Financial Management Series Number 3 Using Net Present Value To Evaluate The Value of Money Over Time Alan Probst Local Government Specialist Local Government.

Financial Management Series Financial Management Series Number 3Number 3

Financial Management Series Financial Management Series Number 3Number 3

Using Net Present ValueUsing Net Present ValueTo EvaluateTo Evaluate

The Value of Money Over The Value of Money Over TimeTime

Alan ProbstAlan ProbstLocal Government SpecialistLocal Government SpecialistLocal Government CenterLocal Government CenterUW-ExtensionUW-Extension

Using Net Present ValueUsing Net Present ValueTo EvaluateTo Evaluate

The Value of Money Over The Value of Money Over TimeTime

Alan ProbstAlan ProbstLocal Government SpecialistLocal Government SpecialistLocal Government CenterLocal Government CenterUW-ExtensionUW-Extension

Financial ManagementFinancial ManagementFinancial ManagementFinancial Management

Fiscal PolicyFiscal PolicySound financial decision-making Sound financial decision-making

results from an informed fiscal results from an informed fiscal policy and a solid understanding of policy and a solid understanding of the value of money and the the value of money and the vehicles through which it is vehicles through which it is managedmanaged..

Financial ManagementFinancial Management Financial 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

Financial Management Financial Management (cont.) (cont.)

Financial Management Financial Management (cont.) (cont.)

• The governmental body’s ability to The governmental body’s ability to acquire financing, now and in the futureacquire financing, now and in the future

• Present and future value of money Present and future value of money when applied to the project being when applied to the project being considered.considered.

Financial Decision-Financial Decision-MakingMaking

When making financial decisions for a When making financial decisions for a governmental body, the same governmental body, the same rational doesn’t necessarily apply as rational doesn’t necessarily apply as is used in managing one’s own is used in managing one’s own personal finances.personal finances.

What looks like a “common sense” What looks like a “common sense” good idea at first may turn out to be good idea at first may turn out to be a bad financial decision when worked a bad financial decision when worked through the formulasthrough the formulas

Financial Decision-Financial Decision-MakingMaking

Performing a Cost/Benefit Performing a Cost/Benefit Analysis is essential to sound Analysis is essential to sound financial decision-makingfinancial decision-making

A critical part of a Cost Benefit A critical part of a Cost Benefit Analysis is determining the value Analysis is determining the value of money over timeof money over time

Time Value of MoneyTime Value of Money

• Money’s value changes over timeMoney’s value changes over time

• A dollar today is worth more than A dollar today is worth more than a dollar tomorrowa dollar tomorrow

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

Today’s dollar is worth Today’s dollar is worth more because:more because:

• Interest ratesInterest rates$100 you invest at a 4% interest rate today will be $100 you invest at a 4% interest rate today will be worth $104 in 1 year, thus making today’s money worth $104 in 1 year, thus making today’s money worth moreworth more

• InflationInflationYou purchase 20 items today at $1.00 each for $20.00You purchase 20 items today at $1.00 each for $20.00After one year, due to inflation, those same items After one year, due to inflation, those same items cost $1.50 each and you can only purchase 13.33 of cost $1.50 each and you can only purchase 13.33 of that same item with our $20.00. Thus, today’s money that same item with our $20.00. Thus, today’s money is worth more.is worth more.

Value of Money Over Value of Money Over TimeTime

Future ValueFuture ValueMeasures what today’s money would be Measures what today’s money would be

worth at a specified time in the future worth at a specified time in the future assuming a certain discount rateassuming a certain discount rate

Present ValuePresent ValueMeasures what money at a specified period Measures what money at a specified period

of time in the future would be worth if of time in the future would be worth if valued in terms of today’s moneyvalued in terms of today’s money

Discount RateDiscount Rate

• The rate used in calculating the The rate used in calculating the present value of expected yearly present value of expected yearly benefits and costsbenefits and costs

• Used to reflect the time value of Used to reflect the time value of moneymoney

• The higher the discount rate, the The higher the discount rate, the lower the present value of future cash lower the present value of future cash flowsflows

Real vs Nominal Real vs Nominal Discount RatesDiscount Rates

A nominal discount rate that A nominal discount rate that reflects expected inflation should reflects expected inflation should be used to discount nominal be used to discount nominal benefits and costsbenefits and costs

Market interest rates are Market interest rates are nominal interest ratesnominal interest rates

Real vs. NominalReal vs. Nominal A real discount rate adjusted to A real discount rate adjusted to

eliminate the effect of expected eliminate the effect of expected inflations should be used to discount inflations should be used to discount constant-dollar or real benefit benefits constant-dollar or real benefit benefits and costsand costs

A real discount rate can be A real discount rate can be approximated by subtracting expected approximated by subtracting expected inflation from a nominal interest rateinflation from a nominal interest rate

Real Discount RateReal Discount Rate

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

Free Cash FlowsFree Cash Flows

Free Cash FlowFree Cash Flow is a measure is a measure of cash flow remaining of cash flow remaining after all expenditures after all expenditures required to maintain the required to maintain the operationoperation

Future VS Present Future VS Present ValueValue• Future Value Future Value = Present Value X = Present Value X

(1+discount rate) raised to a (1+discount rate) raised to a power of the number of yearspower of the number of years

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

ExampleExample

Future value of 100 of today’s Future value of 100 of today’s dollars in five years.dollars in five years.

