Financial Management Series Number 3

Using Net Present ValueTo EvaluateThe Value of Money Over Time

Alan ProbstLocal Government SpecialistLocal Government CenterUW-Extension

Financial Management

Fiscal PolicySound 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 bodys 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 doesnt necessarily 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 when worked through the formulas

Financial Decision-MakingPerforming a Cost/Benefit Analysis is essential to sound financial decision-makingA critical part of a Cost Benefit Analysis is determining the value of money over time

Time Value of MoneyMoneys value changes over time

A dollar today is worth more than a dollar tomorrow

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

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 moreInflationYou purchase 20 items today at $1.00 each for $20.00After 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, todays money is worth more.

Value of Money Over Time

Future ValueMeasures what todays money would be worth at a specified time in the future assuming a certain discount rate

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

Discount RateThe 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 RatesA nominal discount rate that reflects expected inflation should be used to discount nominal benefits and costsMarket interest rates are nominal interest rates

Real vs. NominalA 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 FlowsFree Cash Flow is a measure of cash flow remaining after all expenditures required to maintain the operation

Future VS Present ValueFuture 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

ExampleFuture value of 100 of todays 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)

ExamplePresent 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 years worth of your newborns 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 NPVAssign monetary values to benefits and costsDiscount future benefits and costs using an appropriate discount rateSubtract the sum total of discounted costs from the sum total of discounted benefits

Project ExampleProject 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 ExampleYou cannot directly compare two different years without discounting

2006 is Present Value

2007 is Future Value

Project ExampleYou must find the PRESENT VALUE of Project B in 2006 to compare

Since this is a government project, well 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 ExampleAfter discounting, the present value of :

Project A = $5,000

Project B = $4,976

Choose Project A

Real World ExampleNew County Historical Society & MuseumConstruction cost: $10,000,000Visitor ticket: $15Annual expected visitors 56,700Expected growth of visitors 12% (for 10 year horizon)Annual maintenance costs $10,000 w/7% growthAnnual repair expenses $5,000 w/7% growthDiscount rate 4.85% (10 yr Treasury Bond Rate)Depreciation $285,714 w/5% growthCapital Expenditure $300,000Inventory, etc. $5,000 w/5% growth

Real World ExampleFor each year of payback of 10 year project:Projected revenues annual maintenance and repair expenses = BenefitsAdd benefits + depreciation Subtract capital expenditure for the year and change in working capital to get Free Cash FlowsFree Cash Flows/(1+.0485) to the power of the year number (1-10) for Present Value of Cash Flows (PVCF)Total of ten years PVCF Cost of Construction = NPV NPV this project is $249,758; generally cost effective

Real World ExampleHOWEVER, if you decrease the expected growth rate in paying visitors from 12% to only 5% the entire picture changesWith 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 cost-effective

SummaryAs 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

This is the same calculation done using Excel.

You see here how easy it is to apply the exponential or power number.Again, easy using a spreadsheet program.From an economic and financial perspective, you can decide whether a program is cost effective by determining Net Present Value.

If the NPV is positive; its cost effective.

If the NPV is negative; its not cost effective.

While this doesnt make the decision for you because you still have to consider the more intangible costs and benefits of the program, it does give you a good starting point to making the final decision.