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Hi, welcome back to finance for non finance professionals.

Â In this third video of week one, we're going to take the basic ideas of

Â interest rates and compounding that we learned in the first two videos and

Â apply it to discounting future values back into the present.

Â So, we're going to talk about discounting future cash back into the present.

Â Okay, what is cash worth in the future today?

Â It's kind of a funny concept when we think about it.

Â Usually, in the last lecture, we talked about money that I have today,

Â I put it in the bank and earn some rate of return, some interest rate over time, and

Â that's how much I'm going to have in the future.

Â A lot of us have put money into the bank or waited and watched bonds grow or

Â watch the stock market go up and down.

Â And we understand what it means to have stuff today and

Â watch it grow into the future.

Â What we're going to do in this lecture is a little bit more abstract,

Â we're going to think about a promise of cash coming in, in the future.

Â And then ask how much that promise of future cash is worth today?

Â And that basic concept is called discounting.

Â It's a critical component of finance.

Â Because a lot of what we do in finance is, if you think about bonds or stocks or

Â dividend payments or investments,

Â a lot of what we're thinking about is cash that's coming in in the future.

Â Like I'm going to put money in the stock market and I hope to retire in 20 years.

Â What I'm saying is that I hope I'm going to get cash 20 years from now.

Â And I'm making plans, and decisions,

Â and trade-offs today on the expectation of future cash coming in later.

Â And what we're going to do today is think about how to put a present value,

Â a value today, on what that future cash is worth.

Â Okay, from our last lecture we talked about putting present values,

Â growing them into the future, with compound interest rates.

Â And this was the basic formula that we had from the last lecture.

Â Money that I have today, the present value, grown at some interest rate, r, for

Â a number of periods, t.

Â 1:55

I'm just going to solve for present value, which means taking the (1+r) to the t,

Â moving it down underneath into the denominator.

Â But what we've done is conceptually very sort of tricky.

Â Instead of growing a cash flow at r into the future,

Â we're taking a future value now, think about what the formula says now.

Â It says the present value is equal to the future value.

Â And what's now over the future value, look at the denominator, what's in there?

Â (1 + r) to the t, the same thing, the same interest rate.

Â But instead of growing into the future,

Â we're taking that future value and what are we doing?

Â We're sort of smashing it down, we're beating it down with that 1 + r,

Â r is bigger than 0, so 1 + r is something bigger than 1.

Â 1+r to the t is something,

Â going to be even bigger than 1 which means we're going to take that future value,

Â we're going to smash it down into the present, that's called discounting.

Â Discounting future values into the present.

Â All we've done is flipped that formula, but

Â conceptually we've done something very important.

Â 3:10

Okay, let's look at this table as I've got it laid out here for 5 years.

Â When is that cash coming in?

Â It's coming in 5 years from now.

Â Okay, how much is that worth to me today?

Â What do I need to do?

Â I need to smash it down once.

Â I need to smash it down twice, three times,

Â four times, five times into the present today.

Â So we're going to do that using the same formula that we've been using for

Â the last two lectures.

Â What am I going to do?

Â I'm going to take that 175, the future value,

Â smash it down one period, 1 + 4% raised to the 1.

Â And that's what I've got right here in this formula,

Â 175 divided by (1 + 4%) to the 1 power.

Â That's smashed down one period.

Â That takes that 5 year cash flow of 175 and moves it back in time one period.

Â That's worth 168.27, that's smashing it down one time into year 4.

Â Now I'm going to smash it down again.

Â Divided by, if I take that 175 and smash it down for two periods.

Â What do I do?

Â 1 + 4%, but this time two periods squared.

Â That smashes it down to 161.80.

Â If I smash that 175 down three periods, you're getting the idea now.

Â 175 divided by 1 + 4%, the interest rate cubed,

Â 3 periods from 5, one, two, three periods down.

Â $175 over (1+4%)3 gives me 155.57.

Â Smashing it down 4 periods gives me 149.59.

Â Smashing it down 5 periods, $175 over (1+4%)

Â raised to the 5th period, 143.84.

Â And that's the answer, 143.84.

Â What have I done?

Â I've taken a 5 year cash flow, something coming in 5 years from today.

Â And smashed it down 5 times at 4% into the present.

Â We've taken a future value, something that's coming in in the future.

Â Something that's coming in way out there, 5 years from now.

Â And said how much is it worth to me today?

Â If somebody offered you a promise of 175 5 years from now,

Â how much would you pay for it?

Â If interest rates were 4%, we'd pay about $143.84 for it today.

Â This is a really important concept because it means now

Â we can think about anything, right?

Â Real estate, mortgages, commercial, industrial loans.

Â We can think about sovereign debt from Argentina or Greece.

Â We can think about stocks and bonds.

Â We can think about anything that's really got a cash flow attached to it that's

Â coming in in the future.

Â How much are you willing to pay for

Â it today, ultimately that's going to depend on how much those promises of

Â future cash are worth to me when I put them in present value.

Â 6:00

Okay, two things are driving how hard we sort of smash down those cash flows.

Â The first is, how far out is that cash?

Â The further out it is, the harder we're discounting it.

Â The second is, how big is the interest rate?

Â The bigger the interest rate, the more we're smashing that cash flow down.

