WEBVTT

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<v Speaker 0>Hi, everyone.

NOTE CONF {"raw":[98,100]}

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<v Speaker 0>My name is Simil.

NOTE CONF {"raw":[100,100,100,42]}

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<v Speaker 0>And in this short video, I will walk you through

NOTE CONF {"raw":[100,100,100,100,100,100,97,100,100,100]}

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<v Speaker 0>an example of the importance of geometric series in the

NOTE CONF {"raw":[100,100,100,100,100,100,100,84,100,100]}

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<v Speaker 0>context of economics, and in particular in the context of

NOTE CONF {"raw":[100,100,99,99,100,100,100,100,100,100]}

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<v Speaker 0>investment decisions.

NOTE CONF {"raw":[100,100]}

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<v Speaker 0>So an investment projects typically involves incurring a large cost

NOTE CONF {"raw":[100,72,100,58,100,75,100,95,96,91]}

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<v Speaker 0>today in anticipation of a certain stream of payoffs in

NOTE CONF {"raw":[100,100,100,100,99,100,60,100,86,100]}

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<v Speaker 0>the future.

NOTE CONF {"raw":[100,100]}

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<v Speaker 0>For example, an investment project as well, where a bomb

NOTE CONF {"raw":[100,100,78,100,99,57,82,100,100,98]}

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<v Speaker 0>went build the factory today in order to produce and

NOTE CONF {"raw":[51,97,67,100,100,100,100,100,100,100]}

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<v Speaker 0>sell out for a particular amount of time, for example,

NOTE CONF {"raw":[65,69,97,100,100,100,100,100,100,100]}

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<v Speaker 0>30 years, so long as the factory is in operation.

NOTE CONF {"raw":[89,100,100,100,100,100,100,100,100,100]}

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<v Speaker 0>A firm should implement an investment project.

NOTE CONF {"raw":[91,89,100,100,99,100,95]}

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<v Speaker 0>All if the payoffs from the project exceed the cost.

NOTE CONF {"raw":[60,50,100,87,100,100,100,100,100,78]}

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<v Speaker 0>However, one of the issues that occurs in the context

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

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<v Speaker 0>of investment projects is that that the costs and payoffs,

NOTE CONF {"raw":[100,100,93,100,73,100,100,100,100,98]}

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<v Speaker 0>in fact, the crew at different points in time.

NOTE CONF {"raw":[74,74,100,99,100,100,100,100,100]}

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<v Speaker 0>And this creates a difficulty because of what is known

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,99,100]}

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<v Speaker 0>as the time value of money.

NOTE CONF {"raw":[100,100,100,100,100,100]}

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<v Speaker 0>The time value of money is the principal loosely speaking,

NOTE CONF {"raw":[100,100,100,99,100,100,100,68,80,100]}

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<v Speaker 0>that because if interest rates went down today is not

NOTE CONF {"raw":[65,100,54,100,100,86,77,100,76,100]}

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<v Speaker 0>the same in terms of value as £1.

NOTE CONF {"raw":[100,100,100,100,100,100,100,55]}

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<v Speaker 0>One year from now, for example, if the interest rates

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,76]}

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<v Speaker 0>are equal to five percent.

NOTE CONF {"raw":[100,100,100,100,100]}

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<v Speaker 0>And if I have one thing today, then through my

NOTE CONF {"raw":[100,100,100,99,97,43,100,99,97,100]}

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<v Speaker 0>access to a bank which base interest rates, I can't

NOTE CONF {"raw":[100,100,100,100,100,48,100,100,100,56]}

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<v Speaker 0>convert this one pound today into one point five pounds

NOTE CONF {"raw":[100,100,64,64,100,100,99,99,100,99]}

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<v Speaker 0>one year from now.

NOTE CONF {"raw":[100,100,100,100]}

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<v Speaker 0>By depositing this one pound in a bank.

NOTE CONF {"raw":[100,99,100,93,93,100,51,100]}

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<v Speaker 0>We say in this context that the future value of

NOTE CONF {"raw":[100,100,100,100,100,82,100,100,100,100]}

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<v Speaker 0>one pound today in one year is exactly one pound

NOTE CONF {"raw":[84,50,100,100,99,98,99,100,100,100]}

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<v Speaker 0>multiplied by one, plus the interest rate.

