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So discounting cash flows, what does it entail?

Â Why do we consider it to be the gold standard in finance?

Â Let's take a closer look.

Â We start with a simple example.

Â I've got two propositions for you, which one would you prefer?

Â I either give you $100 now or I promise to give you $100 in a year's time.

Â Which one do you prefer?

Â Wouldn't be surprised if you said that you very much preferred the $100 right now,

Â thank you very much.

Â And that is indeed what most people would intuitively reply.

Â They prefer money in hand rather than to wait for

Â the same amount of money at some point in the future.

Â But why is that?

Â Why is the $100 today somehow valued differently from $100 in the future?

Â Well, we have at least three good reasons why you might want

Â to prefer the $100 right now, expected inflation.

Â We've seen over many, many years that dollars,

Â over time reduce in value due to price increases.

Â Inflation erodes the value of money over time.

Â So what you can buy with $100 today is going to be worth

Â probably more than what you can buy with the $100 in a year's time.

Â Second reason why you might want to prefer the $100 now is that you might not get it.

Â I might walk away and you'll end up empty-handed in one year's time.

Â Risk, will the cash flow actually occur?

Â If you get the money now, there is no risk.

Â But one year from today, who knows what can happen in that time period.

Â And lastly, opportunity costs.

Â We'll discuss the opportunity costs in a lot more detail

Â in the remainder of this module.

Â The key point is that we cannot directly compare dollars,

Â cash flows, that occur at different points in time.

Â We need to consider the actual date that a cash flow eventuates.

Â So, we need to consider the value of those cash flows at different points in time,

Â somehow accounting for expected inflation, for risk, and for

Â opportunity costs, alternative investment opportunities for investors.

Â The way we do that is as follows.

Â So, we account for what we labeled the time value of money,

Â how a dollar changes in value from one time period to the next time period

Â by systematically discounting future cash flows.

Â The formula here tells you how we do that.

Â We take the cash flow and we divide through by 1 plus

Â a discount rate, r, to the power of n.

Â And n indicates the number of years you have to wait until you're entitled

Â to the cash flow, where the cash flow is indicated for

Â the year that it will occur, cash flow at n.

Â If we divide the cash flow through by 1 plus the discount rate,

Â we divide through by something that is larger than 1,

Â weâ€™ll end up with a value which is going to be smaller than the cash flow.

Â That is the present value.

Â The present value in the presence of expected inflation risks and opportunity

Â costs will be less than the cash flow entitlement, and years down the track.

Â It allows us to express future cash flows into present dollars,

Â equivalent present dollars.

Â We label those equivalent present dollars, the present value of a future cash flow.

Â That, then, will allow us to bring all future cash flows,

Â whether they occur in one year's time, two years' time or

Â ten years' time, we can bring them back to the present.

Â And once we've got them all valued at the same decision period, today, now, we've

Â got comparable cash flows that allow us to make an informed investment decision.

Â So, let me give you an example.

Â What is the present value of that $100 that I promised you earlier, but

Â I will only give it to you in one year's time?

Â And an appropriate discount rate, we'll discuss the choice of that discount rate

Â a little later, and appropriate discount rate being 5% per annum.

Â Take the cash flow, $100 in one year's time,

Â divide by 1 plus that discount rate of 5%,

Â 1.05 to the power, the number of the years, 1 in this case,

Â and that tells us that the present value in this example is $95.24.

Â So, $100 in one year's time is valued today at

Â a discount rate of 5% at only $95.24.

Â So, what's the intuition here?

Â Or, consider it another way,

Â take that $95.24, and take that right now,

Â borrow $95.24, invest it at the discount rate.

Â Let's assume a bank is offering you a 5% interest rate per annum.

Â Invest the $95.24 at that 5% and what do you get?

Â Exactly the $100 in one year's time.

Â So that suggests a neat link between an opportunity

Â to invest at 5% over a one-year period,

Â linking a future cash flow to a present value of $95.24.

