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PROFESSOR: So today we're
going to continue our
discussion of capital markets.
If you remember the introduction
from last time,
what we talked about was we
talked about labor as an input
and where it came from.
And these lectures are about
capitals and input, where it
comes from.
We talked about the fact that
while capital, ultimately, is
machines, and buildings, and
things like that, what we
think about in this course,
we're going to think about
financial capital and what's
behind all the different kinds
of capital that businesses
use.
We talked about peoples' savings
decisions as creating
a pool of capital from which
businesses draw.
And then we talked about present
value and the notion
of considering the fact that
dollars in the future are
worth less than dollars today.
So with that as background, what
we want to do now is talk
about how firms and individuals
should make
choices over time.
We talked a couple of lectures
ago about how firms and
individuals make choices when
faced with uncertainty.
So that was sort of a choice
across two different
states of the world.
You could get hit by a car.
You could not get
hit by a car.
Now we'll talk about choices
across two different time
periods, today versus tomorrow,
and how people make
those choices.
And the answer is going to be
pretty simple following what
we did last time, which is
whenever you're faced with two
choices that pay off at
different times, you just want
to choose the choice with the
highest present value.
So if you're faced with two
streams of payments, you know
that you can't just
add them up.
What you need to do is you need
to add them up in a way
that gets present value.
So, for example, consider the
example of a professional
athlete who's considering
two contracts.
One contract pays $1 million
today, and one contract pays
$500,000 today and $2
million in deferred
payments in 10 years.
So that's the two contract
options facing the player.
If you read it in the newspaper,
they would describe
this is a $2.5 million contract
and this as a $1
million contract.
However, the newspaper is wrong,
because they haven't
accounted for the fact
that some of those
payments are deferred.
So they're worth less.
So how do we compare them?
Well, to compare them, we have
to take the present value of
these two streams. So the
present value of the first
stream is just $1 million,
because it's paid today.
So putting it in today's
dollars,
it's worth $1 million.
The second stream is worth, the
present value is $500,000
plus $2 million over 1 plus i
to the 10th, because it's
being paid in 10 years.
And actually here, I'm
going to not use i.
I'm going to use r for the
real interest rate.
Remember last time we talked
about how what really matters
is the real interest rate, the
interest rate you get minus
inflation, minus the costs of
price increases for goods you
have to buy with that interest.
So remember we want
to use the real interest
rate here.
So I'll use r now.
So, basically, whether this
second contract is a better
deal or not depends on what
the real interest rate is.
So if r equals 5%, then the
present value of this second
contract is $1.73 million.
So that is a good deal.
On the other hand, if r equalled
20%, if there's a 20%
interest rate as there was back
in the late '70s, early
'80s, then the present value
is $0.82 million.
So it's not a good deal.
So the key is if you want to
ever compare two streams of
payments that pay off in
different times, you have to
bring them back to a comparable
unit, to today's dollars.
And the way we do that
is by calculating
their present value.
And this is a problem people
have. A common mistake that's
made is people don't
consider this in
evaluating streams of payments.
So a classic example is when
you hear someone wins $100
million in the lottery.
It's actually a lot
less than that.
Because $100 million lottery
win, what it really is is $5
million a year for 20 years.
And you have a choice.
You could take a lump sum now,
or you take the $5 million a
year over 20 years.
So basically, the $5 million
a year over 20 years is, of
course, worth a lot less
than $100 million.
What's it worth?
Well, it's worth $5 million plus
$5 million over 1 plus
the real interest rate plus $5
million over 1 plus the real
interest rates squared plus
dot dot dot dot plus $5
million over 1 plus the real
interest rate to the 20th.
So, for example, for an interest
rate of 5%, if r
equals 5%, this lottery is
really worth $65 million.
Now, that's still pretty good.
But it's a lot less
than $100 million.
When you hear a number about a
player's contract or a lottery
winning, you need to always
recognize that the effective
value is going to be lower than
what you hear on the news
because of the time payment
that takes place.
Now whether that's a big
deal or not depends on
the interest rate.
So Victor Martinez just signed
with the Detroit Tigers for
four years and $50 million.
Now, he could have signed with
the Chicago White Sox for
three years and $42 million.
Or the Boston Red Sox
were offering.
So the Chicago White Sox
were offering three
years and $42 million.