Â To see that graphically, let's talk about a $100 discounted at 10%.

Â And I'm going to show you a graphic of how hard that discounting works as we sort of

Â move further out in time.

Â So think about that $100.

Â If there were no discounting at all, that would be the 0 on the x-axis.

Â And of course, that $100 would be worth exactly $100.

Â But as I smash it down for a year, 2 years, 5 years,

Â 10 years, 20 years, the value of that money goes down, down, down.

Â And you can see it doesn't go down straight,

Â it kind of goes down exponentially.

Â Just like when we talked about compound interest, growing exponentially,

Â discount decay exponentially.

Â So we're sort of saying, how hard are we smashing down those cash flows,

Â the amount that we're smashing down those cash flows, grows exponentially.

Â So it's exponential decay in the present value of future cash, right?

Â You can see that that $100,

Â discounted at 10%, if we go out 50 years, is worth close to nothing, right?

Â It's worth a few pennies because we've discounted it 1 plus that percent,

Â 1 plus that percent, 1 plus that.

Â By the time we're raising that to the 50th power, that exponential decay is

Â hitting so hard that that future promise of cash is essentially worthless.

Â Now the best way to see this is to work a couple of examples, so let's again,

Â let's go to the light board and work a couple of practical examples.

Â All right, let's work a simple example together of using the present value,

Â future value relationship and think about what this might mean for us.

Â So let's say my friend comes up to me and he says, hey, I'm going to start a pizza

Â parlor and I'm trying to raise some money to get it off the ground.

Â And he makes me a promise, he says, I'll pay you $1,000,

Â but I can't pay you that $1,000 for another 7 years.

Â So, 7 years is when I figure the pizza parlor will be up, and

Â I'll be able to pay back my debts.

Â I'm trying to raise money today to get it off the ground, I'll pay you back $1,000,

Â 7 years from now.

Â And I think, all right,

Â well, pizza parlor maybe in downtown Houston is not a bad idea.

Â This guy has been in the restaurant business before.

Â What would be a reasonable rate of return to expect?

Â How about 5%?

Â I'd like to earn 5% on that money over time.

Â 8:23

And I'll say, all right, well, if you're going to pay me back $1, 000,

Â 7 years from now, and I'm thinking 5% is a reasonable return,

Â that's what I'm going to discount that $1,000 at.

Â So let's use the present value, the future value relationship to figure out how much

Â money I will be willing to lend to him today for that promise of a $1,000,

Â 7 years from now, discounting at 5%.

Â I would use my relationship between the present value and the future value.

Â The present value is the future value times 1 over (1 + r) to the t.

Â Okay, so in this case I'm solving for present value.

Â My future value is 1,000 and

Â 1 over 1 + r, what's r here?

Â 5% raised to the 7th power.

Â Okay good, so now I can put this into any financial calculator and solve that.

Â That answer is going to come out to be $710.70.

Â All right, good.

Â So what have we done?

Â I've said, okay, you are willing to pay me $1,000, but not for 7 years, and

Â I want to make sure I earn some kind of rate of return for lending you the money.

Â I'd be willing to give you $710 for

Â that loan, that's how much I'd be willing to finance you at.

Â I'd be willing to give you $710 for

Â that promise of $1,000 coming in 7 years from now, that's 5%.

Â So that's how the straight loan would work.

Â If I gave him $710.70 and he actually paid me the $1000, 7 years from now,

Â I would have earned 5% a year for 7 years.

Â The discounting and the compounding, that r, is the same.

Â 10:06

Now, what if my friend came to me and said, hey, I've changed the concept for

Â the pizza parlor a little bit.

Â I'm going to make it all about fish pizza.

Â And maybe that's a great idea, and my friend is really excited about fish pizza.

Â But I'm not as comfortable with fish pizza as business concept as my friend is, and

Â so I think, all right, that changes the risk to me a little bit.

Â You're still going to pay me a $1,000, 7 years from now.

Â But to invest in a fish pizza business which I'm a little bit skeptical about,

Â I'm going to charge you a 15% rate of return.

Â So I'm going to discount a lot harder that promise of a future cash flow because

Â I feel less comfortable of that cash is actually going to arrive 7 years from now.

Â Okay, so if I go back to my future value,

Â present value relationship, what's the present value of a promise of $1,000,

Â 7 years from now, if I'm discounting at 15%?

Â That's going to be $1,000 over 1 +

Â 15% raised to the 7th power.

Â So, what have I done?

Â I'm just changing the r here from 5% to 15%.

Â What is that going to do,

Â as I discount much harder at same period of time, same amount of money?

Â What's that going to come out to?

Â That's going to come out to $375.90.

Â Much lower value, right?

Â I was discounting at 5%, that got me to $710.

Â Discounting at 15% really smashes down that cash flow.

Â My friend says to me, I want to invest in the fish pizza.

Â That's riskier to me.

Â I'm only willing to lend you $375 for

Â the same promise of a $1,000, 7 years from now.

Â With the lower discount rate,

Â I felt more comfortable about the original business plan.

Â At a 5% discount rate, I'd be willing to lend $710.

Â At the riskier discount rate, only 375.

Â So we can see that relationship between the present value and future value depends

Â really on two things, how far out in time is the money coming in?

Â And how hard am I discounting those cash flows based on risks?

Â