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Cost-Benefit Discounting - YouTube
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in this video we're going to look at why
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you discount the future when doing
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cost-benefit analysis would you rather
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receive $100 today or $100 in 10 years
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I'll tell you what you want before you
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answer and it's going to be right you
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would want $100 today because you can do
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stuff with it now you could lend that
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hundred dollars to the bank who will pay
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you interest for it and after 10 years
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you would just have more than $100 or
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you could buy a violin a crappy violin
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learn to play and in 10 years make some
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sort of profession out of it or just
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simply have gained that enjoyment from
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it an enjoyment that you would have had
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to wait for if you had received $100 in
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10 years also you could be dead in the
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future you know that dog you had when
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you were a kid and your parents said it
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went on doggie vacation it's not on
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vacation it's dead everyday into the
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future is another day we are uncertain
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we will be alive so we prefer to have
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things in the present there is an
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opportunity to do things with money
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goods and services today as well as an
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inherent risk that we might not be able
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to enjoy them in the future whether
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you're going to buy something or save
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the money there is a greater value in
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having something in the present than
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having it in the future it's not that it
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physically has less value this isn't
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about inflation or anything like that
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and for our purposes here we're using
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the real value and assuming that $100
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today buy is the same amount of stuff as
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$100 in ten years
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it's just that having money goods or
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services earlier lets you do things with
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it that may increase its value to you so
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when comparing costs and benefits across
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different time periods we discount the
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future we ask what is $100 gained in 10
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years worth today what is the present
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value of $100 from 10 years from now but
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let's first calculate what $100 from
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today would be in ten years okay
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what's the future value of $100 in ten
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years we'll use the bank's interest rate
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to represent that because that's a good
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basis for what we would be doing with
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the money
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just putting it in a bank let's assume
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the money grows by 5% a year with
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compounding interests we would multiply
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$100 by 1.05 to grow it by 5% one to
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account for the money we already had
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that we'll get back and point zero five
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to account for the interest will earn
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okay then we take that hundred and five
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dollars and multiply it by one point
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zero five again for the next year then
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we do that eight more times or we could
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have just written it like this taking
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the 1 plus the interest rate to the
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power of 10 since we're just multiplying
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it by the interest rate for 10 years
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so $100 after ten years of interest is a
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hundred and sixty two dollars and eighty
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nine cents
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the future value of one hundred dollars
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from today in ten years is one hundred
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and sixty two dollars and eighty nine
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cents back to that first hypothetical
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situation this is how much we would
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expect to receive if we were to give up
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a hundred dollars today we would want at
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least a hundred and sixty two dollars
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and eighty nine cents in ten years time
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because if we got a hundred dollars
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today we could make it into that much by
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lending it out for ten years so if the
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question were would you rather receive a
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hundred dollars today or one hundred and
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sixty two dollars and 89 cents in ten
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years since these are basically
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equivalent you should have no preference
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to do it the other way to determine the
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present value we just divide by one plus
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the interest rate so if we were to get a
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hundred dollars in ten years what is the
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present value of that one hundred
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dollars take one hundred divided by 1.05
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ten times or one point zero five to the
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power of ten and we get sixty one
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dollars and thirty nine cents the
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present value of $100 received ten years
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from now is sixty one dollars and thirty
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nine cents this is the amount of money
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that if we put it into the bank for ten
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years it would become one hundred
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dollars so if you were asked would you
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rather receive sixty $1.39 today or $100
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in ten years these are also basically
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equivalent and you should have no
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preference this works for costs too
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would you rather pay $100 today or $100
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in ten years well let's look if we pay
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$100 today we would be out $100 but
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what's the present value of $100 costs
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in ten years it's the same calculation
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100 divided by 1.05 to the power of 10
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is 60 $1.39 so what that means is we
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could put 60 $1.39 in the bank today and
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it would grow to become $100 in ten
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years so paying in 10 years is easier
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that is if you plan for it by saving now
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otherwise it's still $100 cost
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remember it's not that the costs and
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benefits are less in the future
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discounting the future is just a
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decision-making tool we can use it to
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compare the costs and benefits of
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different projects to find out which
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gives the greater payoffs when
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considering this time preference of
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money and how each dollar is valued at
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different times the discount rate you
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choose is very important in this process
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there's no hard rule for which rate you
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might choose but it should be based on
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what the best alternative use of these
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resources are so if you're a private
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firm doing a financial
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analysis you may simply use the market
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interest rate or some other investment
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very similar to what we've been doing or
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if you have money coming in from
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different sources with different
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interest rates for the same project you
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would want to use a weighted average
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discount rate so like if 30% of your
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money came in from the bank at a 5%
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interest but the other 70% came from
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investors that expect a 17% return you
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would use a weighted average of the two
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interest rates you would take 30% of
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your 5% interest rate and 70% of your
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17% interest rate as your discount rate
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so 3/10 of 5% is one point five percent
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and 7 tenths of 17% is eleven point nine
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percent add them together and you get
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thirteen point four percent and this is
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the discount rate you will use for this
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project if you're doing an economic
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analysis you will look at the economic
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opportunity cost of capital what is the
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next best alternative use of these
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public funds the economic discount rate
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will be different from a financial rate
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it's typically lower this is partly
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because public entities the government
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have more patience than individuals the
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planning horizon accounts for more than
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just the life span of a single
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individuals viewpoint so that preference
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of consuming something in the present
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and that risk of personally not being
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able to experience something in the
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future isn't as important the factor
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from a societal point of view so more
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weight can be put on the future and a
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lower discount rate can be used remember
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with a higher discount rate less weight
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is given to the future with a lower
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discount rate more weight is given to
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the future a discount rate of zero would
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imply that the future has the same
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weight as the present so an individual
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setting up a Conservation Park with a
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fee would expect higher returns and
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discount the future more because he
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expects to enjoy the benefits as soon as
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he can whereas a government is more
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patient and discounts based on
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everyone's ability to enjoy secondly
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governments are usually able to borrow
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money at lower interest rates than
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private citizens or firms and there is
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less pressure to gain immediate benefits
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in other words the opportunity cost to
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public projects is lower so public
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projects use lower discount rates in
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situations where the market is very
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unstable or there is political unrest
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you might have to use a higher discount
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rate for example if you're going to
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invest in the forestry project in a
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place where there is an insurgency and
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slash and burn farming nearby you're
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going to want a bigger return from the
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forest to offset the fact that this
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whole thing might burn down before you
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can harvest it or it might be
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appropriated by rebels and it's
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not yours anymore if the bank or
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investors feel this is a risky
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investment they will expect a higher
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return and the discount rate must be
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hired to account for this contrasted to
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that you'll accept a lower discount rate
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from a forest somewhere peaceful and
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maybe with a big forest firefighting
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team you'll use a smaller discount rate
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because you're more certain your
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investment will pay off you'll apply a
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higher discount rate to the payoffs from
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a risky investment then from the sure
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thing later on in the course we'll talk
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more about how we use discounting for
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now in the next video we'll look at some
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of the limitations of discounting and
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other considerations with respect to the
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time horizon of the project
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you
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