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

Done on Excel:Done on Excel:

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

ExampleExample

Present Value of 100 dollars Present Value of 100 dollars five years in the future.five years in the future.

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

On Excel:On Excel:

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

Would you rather pay Would you rather pay $15,000 now for a year’s $15,000 now for a year’s worth of your newborn’s worth of your newborn’s

education or $30,000 education or $30,000 eighteen years from now?eighteen years from now?

Present value of $30,000 Present value of $30,000 eighteen years into the eighteen years into the future + 30000 divided future + 30000 divided by (1+.04)by (1+.04)18 = $18 = $14,80914,809

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

Understanding the time value of Understanding the time value of money can help you identify money can help you identify misconceptions about real costs misconceptions about real costs and benefits of projects or and benefits of projects or courses of actioncourses of action

So why is this So why is this important?important?• Future value, present value, and discount Future value, present value, and discount

rates are used to determine rates are used to determine Net Present Net Present ValueValue

• Net Present Value Net Present Value is a component of Cost is a component of Cost Benefit AnalysisBenefit Analysis

• Net Present ValueNet Present Value is a criterion for deciding is a criterion for deciding whether a government program can be whether a government program can be justified on economic principles.justified on economic principles.

Net Present Value (NPV)Net Present Value (NPV)• NPV is the future stream of benefits NPV is the future stream of benefits

and costs converted into equivalent and costs converted into equivalent values todayvalues today

• Programs with a positive NPV are Programs with a positive NPV are generally cost effectivegenerally cost effective

• Programs with negative NPV are Programs with negative NPV are generally not cost effectivegenerally not cost effective

CalculatingCalculating NPVNPV

• Assign monetary values to Assign monetary values to benefits and costsbenefits and costs

• Discount future benefits and Discount future benefits and costs using an appropriate costs using an appropriate discount ratediscount rate

• Subtract the sum total of Subtract the sum total of discounted costs from the sum discounted costs from the sum total of discounted benefitstotal of discounted benefits

Project ExampleProject Example

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

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

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

Project ExampleProject Example

• You cannot directly compare two You cannot directly compare two different years without different years without discountingdiscounting

• 2006 is Present Value2006 is Present Value

• 2007 is Future Value2007 is Future Value

Project ExampleProject Example

You must find the PRESENT You must find the PRESENT VALUE of Project B in 2006 to VALUE of Project B in 2006 to comparecompare

Since this is a government Since this is a government project, we’ll use 4.5% interest project, we’ll use 4.5% interest on a US Treasury Bond as the on a US Treasury Bond as the Discount RateDiscount Rate

Project ExampleProject Example

• The PRESENT VALUE of Project The PRESENT VALUE of Project B is determined by:B is determined by:

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

NPV = $4,976NPV = $4,976

Project ExampleProject Example

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

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

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

Choose Project A Choose Project A

Real World ExampleReal World Example

New 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 visitorsAnnual expected visitors 56,700 56,700 Expected growth of visitorsExpected growth of visitors 12% (for 10 year 12% (for 10 year

horizon) horizon) Annual maintenance costsAnnual maintenance costs $10,000 w/7% growth $10,000 w/7% growth Annual repair expensesAnnual repair expenses $5,000 w/7% growth $5,000 w/7% growth Discount rateDiscount rate 4.85% (10 yr Treasury 4.85% (10 yr Treasury

Bond Rate) Bond Rate) DepreciationDepreciation $285,714 w/5% growth $285,714 w/5% growth Capital ExpenditureCapital Expenditure $300,000 $300,000 Inventory, etc.Inventory, etc. $5,000 w/5% growth $5,000 w/5% growth

Real World ExampleReal World Example

For each year of payback of 10 For each year of payback of 10 year project:year project:

Projected revenues – annual maintenance and repair Projected revenues – annual maintenance and repair expenses = Benefitsexpenses = Benefits

Add benefits + depreciation Add benefits + depreciation Subtract capital expenditure for the year and change Subtract capital expenditure for the year and change

in working capital to get Free Cash Flowsin working capital to get Free Cash Flows Free Cash Flows/(1+.0485) to the power of the year Free Cash Flows/(1+.0485) to the power of the year

number (1-10) for Present Value of Cash Flows number (1-10) for Present Value of Cash Flows (PVCF)(PVCF)

Total of ten year’s PVCF – Cost of Construction = Total of ten year’s PVCF – Cost of Construction = NPV NPV

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

Real World ExampleReal World Example

HOWEVER, if you decrease the HOWEVER, if you decrease the expected growth rate in paying expected growth rate in paying visitors from 12% to only 5% the visitors from 12% to only 5% the entire picture changesentire picture changes

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

SummarySummary

As local officials and decision-As local officials and decision-makers, it is only necessary to makers, it is only necessary to understand the concepts so you understand the concepts so you can make informed decisions can make informed decisions based on data presented to you based on data presented to you by your financial staff or by your financial staff or consultants, it is not necessary to consultants, it is not necessary to be able to perform these be able to perform these calculations calculations