Now, you might say that you
can't really compare those
two, because one is out
three years, and
one is out four years.
But the truth is the interest
rate right now is so low that
you can pretty much
compare them.
Right now, the interest
rate you can get in a
bank is close to 0.
So, basically, if the interest
rate is 0, the present value
is the nominal value.
So right now, you can sort
of compare players'
contracts like that.
On the other hand, when the
interest rate is higher, you
can't do that comparison.
And, in particular, what you'll
hear a lot of times is
these contracts have very
deferred payments.
So even for a low interest rate,
it's still worth a lot
less in the end.
So that's the key point to
remember when you hear values.
It's to know that you have
to discount them
by when they happen.
And that's going to depend on
how high the interest rate is.
Now, this leads us directly to
the important implication of
present value which is how firms
and individuals make
investment decisions.
So we've talked about firms
choosing a level of capital
and a level of labor.
And we talked about in a simple
isoquant-isocost framework.
But, in reality, firms
don't really deal
with that simple framework.
In reality, for any given
investment decision, they
essentially want to compare the
cost of that investment to
the benefits of that
investment.
And that depends on
things like the
isoquants and the isocosts.
But it also depends critically
on the time frame over which
that investment will pay out.
And what firms consider when
they make an investment
decision is the net present
value of that decision.
On net, what's the
present value?
Because often, for the
investment decisions, you have
to lay out money up front to
recoup that money later on.
So this adds an extra
dimension.
Which is not just you're
adding up a
stream of future payments.
You're actually contrasting a
debit now versus credits in
the future.
And the math is the same, but
it's a little bit more
complicated.
So the net present value of any
investment is going to be
the revenues from that
investment in period 0 minus
the cost of that investment in
period 0 plus the revenues
from that investment in the
period 1 minus the cost of
that investment in period 1 over
1 plus r plus dot dot dot
dot dot plus the revenues in
year t minus the costs in year
t over 1 plus r to the t.
So the net present value is
going to be a function of at
every year is the investment
making or losing money and
then adding those future gains
or losses up discounting by
when they occur.
And the bottom line
is firm investment
decisions are very simple.
If this is greater than 0, then
it's a good investment.
If it's less than 0, it's not.
And this matters a lot, because
you'll often see
investments that have
cash losses up
front and gains later.
In fact, that's sort of the
definition of investment.
It's that you're investing some
money up front to yield
returns later on.
So, for example, if you have an
investment with an upfront
cost of $100 in year 1, it's
going to cost you $100 in year
1 to buy some machine, and
you get no revenues.
So it's minus $100 in year 1.
But in year 2, you're going to
earn $200 from that machine
minus you're going to have
a $50 maintenance on the
machine, so $150 in year 2.
So in year 1, you buy the
machine for $100.
In year 2, the machine produces
some widgets which
you can sell for $200.
But, along the way, you have
to maintain that machine.
And that costs you
$50 in year 2.
The net present value is minus
$100 plus $150 over 1 plus r.
That's the net present value.
Whether that's positive or not
is going to depend critically
on what the interest rate is.
So the key thing is we want to
take that stream of payments,
positive or negative, and put
them in today's terms. Are
there questions about that?
But this raises the question of
well, what interest rates
should a firm use?
So the firm has got to
make this decision.
Should all firms just walk by
BayBank, or Fleet Bank, or
whatever the hell
it's called now?
What is the big bank called?
Fleet, I guess.
Should they walk by now and look
in the window and say the
interest rate is 1%, or
2%, 3% and use that?
What should firms do?
Basically, the key issue is that
different firms will have
different interest rates
that they want to use.
Or firms will have different,
what we call, discount rates.
You can have a firm-specific
discount rate.
You can have a firm-specific
discount rate that firms might
want to use.
And what's going to determine
that is going to be the
opportunity cost of
money to the firm.
What is the firm's next
best use of that
money they're investing.
So, for example, let's say a
firm has a bunch of cash
sitting around.
Let's say the firm has $100 in
cash sitting around, and it's
trying to decide whether or not
to make this investment.
How do we decide on what the
opportunity cost on that
investment is, what the right
discount rate is to use?
How should the firm
think about that?
If it's got the cash sitting
around, how should the firm
think about whether it
should invest $100?
Yeah.
AUDIENCE: Well, whether or not
it has some other place that
it can invest it.
Or it's just going to rot
in a safe somewhere.
