Lesson 4: Net Present Value (NPV) -
Transcript of Lesson 4: Net Present Value (NPV) -
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Lesson 4:Net Present Value (NPV)
The Bottom Line
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Learning Objectives
1. Understand the concept of net present value (NPV)A. What it isB. What it meansC. Why it is important
2. Understand the importance of a common time horizon
3. Understand the concept of internal rate of return (IRR) and its relationship to NPV
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Comparing Economic Performance
• Suppose we are trying to choose between two forestry rotations that each would require a $500/ac cost today for site preparation and planting– Rotation A would yield $1,000/ac at year 20 and $2,000/ac at
year 40– Rotation B would yield $4,000/ac at year 40
• Which rotation performs better economically? Should we invest in either??
• We cannot simply add the yields and subtract the costs, because they occur at different times– Rotation A: $1,000 + $2,000 - $500 = $2,500– Rotation B: $4,000 - $500 = $3,500
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Apples to Apples
• In order to make an “apples to apples”comparison, we need to have a common time reference
• We can do this by finding the present value of each cash flow
• When we add up these discounted cash flowswe arrive at the Net Present Value (NPV)
• The higher the NPV, the better the economic return
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Finding the NPV of our example rotations
• Rotation A:
• Rotation B:
0 20 40
Plant-$500
Harvest$1,000
Harvest$2,000
0 40
Plant-$500
Harvest$4,000
$
$
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NPV of our example rotations @ 5% interest
• NPV of Rotation A:
• NPV of Rotation B:
( ) ( )
161$284$377$500$
05.1000,2$
05.1000,1$500$ 4020
=++−=
++
++−=ANPV
( )
68$568$500$
05.1000,4$500$ 40
=+−=
++−=BNPV
Higher NPV
Try it using the Economagic Calculator
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Interpreting NPV
• Positive NPV– Present value of revenues > Present value of
costs– Future revenues exceed costs plus interest
• Negative NPV – Present value of revenues < Present value of
costs– Future revenues do not cover costs plus
interest• High costs (relative to revenues)• High interest rate
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Example
Suppose you are considering pruning your stand at a cost of $150/ac. You expect this to increase your stumpage value by $500/ac when you harvest in 20 years. Is this a good investment given a 5% interest rate?
( )
38$188$150$
05.1500$150$ 20
=+−=
++−=NPV
NPV is > 0, so it is a good investment
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Example• Suppose you are considering growing a
rotation of Douglas-fir. – Cost of $300/ac for site preparation and planting in
year 0– Cost of $100/ac for precommercial thin (PCT) in
year 15 – $1,500/ac commercial thin (CT) revenue in year 35– $10,000/ac revenue in year 50 for final harvest
• What is the NPV of this project at:– 5%? – 10%?
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• NPV @ 5%:
• NPV @ 10%:
NPV at different interest rates
( ) ( ) ( )
$796=
++−−=+
++
++
−−
872$272$48$300$05.1000,10$
05.1500,1$
05.1100$300$ 503515
( ) ( ) ( )
$186−=++−−=
++
++
+−−
85$53$24$300$10.1000,10$
10.1500,1$
10.1100$300$ 503515
0 15 35 50
Plant-$300
PCT-$100
CT$1,500
H$10,000
$
Try it with the Economagic Calculator
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Appropriate rate of return
• The interest rate makes a huge difference!• What should we use for i when evaluating
NPV?• The interest rate should reflect:
– An individual’s time preference– Cost of capital (if borrowing the money to
cover expenses)– Alternative rate of return—what you could get
if investing money elsewhere (opportunity cost)
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Mixing Series and Single Sums (the real world)
• Often a project will include cash flow series and individual cash flows. NPV calculations can include both of these.