Â Now what would happen if that cash flow didn't occur in one year's time, but

Â in two years' time instead?

Â No problem, same formula.

Â Take that cash flow.

Â In two years, n equals 2 of $100, but

Â now discount by a slightly higher discount factor,

Â and that is going to be 1 plus the same discount rate of 5%, but

Â now to the power of n equals 2 years.

Â And it will tell us that the present value of a $100 cash flow that you will be

Â entitled to in two years' time, today is only worth the present value of $90.70, so

Â you've lost the further $5, almost $5, in terms of present value.

Â The further away the cash flow entitlement,

Â the smaller the present value.

Â So the intuition here is the same.

Â Borrow the $90.70 today.

Â Go to the bank, invest it now for two years.

Â And what will you get after two years?

Â Exactly the $100.

Â So there is a very clear link between

Â future values of cash flows and present values of cash flows.

Â And we can in fect move either way.

Â 7:06

So rather than discounting future cash flows to find their equivalent present

Â value, we can also move cash flows into the future,

Â take a present value, take a present cash flow, today's cash flow, and

Â see what that is worth at some point after some number of years in the future.

Â We call that compounding, rather than discounting.

Â So, we discount future cash flows to the present,

Â we compound present cash flows to the future.

Â So how does that work for our example?

Â Well let's assume that you opted for the $100 today,

Â you could go to the bank, invest the $100 today for two years,

Â n equals 2 at a discount rate and an interest rate of 5% per annum.

Â The future value, FV, after two years, n equals 2,

Â would be that cash flow today, the present value of $100,

Â multiplied by 1 plus the discount rate,

Â the interest rate of 5%, to the power n, two years.

Â And that tells you that the future value of $100 today invested for

Â two years at 5% is worth $110.25.

Â Now why would we want to do that?

Â Why would we want to move money forwards in time, into the future?

Â Well consider the case where you have a decision date which isn't today.

Â The example I gave you before that an investor has to make up their mind about

Â investing in Kellogg's today, at the share market price, as it is quoted today,

Â that would require us to work out present values

Â of future cash flows entitled by ownership in Kellogg's.

Â Consider the scenario where the decision point is not today but

Â some time in the future.

Â For example, where you want to work out what you need to do at the time of

Â retirement, when you are entitled to the pension, in that scenario your

Â decision point is not today, but you would be investing in your pension fund today.

Â But you would want to know the future value of that pension

Â fund sometime in the future when you decide to retire.

Â So there is a need to move money

Â to the future as there is a need to move money to the present.

Â 11:58

So continuing our example here, our expectation of $100 in a year's time,

Â let's boost the risk of this investment.

Â We're now really unsure of whether we will actually be receiving the cash flow

Â of $100 in a year's time.

Â So, rather than use a discount rate of 5%,

Â we've increased the discount rate by a further 10% to 15% per annum.

Â Take that same cash flow, divide now by 1.15,

Â and we find that the present value of that same $100

Â has dropped from $95 to $87

Â A significant drop from the $95.24 that we saw with a discount rate of 5%.

Â So the higher the risk, the higher the discount factor,

Â the lower the present value, the more we discount future cash flow entitlements.

Â Just to illustrate that with a bit more detail, for

Â a series of cash flow entitlements, let's assume that Kellogg's was actually

Â promising cash flows of $100 for the next ten years.

Â If we discount these $100 cash flow entitlements,

Â as they occur at the end of each year at 5%, look at the red bars,

Â you see that they steadily decrease in present value.

Â So whereas the first entitlement would be worth $95.24 after one year,

Â then after ten years, the cash flow that Kellogg promises in ten years' time

Â is going to be worth only slightly over $60 in present value.

Â If we increase the discount rate to reflect the riskiness of those cash flows

Â to 15%, look at the green bars, you can see that there

Â is an immediate drop off in the present value of future cash flows.

Â And you can see that the cash flow that is promised after ten

Â years is now only worth about $17, in present value.

Â