NOTE CONF {"raw":[97,100,100,100,100,100,90]}

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<v Speaker 0>But similarly, if I actually hold my money in the

NOTE CONF {"raw":[100,100,100,100,100,97,100,100,100,99]}

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<v Speaker 0>deposit for two years, I can convert my one pump

NOTE CONF {"raw":[48,99,100,100,100,100,100,98,100,88]}

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<v Speaker 0>even more money to pyrates into the future.

NOTE CONF {"raw":[100,100,100,98,89,100,100,100]}

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<v Speaker 0>And we say equivalently that the future value of £1

NOTE CONF {"raw":[100,100,96,100,100,100,100,100,100,82]}

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<v Speaker 0>today in two years is this one bond multiplied by

NOTE CONF {"raw":[100,100,100,100,100,100,88,30,100,100]}

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<v Speaker 0>one, plus the interest rate squared and so forth.

NOTE CONF {"raw":[100,100,99,100,100,73,100,100,86]}

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<v Speaker 0>Now, this arguments underlying the time value of money also

NOTE CONF {"raw":[100,56,49,91,100,100,100,99,100,100]}

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<v Speaker 0>works backwards.

NOTE CONF {"raw":[100,100]}

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<v Speaker 0>For example, if the interest rate is five percent and

NOTE CONF {"raw":[100,100,99,100,100,99,100,100,100,99]}

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<v Speaker 0>I am to receive £1 one year into the future,

NOTE CONF {"raw":[92,92,100,100,58,100,100,100,100,100]}

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<v Speaker 0>then this is very much like receiving one divided by

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

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<v Speaker 0>one point five or approximately ninety five pence today, because

NOTE CONF {"raw":[99,98,78,80,100,75,75,61,100,100]}

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<v Speaker 0>if I had ninety five pence today, I can deposit

NOTE CONF {"raw":[99,100,43,86,86,97,100,100,95,100]}

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<v Speaker 0>them in a bank at the interest rate, the five

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,64,99]}

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<v Speaker 0>percent, and convert it into account.

NOTE CONF {"raw":[99,100,100,98,100,83]}

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<v Speaker 0>One year from now.

NOTE CONF {"raw":[100,100,100,100]}

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<v Speaker 0>In this context, we say that the present value of

NOTE CONF {"raw":[100,100,100,100,100,100,100,97,100,100]}

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<v Speaker 0>£1 received one year from now is Wangan divided by

NOTE CONF {"raw":[91,100,100,100,100,100,100,76,99,100]}

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<v Speaker 0>one.

NOTE CONF {"raw":[100]}

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<v Speaker 0>Plus, the interest rate, the present value of £1 received

NOTE CONF {"raw":[98,100,100,92,100,100,100,98,92,97]}

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<v Speaker 0>two years from now is £1 divided by one plus

NOTE CONF {"raw":[86,100,100,100,91,93,100,100,100,100]}

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<v Speaker 0>R squared.

NOTE CONF {"raw":[49,48]}

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<v Speaker 0>And so far.

NOTE CONF {"raw":[100,51,49]}

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<v Speaker 0>When a firm decides whether to implement an investment project

NOTE CONF {"raw":[100,100,100,98,100,99,100,100,100,100]}

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<v Speaker 0>or not, it should compare all the payoffs and costs

NOTE CONF {"raw":[100,100,100,98,99,93,100,80,100,100]}

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<v Speaker 0>from the project in present value terms.

NOTE CONF {"raw":[100,100,88,69,94,100,100]}

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<v Speaker 0>And one January to do this is to use the

NOTE CONF {"raw":[100,100,41,98,97,99,100,100,100,99]}

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<v Speaker 0>what's known as the net present value calculation.

NOTE CONF {"raw":[100,100,100,98,100,100,100,96]}

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<v Speaker 0>So the net present value of a project is the

NOTE CONF {"raw":[100,100,100,100,100,60,79,100,100,100]}

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<v Speaker 0>sum of for the present value of all payoffs from

NOTE CONF {"raw":[99,39,60,100,100,100,87,83,95,100]}

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<v Speaker 0>the project, minus the present value of all costs from

NOTE CONF {"raw":[100,100,100,100,100,81,97,66,100,100]}

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<v Speaker 0>the project.

NOTE CONF {"raw":[100,99]}

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<v Speaker 0>If the net present value of the project exceeds zero,

NOTE CONF {"raw":[98,99,100,100,100,97,63,100,82,100]}

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<v Speaker 0>then the project is worthwhile implementing.

