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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 Center UW-Extension Using Net Present Value To Evaluate The Value of Money Over Time Alan Probst Local Government Specialist Local Government Center UW-Extension

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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.

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Financial Management Financial Management Financial Decisions require consideration of: Projected revenues over the period of time being considered Projected revenues over the period of time being considered Projected operating expenditures over the period being considered Projected operating expenditures over the period being considered

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Financial Management (cont.) The governmental bodys ability to acquire financing, now and in the future 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. Present and future value of money when applied to the project being considered.

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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

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Financial Decision-Making Performing a Cost/Benefit Analysis is essential to sound 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 A critical part of a Cost Benefit Analysis is determining the value of money over time

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Time Value of Money Time Value of Money Moneys value changes over time Moneys value changes over time A dollar today is worth more than a dollar tomorrow A dollar today is worth more than a dollar tomorrow When time value is considered, the cost- effectiveness of a project can change 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 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 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, todays money is worth more.

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Value of Money Over Time Future Value Measures what todays 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 todays money

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Discount Rate The rate used in calculating the present value of expected yearly benefits and costs The rate used in calculating the present value of expected yearly benefits and costs Used to reflect the time value of money Used to reflect the time value of money The higher the discount rate, the lower the present value of future cash flows The higher the discount rate, the lower the present value of future cash flows

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Real vs Nominal Discount Rates A nominal discount rate that reflects expected inflation should be used to discount nominal benefits and costs A nominal discount rate that reflects expected inflation should be used to discount nominal benefits and costs Market interest rates are nominal interest rates 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 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 A real discount rate can be approximated by subtracting 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 Flow is a measure of cash flow remaining after all expenditures required to maintain the operation

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Future VS Present Value Future Value = Present Value X (1+discount rate) raised to a power of the number of years 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 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 = $82.19 100 / (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 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 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 is a criterion for deciding whether a government program can be justified on economic principles.

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Net Present Value (NPV) NPV is the future stream of benefits and costs converted into equivalent values today 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 a positive NPV are generally cost effective Programs with negative NPV are generally not cost effective Programs with negative NPV are generally not cost effective

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Calculating NPV Assign monetary values to benefits and costs Assign monetary values to benefits and costs Discount future benefits and costs using an appropriate discount rate Discount future benefits and costs using an appropriate discount rate Subtract the sum total of discounted costs from the sum total of discounted benefits Subtract the sum total of discounted costs from the sum total of discounted benefits

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Project Example Project A produces $5,000 of revenue in 2006 Project A produces $5,000 of revenue in 2006 Project B produces $5,200 of revenue in 2007 Project 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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Project Example You cannot directly compare two different years without discounting You cannot directly compare two different years without discounting 2006 is Present Value 2006 is Present Value 2007 is Future Value 2007 is Future Value

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Project Example You must find the PRESENT VALUE of Project B in 2006 to compare You 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 Since this is a government project, well use 4.5% interest on a US Treasury Bond as the Discount Rate

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Project Example The PRESENT VALUE of Project B is determined by: 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 Construction cost: $10,000,000 Visitor ticket: $15 Visitor ticket: $15 Annual expected visitors 56,700 Annual expected visitors 56,700 Expected growth of visitors 12% (for 10 year horizon) Expected growth of visitors 12% (for 10 year horizon) Annual maintenance costs $10,000 w/7% growth Annual maintenance costs $10,000 w/7% growth Annual repair expenses $5,000 w/7% growth Annual repair expenses $5,000 w/7% growth Discount rate 4.85% (10 yr Treasury Bond Rate) Discount rate 4.85% (10 yr Treasury Bond Rate) Depreciation $285,714 w/5% growth Depreciation $285,714 w/5% growth Capital Expenditure $300,000 Capital Expenditure $300,000 Inventory, etc. $5,000 w/5% growth Inventory, etc. $5,000 w/5% growth

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Real World Example For each year of payback of 10 year project: Projected revenues – annual maintenance and repair expenses = Benefits Projected revenues – annual maintenance and repair expenses = Benefits Add benefits + depreciation Add benefits + depreciation Subtract capital expenditure for the year and change in working capital to get Free Cash Flows 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) Free 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 Total of ten years PVCF – Cost of Construction = NPV NPV this project is $249,758; generally cost effective 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 same formula, 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 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

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