• Example: suppose you want to grow a rotation of Douglas-fir. – Cost of $300/ac for planting and site prep in year 0– Cost of $100/ac in year 15 for PCT– $1,500/ac CT revenue in year 35– $10,000/ac revenue in year 50 for final harvest– $20/ac/year annual administrative costs
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NPV @ 5% Interest
( ) ( ) ( )( )
( )
431$365$872$272$48$300$
05.105.105.120$
05.1000,10$
05.1500,1$
05.1100$300$ 50
50
503515
=−++−−=
⎥⎦
⎤⎢⎣
⎡
+−+
−+
++
++
−−
Try it with the Economagic Calculator
Present values of single sumsPresent values of terminating annual series
0 15 35 50
Plant-$300
PCT-$100
CT$1,500
H$10,000
-$20 each year
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NPV and unequal time horizons
• Suppose you are trying to choose between using an acre of land to grow different species at an interest rate of 5%:– Grow Douglas-fir
• $250/ac planting and site prep• $100/ac PCT in year 15• $3,000/ac CT revenue in year 40• $18,000/ac final harvest revenue in year 60
– Grow red alder• $250/ac planting and site prep• $5,000/ac final harvest revenue in year 30
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Timeline
0 15 40 60
0 30
Plant-$250
PCT-$100
CT$3,000
H$18,000
Plant-$250
H$5,000
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• Douglas-fir:
• Red alder:
• So is Douglas-fir really the best option?
( ) ( ) ( )092,1$
05.1000,18$
05.1000,3$
05.1100$250$ 604015
=
++−−=NPV
( )907$
05.1000,5$250$ 30
=
+−=NPV
Compare the NPVs
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But wait—We could grow two rotations of red alder in the time it takes to grow
one Douglas-fir rotation
0 15 40 60
0 30
Plant-$250
PCT-$100
CT$3,000
H$18,000
Plant-$250
H$5,000
Plant-$250
H$5,000
60
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• Douglas-fir:
• Red alder:
( ) ( ) ( )$1,092=
++−−= 604015 05.1000,18$
05.1000,3$
05.1100$250$NPV
( ) ( ) ( )$1,117=
+−+−= 603030 05.1000,5$
05.1250$
05.1000,5$250$NPV
Now which is the best option?
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Internal Rate of Return
• The Internal Rate of Return (IRR) is the interest rate i that makes the NPV = zero
• This is another approach to comparing investments that is not dependent on a particular interest rate
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Finding IRR
• “Guess & Check”• Example: Find the IRR of the following
rotation. – Cost of $350/ac for planting and site prep in
year 0– Cost of $100/ac in year 15 for PCT– $14,273/ac revenue in year 50 for final
harvest
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1st Attempt: 7%
( ) ( )5015 07.1273,14$
07.1100$350$ +−−=NPV
98$484$36$350$
=+−−=
If NPV is positive, try a higher i
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2nd Attempt: 8%
( ) ( )5015 08.1273,14$
08.1100$350$ +−−=NPV
77$304$31$350$
−=+−−=
If NPV is negative, try a lower i
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3rd Attempt: 7.5%
( ) ( )5015 075.1273,14$
075.1100$350$ +−−=NPV
IRR==
+−−=
%5.70$
384$34$350$
When NPV = 0, i = IRR
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NPV vs. IRR
• The alternative with the highest NPV at a given interest rate might not be the one with the highest IRR—which is the better measure?
• Identifying the appropriate interest rate and computing NPV will best reflect performance given the time preference of the investor
• IRR can be useful if the appropriate interest rate is unknown
• NPV and IRR together tell us more than either one alone
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References• Gansner, D.A. and D.N. Larsen. 1969. Pitfalls of using
internal rate of return to rank investments in forestry. Research Note NE-106. USDA Forest Service Northeastern Forest Experiment station. 5 p.
• Gunter, J.E. and H.L. Haney. 1984. Essentials of Forestry Investment Analysis. Oregon State University Bookstores Inc., Corvallis, Oregon. 337 p.
• Klemperer, D.W. 1996. Forest Resource Economics and Finance. McGraw Hill, New York. 551 p.
• Zobrist, K.W. 2005. Economically Sustainable Working Forests: Financial Analysis Principles and Applications. Northwest Environmental Forum, College of Forest Resources, University of Washington, Seattle, WA. 16 p.