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Cost-Benefit Net Present Value - YouTube
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in an earlier video we looked at
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discounting now we're gonna see how to
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apply it to determine a project's
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feasibility let's look at the net
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present value let's say these are your
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total cash flows for the project you've
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got the large costs at the beginning to
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build it and get started
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you've got the upkeep and maintenance
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costs every year and every year you gain
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the benefits I don't know what this
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project would be maybe it's like a train
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or something adding the costs and the
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benefits for each of the years gives you
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the net benefits or costs for each year
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and then combining the net benefits for
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the whole project shows you you will net
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two thousand dollars for the whole
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project but we haven't discounted yet so
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let's do that now let's use a discount
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rate of 10% so we divide each year by
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one plus the discount rate to the power
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of the year so that's one point one to
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the power of zero for the present year
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which is just one so it doesn't change
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which makes sense for the present year
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one point one ^ 1 for the first year 1
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point 1 ^ 2 for the second year 1 point
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1 ^ 3 for the third year and so on these
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are now the net present benefits or net
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present costs for each year now if we
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add all this up we find the net present
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value for the project 355 dollars so
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that's bad why is it so much less now we
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value gains and losses in the future
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less than me value gains and losses
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today so the gains we got later in the
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project aren't as important when we
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consider the opportunity cost of capital
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for most projects we pay money upfront
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that isn't discounted much because they
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happen in the present whereas the
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benefits that accrue over the life of
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the project are discounted more and more
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because they happen later in the future
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so in general as a discount rate
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increases the net present value will
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decrease let's look at something a
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little different let's pretend putting
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our money into an investment at 10
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percent interest is our project let's
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use a discount rate that is also 10
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percent in year zero we will be down
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$1,000 from putting it into the
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investment and in five years we will
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receive five years of compound interest
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six hundred and ten dollars and 51 cents
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plus our principal sum of $1,000 so
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let's discount to factor in the time
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preference since the interest rate is
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the same as the discount rate you can
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probably predict what's going to happen
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1600 $10.51 divided by 1.1 ^
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is $1,000 so adding up our present
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values we get a thousand minus a
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thousand which equals zero so what does
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that mean remember our discount rate is
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meant to represent the opportunity cost
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of capital we want to compare all costs
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and benefits from each year to that
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opportunity cost in an economic analysis
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and that present value of zero tells us
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Society is just as well off with or
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without the project the marginal
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opportunity cost of society's money is
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the same as this project our project in
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this case just being the interest rate
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let's say the interest rate of our
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project was 8% but we're still going to
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discount at a rate of 10%
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well our return becomes fourteen hundred
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and sixty nine dollars and 33 cents
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obviously less than the previous example
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which makes the net present value of
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this project using a 10% discount rate
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to be negative eighty-seven dollars and
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67 cents that negative number is telling
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us that society is better off without
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this project that we would be losing
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money if we invested in this project if
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the interest rate was 12% higher than
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our discount rate then the net present
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value would be 94 dollars and 28 cents
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which is telling us that this project is
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better than our opportunity cost of
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capital that we can make more money by
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investing in this project so our most
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basic decision rule when considering net
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present value is to reject any project
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that has a negative net present value
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and then only consider projects with a
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positive net present value so how do we
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compare projects let's look at four
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different projects a B C and E project V
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has the highest net present value does
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that mean it's the best option in a way
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maybe but maybe not pragmatically
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the net present value only tells us the
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net value but we will probably be
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working on a budget for example two
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projects can have a net present value of
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$500 but one could have the present
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value of cost of a thousand and a
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present value of benefits of 1500 and
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the other a present value cost of a
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million dollars and a present value
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benefits of a million five hundred
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dollars technically the same societal
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benefit and they're equally justified
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but we may not have a million dollars to
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work with we need to look at the
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investment costs of these projects let's
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assume these are all separable we can do
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any combination of them this present
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value of investment cost represents what
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amount is required from us to fund the
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project it's not necessarily a measure
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of the total present costs it's just
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telling us how much money we would need
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to start with so if our budget is four
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million dollars then what are our
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our possible combinations here we could
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go with project a and B or we go with
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project C and D or just a just B just C
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or just D there are a couple other
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combinations but they won't fit on the
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screen so screw them since project a and
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B together give the highest net present
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value we should go with that option we
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always want to pick the projects that
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give the highest net present value let's
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say project a was no longer an option
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then we would just pick the next best
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project the one that has the next
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highest net present value in this case
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just project B the extra money left over
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from our budget can be spent somewhere
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else which might be good but this
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shouldn't affect our decision at all
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it's not like we add the leftover budget
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to our net present value or anything
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like that because unless there is a
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project explicitly planned for this
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money we will assume it will sit
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somewhere at the same interest rate as
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the discount rate and remember from our
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first example the net present value will
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then be zero okay let's look at another
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bunch of projects but this time we'll
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assume there's no budget constraints
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also these projects are making use of
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the same land and there non-separable
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which would you pick project death gives
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the highest net present value but
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project G gives a really good net
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present value for significantly less
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cost should we go with that one the one
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with more net present value per
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investment costs well no with no budget
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constraints this doesn't matter it costs
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six million more dollars to get started
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than project G but the higher net
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present value also tells you that it has
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way higher benefits and in the end is
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offering more benefits than project G so
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choosing project F gives the higher
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value to society even though it has
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higher costs okay so in summary reject
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projects that have a negative net
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present value and only consider projects
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that have a positive net present value
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with no budget constraints just pick the
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project or a series of projects that
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have the highest net present values and
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lastly with budget constraints you will
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also have to look at the investment
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costs and pick the project or series of
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projects that give the highest net
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present value while also conforming to
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the budget in the next video we'll look
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at the internal rate of return as
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another measure of project feasibility
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you
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