PROFESSOR: Well, at a minimum,
we can put it in the bank.
So at a minimum, it can always
earn 1% or 2% of whatever
banks are paying now.
But what you're saying
is right.
It may also have other
investment opportunities.
So, in some sense, the
discount rate for any
investment opportunity is what
you could earn on the next
best investment opportunity.
So if I've got $100 sitting
around, and I've got a
guaranteed 10% I can make
somewhere, then if I decide
whether or not I should take
this investment, I should use
a discount rate of 10%.
If I can make 20% somewhere,
I should use 20%.
So, in some sense, what you
want to do is you want to
stack up your investment
opportunities from worst to
best in terms of
rate of return.
And then you start at the top
of the list and ask, OK,
discounting at the best
alternative opportunity, is
this one worth it given
the steam of payments?
And then work your way down the
list. So, basically, the
key thing is that for any firm,
their opportunity cost,
their discount rate is the next
best thing they could
have done with the money.
Similarly, if a firm doesn't
have the money and is deciding
whether or not to borrow the
money to do this investment,
then the discount will be the
cost of borrowing the money.
Right now the bank only
pays 1% on your money.
But if you want a loan, you
still have to pay 4% for it.
So it may be that you could end
up in a situation where
your $100 doesn't really do
you that much good saved.
And it would cost so much to
borrow the $100, that it's
better to use the $100 that's
sitting around.
So, basically, let's say you
have $100 sitting around, and
you're trying to decide how
to finance its investment.
Well let's say you have an
alternative investment that
yields 10%.
What you do is you put the
$100 on the alternative.
And then you say, well, should
I then borrow to finance this
investment?
Well, I have to ask, is the
borrowing rate low enough that
this net present value
is positive?
So the firm wants to consider
all of its options it can do
with its money that it's
borrowing and consider a
discount rate for each, which
is the alternative next best
use of the money.
Now it's not just
firms that make
these investment decisions.
People have to make these
decisions too.
In fact, I faced one, a number
of years ago, when I was first
teaching this course.
So it's good for me to work
it out in the context.
I was decided this just
about the time I was
delivering this lecture.
And here was my choice.
Basically, I had to decide
on whether to invest in
insulation for my 100-year-old
house.
I've got this old house, windy,
crappy, whatever, and I
had to decide whether to
invest in insulation.
And the math was that my heating
bills were costing me
$2,000 a year.
I was spending $2,000
a year in heat.
It's a lot more now.
Back then it was
$2,000 a year.
My best estimate was that if I
insulated my house, I could
lower my heating costs by
about 25%, or about
minus $500 per year.
But to do that insulation
would cost $4,000.
So my question was, do I make
a $4,000 investment to lower
my heating costs
by $500 a year?
Well, I know how to do that.
I say, I take my $4,000, that's
a negative in year 1.
So let's say there's no effect
in year 1 of the heating
costs, because they're
putting it in.
So the heating savings
start in year 2.
So then in year 2 I'm
going to save $500.
But that I'm going to
have to discount at
some interest rate.
In year 3, I'm going to
save another $500.
I'll discount that at some
interest rate, and so on.
Now, the tricky thing about this
calculation is twofold.
What are the two things I still
have to figure out to do
this calculation?
Yeah.
AUDIENCE: The time frame that
you're going to spend in the
house and the interest rate.
PROFESSOR: One is the
interest rate.
Now, for that one, I have to
think well, if I had money
sitting around, what was the
next best investment
opportunity.
This was the early 2000s when
the stock market didn't look
like a very good investment
opportunity.
The next best was the interest
rates were probably on the
order of about 5% back then.
So let's say I could have put
it in the bank at 5%.
But the other tricky thing
is how long will I
have the house for?
If I'm going to own the house
forever, or for long enough
that it's equivalent to forever,
then I know I can
just rewrite this as minus
$4,000 plus $500 over r.
So if the interest rate was 5%,
then that's minus $4,000
plus $500 over 5% or plus
$10,000 which is well above 0.
So at a 5% interest rate, if I
was going to own the house
forever, this is a
great investment.
Yeah.
AUDIENCE: Wouldn't you also have
to consider how much it
would add to the value of
your house when you
attempt to sell it?
PROFESSOR: Excellent point.
Even if I'm not going own the
house forever, it still might
be a good investment.