NOTE CONF {"raw":[100,100,100,99,100,68]}

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<v Speaker 0>But if it is below zero, then the project should

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,89,100]}

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<v Speaker 0>not be implemented and the firm is better off depositing

NOTE CONF {"raw":[100,100,100,84,100,78,100,100,100,100]}

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<v Speaker 0>their money in a bank account instead.

NOTE CONF {"raw":[100,100,100,100,100,100,99]}

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<v Speaker 0>Let's consider a numerical example which will clarify the importance

NOTE CONF {"raw":[90,100,99,99,100,100,100,100,100,100]}

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<v Speaker 0>of geometric series in this discussion, so suppose that there

NOTE CONF {"raw":[100,100,84,100,100,100,100,100,100,100]}

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<v Speaker 0>is a project, a form Kesem project, and the cost

NOTE CONF {"raw":[100,94,100,88,46,60,100,69,100,82]}

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<v Speaker 0>of implementing this project is one point five million pounds,

NOTE CONF {"raw":[100,100,100,100,97,100,100,100,100,100]}

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<v Speaker 0>which has to be incurred today, for example, in order

NOTE CONF {"raw":[100,99,100,100,98,99,100,100,100,100]}

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<v Speaker 0>to build the factory.

NOTE CONF {"raw":[100,100,98,100]}

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<v Speaker 0>If implemented, the project will pay off one hundred thousand

NOTE CONF {"raw":[100,100,100,99,100,100,100,100,100,100]}

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<v Speaker 0>pounds each year for 20 years with the first payoff.

NOTE CONF {"raw":[100,100,100,100,71,100,100,100,99,96]}

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<v Speaker 0>A great one year into the future after the cost

NOTE CONF {"raw":[100,99,100,100,100,100,100,100,100,93]}

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<v Speaker 0>is incurred, perhaps because it takes one year to build

NOTE CONF {"raw":[93,92,100,100,100,100,100,100,100,94]}

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<v Speaker 0>the factory and then you start producing and selling out,

NOTE CONF {"raw":[80,100,100,100,100,100,100,97,100,87]}

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<v Speaker 0>but only from one year into the future.

NOTE CONF {"raw":[36,80,100,100,100,100,100,100]}

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<v Speaker 0>So an interesting question is, is this project worthwhile?

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,100]}

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<v Speaker 0>Should it be implemented by the four?

NOTE CONF {"raw":[100,100,100,100,100,100,30]}

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<v Speaker 0>Well, in order to answer this question, we should calculate

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,99,100]}

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<v Speaker 0>the net present value of the project.

NOTE CONF {"raw":[100,94,100,100,99,73,97]}

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<v Speaker 0>Well, given that the interest rate is denoted by the

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,94,94]}

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<v Speaker 0>net present value of this project in thousands of pounds,

NOTE CONF {"raw":[100,100,100,100,100,100,80,100,100,86]}

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<v Speaker 0>this minus fifteen hundred thousand pounds, this is the negative

NOTE CONF {"raw":[42,100,100,100,100,100,100,100,100,92]}

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<v Speaker 0>of the cost incurred today.

NOTE CONF {"raw":[100,100,70,100,100]}

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<v Speaker 0>And then one year into the future, where receive pay

NOTE CONF {"raw":[100,100,100,91,100,100,100,64,66,63]}

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<v Speaker 0>of one hundred thousand.

NOTE CONF {"raw":[81,94,94,95]}

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<v Speaker 0>But because it's one year into the future, we have

NOTE CONF {"raw":[99,100,99,100,100,100,100,100,100,100]}

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<v Speaker 0>to divide it by one.

NOTE CONF {"raw":[97,97,73,100,100]}

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<v Speaker 0>Plus, sorry to convert the present values that three years

NOTE CONF {"raw":[97,27,99,100,99,99,98,100,76,76]}

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<v Speaker 0>into the future, we receive another 100000.

NOTE CONF {"raw":[100,100,100,100,83,100,72]}

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<v Speaker 0>But in order to discount them in present value terms,

NOTE CONF {"raw":[100,98,98,99,100,100,100,100,100,100]}

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<v Speaker 0>we divide by one plus our square and so forth,

NOTE CONF {"raw":[100,100,100,100,100,97,97,100,100,99]}

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<v Speaker 0>all the way until twenty one years into the future.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

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<v Speaker 0>We receive 20 years into the future, receive £100, and

NOTE CONF {"raw":[97,100,68,100,96,98,100,84,95,100]}

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<v Speaker 0>we discounted by one.

