPV

Assign monetary values to benefits and costs Assign monetary values to benefits and costsDiscount future benefits and costs using anDiscount future benefits and costs using anappropriate discount rateappropriate discount rateSubtract the sum total of discounted costsSubtract the sum total of discounted costsfrom the sum total of discounted benefitsfrom the sum total of discounted benefits

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Project E xampleProject E xample

Project A produces $5,000 of revenue in 2006Project A produces $5,000 of revenue in 2006

Project B produces $5,200 of revenue in 2007Project B produces $5,200 of revenue in 2007

Which is the more fiscally sound project? Which is the more fiscally sound project?

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You cannot directly compare two different You cannot directly compare two different years without discounting years without discounting

2006 is Present Value2006 is Present Value

2007 is Future Value2007 is Future Value

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You must find the PR E SE N T VALU E of You must find the PR E SE N T VALU E of Project B in 2006 to compareProject B in 2006 to compare

Since this is a government project, well useSince this is a government project, well use4.5% interest on a US T reasury Bond as the4.5% interest on a US T reasury Bond as theDiscount RateDiscount Rate

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After discounting, the present value of : After discounting, the present value of :

Project A Project A == $5,000$5,000

Project B = $4,976Project B = $4,976

Choose Project A Choose Project A

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Real World E xampleReal World E xampleNew County Historical Society & MuseumNew County Historical Society & Museum

Construction cost:Construction cost: $10,000,000$10,000,000 Visitor ticket: Visitor ticket: $15$15 Annual expected visitors Annual expected visitors 56,70056,700E

xpected growth of visitorsE

xpected growth of visitors 12% (for 10 year12% (for 10 yearhorizon)horizon) Annual maintenance costs Annual maintenance costs $10,000 w/7% growth$10,000 w/7% growth Annual repair expenses Annual repair expenses $5,000 w/7% growth$5,000 w/7% growthDiscount rateDiscount rate 4.85% (10 yr T reasury4.85% (10 yr T reasury

Bond Rate)Bond Rate)

DepreciationDepreciation $285,714 w/5% growth$285,714 w/5% growthCapital E xpenditureCapital E xpenditure $300,000$300,000Inventory, etc.Inventory, etc. $5,000 w/5% growth$5,000 w/5% growth

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Real World E xampleReal World E xample

For each year of payback of 10 year project:For each year of payback of 10 year project:Projected revenuesProjected revenues annual maintenance and repair expenses =annual maintenance and repair expenses =BenefitsBenefits

Add benefits + depreciation Add benefits + depreciationSubtract capital expenditure for the year and change in working capitalSubtract capital expenditure for the year and change in working capitalto get Free Cash Flowsto get Free Cash FlowsFree Cash Flows/(1+.0485) to the power of the year number (1Free Cash Flows/(1+.0485) to the power of the year number (1- -10) for10) forPresent Value of Cash Flows (PVCF)Present Value of Cash Flows (PVCF)T otal of ten years PVCF T otal of ten years PVCF Cost of Construction = NPV Cost of Construction = NPV

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

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Real World E xampleReal World E xample

HOW E V E R, if you decrease the expected growthHOW E V E R, if you decrease the expected growthrate in paying visitors from 12% to only 5% therate in paying visitors from 12% to only 5% theentire picture changesentire picture changes

With only a 5% expected increase, using the same With only a 5% expected increase, using the sameformula, our NPV result is a negativeformula, our NPV result is a negative ($2,698,349)($2,698,349),,a major loss and commonly viewed asa major loss and commonly viewed as not costnot cost--effectiveeffective

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SummarySummary

As local officials and decision As local officials and decision- -makers, it ismakers, it isonly necessary to understand the conceptsonly necessary to understand the conceptsso you can make informed decisions basedso you can make informed decisions basedon data presented to you by your financialon data presented to you by your financialstaff or consultants, it is not necessary to bestaff or consultants, it is not necessary to beable to perform these calculationsable to perform these calculations

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Fm 3 Value