taking time into account and making investment decisions
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- Taking Time Into Account and Making Investment Decisions
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- Overview What economic concepts do we draw on? Capital theory Discounting (time value of money) Cost Benefit Analysis What will we do? Computing Future Values and Present Values Evaluating Investments Using Different Investment Criteria And Examples And Formulas More formulas And even more
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- Example: Do you rebuild in Burns Lake? What information do you need?
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- Capital Theory Used to evaluate the value of assets and investments Examples of assets Durable goods (piece of equipment) Financial Assets (stocks and bonds) Land and natural resources (timberland or timber license) Used to evaluate investments and alternatives-should you invest in new equipment? How much? Can use to determine how much can you withdraw over time without compromising the value of your asset
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- Timberland Values Forests serve as an asset (a store of value) and also generate income In the standard model (private land) these values are embodied in land values (on which the timber grows) Estimated value of timberlands as an asset class $35-$40 billion (Reid Carter, Brookfield Asset Management)(2010) http://www.forestweb.com/Corporate/timberlandInvesting.cfm http://www.forestweb.com/Corporate/timberlandInvesting.cfm http://www.forestlegacy.com/fundamentals/ The Peel Commission in BC in 1991 estimated that the value of timber in BC ranged from $1 billion to $12 billion http://www.for.gov.bc.ca/hfd/pubs/Docs/Mr/Rc/Rc001d/V4BP001.pdf
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- Interest Rates Interest or rate of return Payment expected from holding an asset Types of interest Simple interest Earn interest only on principal Compound interest Earn interest on principal and accumulated interest What interest rate to use? Best alternative (opportunity cost), minimum acceptable rate; real or nominal What perspective? Private or public?
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- Why do we use interest rates? Time preference (social preferences) Opportunity cost Accounting for risk and chance of failure Accounting for inflation
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- Compounding and Discounting If you know value today (or series of values) you can compound them forward to some future point in time This gives you future value Alternatively you can convert those series of values into what they are worth today-this is present value (invert the formula)
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- How important is compounding and future value calculations? $5,000 invested in a tax free account today (with no further investment) at 8% and no taxes would yield $50,313 in 30 years $5k$50k if the account did incur taxes the same investment (at a 40% tax rate) would yield only $20,408 in 30 years. $5,000 invested each year for the next 30 years in a tax free account at 8% and no taxes would yield $566,416 in 30 years $150k $566k if the same investment was made in an account that did incur taxes the same investment (at a 40% tax rate) would yield only $321,008 in 30 years (44% less). TFSAs offer a good example.
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- Future Value of a Single Sum: V 1 = V 0 (1 + i) V 2 = V 0 (1 + i) (1 + i) V 3 = V 0 (1 + i) (1 + i) (1 + i) V n = V 0 (1 + i) n V n = V 0 (1 + i) (1 + i) .(1 + i) n - times............ Here V n is future value n periods in the future using compounding
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- Present Value of a Single Sum: V n = V 0 (1 + i) n V 0 = V n / (1 + i) n Divide both sides By (1 + i) n Here we calculate the present value, given the future value
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- Net Present Value: Definition: Present value of revenues minus the present value of costs. NPV = ( ) RyRy (1+i) y CyCy - y=0 n
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- Conventions Interest rates are given in yearly percentage rates of change unless otherwise stated. Costs and revenues occur at the same time of the year. Interest rates can be given either as a percentage (e.g. 8%) or a decimal value (e.g. 0.08). Year 0 is now.
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- Why Do This? Provides basis on which to make decisions Evaluate investment decisions-yes or no Compare alternative investments Determine proper investment amounts Establish valuations
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- Cost and Revenue Streams: 0123456789 10 Years $10,000 $5,000 $2,000 $3,000 $2,000 0123456789 10 Years $10,000 $5,000 Payment stream #1 Payment stream #2 Costs are shown in red and revenues in orange
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- Evaluating Payment Streams with no Discounting Here payment stream #1 is preferred (it pays off more)
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- Evaluating Payment Streams with a 5% Discount Rate Here payment stream #1 is still preferred (it pays off more) but not as much as in the previous example as it is discounted (note that $2,326 is the NPV)
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- Evaluating Payment Streams with a 10% Discount Rate Here payment stream #2 is now preferred. Note that payment stream #1 is now negative; this is because the future revenues are discounted more so the upfront costs are proportionately Greater.