NOTE CONF {"raw":[88,99,100,100]}

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<v Speaker 0>Plus are the power of twenty.

NOTE CONF {"raw":[99,63,100,100,76,37]}

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<v Speaker 0>Now, the usefulness of geometric series in the context of

NOTE CONF {"raw":[100,100,100,100,99,98,100,100,100,100]}

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<v Speaker 0>this calculation comes from recognising that the payoffs shown on

NOTE CONF {"raw":[98,98,100,100,97,100,100,61,74,100]}

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<v Speaker 0>the slides, in fact, form a geometric series with first

NOTE CONF {"raw":[100,96,100,100,99,96,100,100,100,97]}

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<v Speaker 0>element.

NOTE CONF {"raw":[74]}

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<v Speaker 0>Why can't rates over one plus are a common ratio

NOTE CONF {"raw":[57,51,52,100,99,74,96,98,100,100]}

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<v Speaker 0>of the elements?

NOTE CONF {"raw":[100,100,93]}

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<v Speaker 0>One over one, plus the interest rate and with 20

NOTE CONF {"raw":[100,100,100,100,100,100,96,99,99,87]}

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<v Speaker 0>terms.

NOTE CONF {"raw":[54]}

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<v Speaker 0>If we know the formula for the sum of the

NOTE CONF {"raw":[100,100,100,100,93,92,100,93,100,100]}

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<v Speaker 0>first 20 terms of a geometric.

NOTE CONF {"raw":[100,95,94,99,98,100]}

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<v Speaker 0>Sequence.

NOTE CONF {"raw":[79]}

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<v Speaker 0>We can therefore rewrite this some as simply one over

NOTE CONF {"raw":[100,100,100,98,100,62,99,100,85,100]}

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<v Speaker 0>one, plus the interest rate multiplied by one minus Y,

NOTE CONF {"raw":[100,100,99,100,99,100,100,100,100,68]}

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<v Speaker 0>plus the interest rate to the power of twenty oh,

NOTE CONF {"raw":[100,100,100,99,93,100,100,100,88,79]}

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<v Speaker 0>divided by one minus one over one, plus the interest

NOTE CONF {"raw":[100,100,97,100,100,100,100,100,100,100]}

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<v Speaker 0>rate.

NOTE CONF {"raw":[98]}

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<v Speaker 0>And this is the formula for the sum of geometric

NOTE CONF {"raw":[100,100,100,100,100,100,100,79,100,100]}

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<v Speaker 0>series with 20 elements and the common ratio one over

NOTE CONF {"raw":[87,100,68,100,90,99,100,100,100,100]}

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<v Speaker 0>one plus hour in the first element, one hundred over

NOTE CONF {"raw":[100,95,51,97,90,100,100,80,80,100]}

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<v Speaker 0>one.

NOTE CONF {"raw":[98]}

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<v Speaker 0>So therefore this formula signifies that whether the project is

NOTE CONF {"raw":[68,97,100,100,100,100,100,100,100,100]}

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<v Speaker 0>worthwhile undertaking will ultimately depend not only on what are

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

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<v Speaker 0>the payoffs and the costs of the project, but also

NOTE CONF {"raw":[100,99,100,100,97,100,100,100,100,100]}

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<v Speaker 0>on the interest rate.

NOTE CONF {"raw":[100,100,100,94]}

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<v Speaker 0>For example, suppose that the interest rate is five percent.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

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<v Speaker 0>If we plug in zero point zero five into our

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,52,100]}

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<v Speaker 0>formula for the net present value, we are going to

NOTE CONF {"raw":[100,100,99,100,100,100,100,100,100,100]}

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<v Speaker 0>find that the net present value of the project would

NOTE CONF {"raw":[100,100,100,97,100,100,100,100,100,82]}

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<v Speaker 0>be negative.

NOTE CONF {"raw":[100,100]}

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<v Speaker 0>Two hundred and fifty four thousand pounds.

NOTE CONF {"raw":[100,100,99,100,95,100,100]}

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<v Speaker 0>And since the net present value is negative, it implies

NOTE CONF {"raw":[100,100,99,99,100,100,100,100,100,100]}

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<v Speaker 0>that the project should not be undertaken because it is

NOTE CONF {"raw":[100,100,98,100,100,100,100,100,100,100]}

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<v Speaker 0>better to deposit your money in a bank account, instead

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:07:36.400 --> 00:07:38.650
<v Speaker 0>yielding the interest rate of five percent.

