Cost-Benefit Discounting

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

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