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- Terminating Present or Future Value Series Single Sum Annual Payment Annual Periodic Annual Periodic Perpetual Meaning of Symbols: a = equal annual or periodic payment i = interest rate n = number of years or interest bearing periods t = interval between periodic payments V o = present (initial) value V n = future (end) value FormulaFormula Name Future ValueFuture Value of a Single Sum1 Present ValuePresent Value of a Single Sum2 Future Value Future Value of a Terminating Annual Series 3 Present Value Present Value of a Terminating Annual Series 4 Future Value Future Value of a Terminating Periodic Series 5 Present Value Present Value of a Terminating Periodic Series 6 Present Value Present Value of a Perpetual Annual Series 7 Present Value Present Value of a Perpetual Periodic Series 8 to accumulate a future amount Sinking Fund Formula9 to pay off an original investment Installment Payment (capital Recovery) Formula 10
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- Problem 1 Present value of a Periodic Series (pg. 109-110 in text) pppp 10203040 Common in forestry-recurring payments or costs as set intervals In example in book, assume $3,000 in Christmas tree revenues every 10 years and assume a 6% interest rate-what is the present value of this?
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- Problem 1 associated math V0=V0= p (1 + r) t - 1 V0=V0= $3,000 (1 +.06) 10 - 1 Use formula for present value of a perpetual periodic series (#8) Substitute in the values and determine that the present value is $3,739 This means that if you can earn 6% somewhere else, this is the most youd pay So if someone offered it to you for $3,500 youd be interested-but not if they wanted $3,800
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- Problem 2 How much will I need to make to justify my investment? Land purchase - $400/ha Planting cost - $200/ha Brushing and thinning (in 10 years time) - $75/ha 7% interest rate Expected harvest in 30 years
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- Problem 2 associated math Setting problem up -estimate how much revenue you will need in the future Calculating future values -600(1+.07) 30 = -$4,567.35 -$75(1+.07) 20 = - $290.23 Land and planting cost Brushing cost Total revenues needed in 30 years-$4,857.58
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- The Power of Time Note how much greater revenues have to be the longer you wait; Also notice the reduction in revenue required if you can shorten the harvest period by only one year (you need $318 less)
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- Decision Rules NPV = ( ) RtRt (1+r) t CtCt - t=0 n Criteria: a project is acceptable if the NPV exceeds 0. If you have multiple projects, you can rank them in preferred order by NPV (highest to lowest).
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- The IRR is the discount rate at which the present value of revenues minus the present value of costs is zero. R t C t (1 + IRR) t nn t=0 = 0 Therefore, the IRR is unique to each project. Projects are acceptable if IRR is greater or equal to the minimum acceptable rate of return [MAR]. Projects can be ranked by their IRR (highest is best). Typically assume MAR is equal to r, the real discount rate. When IRR=MAR=r(real discount rate) then NPV=0 Internal Rate of Return [IRR]
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- The benefit/cost ratio (or profitability index) is the present value of benefits divided by the present value of costs, using the investors MAR. If B/C=1 then NPV=); if B/C
- Using NPV to Evaluate Projects So Project D has an NPV of $758, greater than Project N with an NPV of $713 (based on 6% real rate). Both are acceptable (NPV>0); Project D>Project N. Note that the original outlay (expenditure) is included.
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- Evaluation Dependent on Interest Rate If the interest rate increases to 10%, note that Project D is no longer acceptable (negative NPV of -$36) while Project N is still acceptable (positive NPV).
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- Calculating the Internal Rate of Return for Project D Accept if IRR is greater than your Minimum Acceptable Rate of Return (MAR)
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- Calculating the Benefit/Cost Ratio B/C = 6,600 (1.06) 30 200 (1.06) 15 + 100 (1.06) 5 + 400 = 2.60 Here it is acceptable since B/C > 1 (benefits exceed costs)
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- Payback period For project D, you do not recover outlays until Year 30; for Pro
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