NOTE CONF {"raw":[99,100,100,100,89,100,100]}

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<v Speaker 0>And over the duration of 20 years, this is going

NOTE CONF {"raw":[100,100,100,100,100,57,100,100,100,100]}

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<v Speaker 0>to hold your fire profits.

NOTE CONF {"raw":[100,100,100,100,98]}

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<v Speaker 0>Then investing in the project.

NOTE CONF {"raw":[97,94,100,100,100]}

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<v Speaker 0>However, if the interest rate lasts only one percent, then

NOTE CONF {"raw":[100,100,100,100,100,43,100,100,100,100]}

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<v Speaker 0>by blackening one percent inside this formula, we are going

NOTE CONF {"raw":[99,42,100,100,98,99,100,100,100,100]}

00:07:53.190 --> 00:07:55.200
<v Speaker 0>to be able to calculate that the net present value

NOTE CONF {"raw":[100,100,100,100,100,98,99,100,100,100]}

00:07:55.200 --> 00:07:58.140
<v Speaker 0>is, in fact, positive and large, positive and equal to

NOTE CONF {"raw":[100,100,100,100,93,100,100,95,100,100]}

00:07:58.440 --> 00:08:00.990
<v Speaker 0>three hundred and four thousand pounds.

NOTE CONF {"raw":[95,95,99,100,100,100]}

00:08:01.380 --> 00:08:03.990
<v Speaker 0>Therefore, in this case, if the interest rate to slow

NOTE CONF {"raw":[100,100,100,100,90,100,100,92,92,98]}

00:08:04.110 --> 00:08:08.580
<v Speaker 0>the project should be undertaken because it yields better returns,

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:08:08.580 --> 00:08:11.250
<v Speaker 0>then the next best option, which is to deposit your

NOTE CONF {"raw":[83,100,100,100,100,100,100,100,100,100]}

00:08:11.250 --> 00:08:12.420
<v Speaker 0>money in a bank.

NOTE CONF {"raw":[100,100,100,100]}

00:08:13.370 --> 00:08:20.390
<v Speaker 0>This brief example demonstrates the usefulness of geometric series in

NOTE CONF {"raw":[100,95,100,100,100,100,100,100,78,100]}

00:08:20.390 --> 00:08:28.520
<v Speaker 0>the context of economics and also demonstrates one important, you

NOTE CONF {"raw":[100,100,100,100,100,100,100,86,98,100]}

00:08:28.520 --> 00:08:31.700
<v Speaker 0>know, concept in economics, which is about the relationship between

NOTE CONF {"raw":[100,100,99,100,100,100,100,100,100,100]}

00:08:31.880 --> 00:08:33.289
<v Speaker 0>interest rates and investment.

NOTE CONF {"raw":[100,100,98,90]}

00:08:33.770 --> 00:08:38.780
<v Speaker 0>As we know often in macroeconomics, we assume that higher

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:08:38.780 --> 00:08:40.969
<v Speaker 0>interest rates discourage investment.

NOTE CONF {"raw":[100,100,100,100]}

00:08:42.150 --> 00:08:46.980
<v Speaker 0>And the underlying logic behind this, the underlying argument behind

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,98,100]}

00:08:46.980 --> 00:08:50.280
<v Speaker 0>this statement is exactly one based on net present value.

NOTE CONF {"raw":[96,100,98,100,85,100,100,100,100,100]}

00:08:51.030 --> 00:08:54.120
<v Speaker 0>As we have seen here, when the interest rates are

NOTE CONF {"raw":[92,100,100,100,99,100,93,100,100,100]}

00:08:54.120 --> 00:08:59.310
<v Speaker 0>low, the project was worthwhile undertaking and therefore investment should

NOTE CONF {"raw":[100,100,100,100,100,99,85,100,88,100]}

00:08:59.310 --> 00:09:00.060
<v Speaker 0>be undertaken.

NOTE CONF {"raw":[100,100]}

00:09:00.300 --> 00:09:04.440
<v Speaker 0>But atai interest rates, investment should not be undertaken.

NOTE CONF {"raw":[100,45,100,95,97,100,100,100,93]}