Let's say I was going to sell
the house in two years, then
it would be minus $4,000
plus $500 over 1.05--
Well, let's say I was going to
sell it after two years.
So this is the first year
and the second year.
So you might say, well, this
is clearly a bad deal.
I'm spending $4,000, and
all I'm saving is $500.
And that's in this future
where it's worth less.
But then the question is, how
much does it raise the value
of my house?
In a perfect world, given that
my house will live on forever,
it should raise the value
of my house by $10,000.
Because what I've done is
I've saved $500 forever.
So whoever buys it after me
should be willing to pay
$10,000 more for it.
But the question is that
information, will that
percolate down?
Will people actually include
that in the value?
So in some sense, the decision I
had to make was, will I live
there long enough that even if
the next people don't value
it, I'll still end
up having the
positive net present value.
If I lived there for more than
about 10 or 12 years, that
would be true.
And the second thing is if I'm
going to live there less than
that, will the price go up
enough that the net present
value will be positive?
I decided to do it.
I've been there at least
10 years since.
So it was a good decision.
But this is exactly how
consumers face these kinds of
decisions every day.
Just as uncertainty affects
decision making of people
every day, so does thinking
about streams of
payments over time.
Yeah.
AUDIENCE: Did you leave
out the square on
the $500 over 1+r?
PROFESSOR: Yeah.
You're right.
Good point.
OK.
so now another very interesting
application of
this that may be more
relevant to you.
You guys aren't thinking
about insulating your
houses right now.
But your family has recently
thought about a
very important decision.
It's not about investing in
physical capital, like
investing a machine,
but investing
in your human capital.
An important theory due to
Gary Becker, Nobel Prize
winning economist at Chicago,
was that just as we can think
of firms buying machines as
investing in physical capital,
we think of people investing in
education as like building
your human capital.
You're spending money to
improve your long run
productivity just like buying a
machine improves the firm's
long run opportunity.
So it's exactly the
same thing.
It's just instead of investing
in a building or a machine, we
invest in you.
And, likewise, human capital
investment decisions are
subject to the same net present
value considerations
that physical capital production
decisions are
subject to.
Let's think about this with
an example from the book.
So imagine that if you don't go
to college, you're going to
work for age 18 to age 70.
And if you do go to college,
you work from
age 22 to age 70.
You get the extra year dinking
around Europe or whatever.
No, that's right, 18
to 22, four years.
So you either work from 18 to 70
if you don't go to college
or 22 to 70 if you
do go to college.
Imagine, moreover, that college
costs $10,000 a year,
obviously not MIT.
Some state school, $10,000 a
year is what college is going
to cost. And the cost of going
to college is twofold.
One is you pay the
$10,000 a year.
Second, you forgo earning
while you're in college.
The benefit of going to college
is you learn a lot
more once you graduate.
On average, at age 22, the
typical college educated
person-- once again, not MIT--
but the typical college
educated person earned about
$30,000 while someone with a
high school diploma only
earned about $20,000.
So you earn a lot
more thereafter.
So, basically, the trade-off is
you pay tuition up front,
and you lose earnings up front,
but you earn a lot more
starting at age 22.
Well, how do we think about
whether that's a good
investment or not.
Well, let's look at
Figure 22-1, the
present value of education.
What you see is a diagram
of the net present value
calculation.
So from age 18 to 22 there's
a huge cost, which is your
forgone earnings plus
the amount that you
had to pay to go.
Then starting at age 22, there's
a net benefit, which
is you earn more.
Basically, whether the net
present value is positive
depends on comparing the shape
of these and discounting the
fact that the earnings you make
from going to college are
worth a lot less.
So what's striking here is that
basically if the discount
rate is more than 5.1%, it turns
out not to make sense to
go to college.
It's pretty amazing, if
you think about it.
You earn 50% more if you go
to college, 50% more.
And yet if the discount rate is
more than 5.1%, which it's
been, typically, in many years
in our society, it's going to
end up not making sense
to go to college.
Why?
Because the upfront costs
are worth so much more.
The upfront benefits of
excluding college are now.
And the benefits of your
education are distant.
So, as a result, because
of net present value
considerations, unless the
discount rate is very low,
it's not going to make sense
to go to college.
It turns out now, of course, the
discount rate is very low.
Now we ask ourselves, OK, what
is the discount rate your
parents face when they
decide whether
to send you to college?
Or maybe you faced it?
Maybe you're paying for
your own college.
What's the discount
rate you face?
Well, once again, it's the
opportunity cost of the money
you use to go to college and the
opportunity cost of what
you could have done with the
money you made if you were
working now at gap.
The opportunity cost of the
money you could have made, is
you could have saved that
at some interest rate.
But the truth is whatever you
could have saved it at,
nothing is yielding much
more than 0 right now.
There's no investment that
yields anything.
So the interest rate is very
low on that savings.
Moreover, you had to borrow
the $10,000 a year and, in
your case, the $50,000 a year,
to come to college.
And that's at the borrowing rate
which is still above 5%
even in this economy.
Yeah.
AUDIENCE: Can you explain to me
what the discount rate is.
PROFESSOR: Oh, the discount rate
is the interest rate in
this net present value
calculation.
So when you're considering
whether to go to college, it's
the rate at which you discount
those future extra earnings
that you're going to get.
So the discount rate is your
version of the interest rate.
It's the opportunity cost, the
opportunity cost to you of
what you could have done
with that money.
What you could have done with
the savings from working is
basically nothing.
It would have just sat
under your mattress.
However, the money you had to
borrow to come to college,
that you paid 7%, 8%.
That's money that has a pretty
high discount rate.
That's money that's worth a
lot less in the future.
So at the end of the day, with
today's interest rates, it
almost certainly makes sense
to go to college.
However, when interest rates
are high, it might not.
And that's an argument for why
the government may want to
subsidize student loans.
The government is in the
business of subsidizing
student loans and making
student loans
artificially cheap.
That's a pretty big government
expenditure.
It's on the order of
$30 billion a year.
Why is the government
doing that?
Well, this table
tells you why.
If the government thinks that
there's social benefits for
having a more highly educated
population, then, essentially,
by intervening to lower the
discount rate through
subsidizing college loans, the
government can encourage
people to go to college.
OK.
Questions about that?
So that's how we think about
net present value in
investment decisions which is
basically to put everything in
today's dollars and then,
on net, ask if
it's positive or negative.
Now, the other thing I want
to talk about, in terms of
government policy, and in terms
of important issues in
this area, is about increasing
savings.
I want to talk about increasing
savings in the US.
Why do we care about increasing
savings in the US?
Why do we care about
that as a goal?
After all, I said savings
is a bad.
Consumption is the good.
Why do we care about savings?
Well, the fact is the
US government does.
The US government spends
hundreds of billions of
dollars a year encouraging
individuals to save in ways
I'll describe in a moment.
Why do they do that?
Well, the reason they do that is
because savings becomes the
engine for growth
in our economy.
Basically, as savings goes up,
that increases the pool of
capital available for
firms to draw from.
In other words, that shifts
out the capital
market supply curve.
In terms of the diagram that
we made last time of the
capital market, that shifts out
the capital market supply
curve or increases that
pool of capital.
As the capital market supply
curve shifts out, what happens
to the interest rate?
It falls.
That leads the real interest
rate to fall.
Because there's a bigger pool.
It's cheaper to get from it.
As a pool grows, it's cheaper
to draw from it.
That lowers the interest rate.
What does a lower interest
rate mean for any given
investment to its net
present value?
It means it's higher.
In means that any given
investment has a higher net
present value now.
Because a lower interest rate
means you might as well invest
instead of just putting the
money off to the future.
And a higher net present value
means more investment.
So more savings becomes
the engine of
growth for our economy.
Because savings promotes
investment.
When people save, it lowers
the price of borrowing.
Firms are more likely to borrow,
and they invest more.
And so that's why savings
is so important.
And this is basically a lot
of what Bob Solow won
his Nobel Prize for.
A famous professor from MIT
won his Nobel Prize for
pointing out the critical
role in savings is
an engine of growth.
It's that basically savings
becomes the
key engine to growth.
And as a result, society should
care about how much
individuals save, not just
how much they consume.
And that's why savings
is so important.
The problem is we don't save
a whole lot in the US.
In China, for example, the
savings rate, depending on how
it's measured, is on
the order of 30%.
So for every dollar people
earn in China,
they save about $0.30.
In the US, it's about 3%.
For every dollar we earn,
we save about $0.03.
It was negative for a while.
Yeah.
AUDIENCE: Are those rates
including taxes and other
things that people
have to pay.
So is it like revenue?
PROFESSOR: Its a share of your
disposable income you save.
The check you take home, how
much of it do you save, and
how much of it do you spend?
US citizens spend about $0.97 on
every dollar we take home.
Chinese citizens spend
about $0.70 on every
dollar they take home.
You might have noticed that
China's grown a hell of a lot
faster than the US over
the last 30 years.
It's no coincidence.
They're basically building up
a stock of capital that's
allowing their firms to draw
on it at a cheap rate and
invest. And that's why something
like 20% of all the
world's cranes are in
Shanghai right now.
Because they have a huge pool
of capital they can drawn to
build all of those new
buildings and invest.
So this is a big problem
for our place
in the world economy.
The US is falling behind in
the world economy, because
we're not saving enough.
We're not building up
that pool of capital
that our firms need.
As a result, there's a huge
public policy effort to
promote savings.
And, in particular, there's an
enormous amount of emphasis on
tax subsidies to retirement
savings.
The basic idea here is that when
you put money in the bank
to save for your retirement, the
interest you earn on that
money is taxed.
The interest you earn on
that money is taxed.
That lowers the rate of
return to savings.
And, assuming substitution
effects dominate, that means
you save less.
So in today's system, since we
tax the interest you earn in
the bank, you save less
people think.
We still don't have quite
convincing evidence on that.
But people usually presume
substitution effects dominate.
There's less savings partly
because we're taxing savings.
And, as a result, there's
less investment.
Yeah.
AUDIENCE: When we're talking
about savings here, are we
just talking about just
private savings?
Or are we also concerned with
what the government is doing?
PROFESSOR: Excellent question.
Let me actually come
back to that.
Let me answer that, but I want
to come back to that.
That's important.
What we care about,
of course, is the
total net pool of savings.
And if the government draws from
that, that's less money
that firms can draw from.
So you're absolutely right.
We about the net level of social
savings which is people
plus government.
If people save a lot, but the
government has a huge deficit,
that cancels out.
And I want to come
back to that.
It's very important.
This is a good point
you raise.
We take these taxes.
We tax your interest. That
discourages savings, but at
least it raises money
for the government.
So on net, it's not clear if
it's a bad thing or a good
thing for savings.
On the one hand, at least we get
money for the government
which can reduce the
government's deficit.
On the other hand, we discourage
your savings which
may reduce your savings.
So on net, it's not clear.
But, generally, the assumption
is that on net, total social
savings falls.
But as that question points out,
that assumption relies on
two things.
The first one relies on the
substitution effects
dominating income effects.
And it relies on the
substitution effects being so
strong that the reduced savings
because we're taxing
it exceeds the extra revenues
we get from taxing it.
But under those two assumptions,
the government
might want to offer some tax
subsidies or try to offset
this taxation of capital
income by offering tax
subsidies to individuals.
And the way we do that is we say
that you can save for your
retirement tax-free.
Actually, it's not tax-free.
Let me say it again.
We allow you to save for
your retirement on a
tax-deferred basis.
So, for example, we have
employer-provided pensions.
Pensions are plans that
your employer sets up.
where you take part of your
salary, and that is not taxed.
Instead it's saved.
And when you retire, you
get that savings,
and then it's taxed.
So, in other words, right now
MIT takes $2,000 from my
salary every year and
puts it aside.
When I report my income to the
IRS, it's $2,000 lower.
So I'm not paying taxes on that
even though I earned it.
That money is in an MIT
pension account that's
building up.
MIT has invested, and
it's building up.
And when I retire, I'm going to
get that money and then pay
taxes on it.
Now, you might ask yourself,
so what?
What the hell is the
advantage of that?
You pay taxes now or you
pay taxes later.
Who cares?
Why is that a benefit to me?
AUDIENCE: Because the present
value of the money in the
future is less.
The after tax amount is going to
be less assuming that taxes
don't rise by a substantial
amount in the future.
PROFESSOR: Exactly.
Assuming tax rates
stay the same.
Let's leave that.
The point is just as money in
the future is worth less than
money today, paying taxes in
the future is better than
paying taxes today.
So if MIT take the $2,000 aside
for me and saves it, and
I pay taxes on it in 25 years
when I retire, that's 25 years
with a 5% discount rate.
That's nothing.
25 years at a 5% discount rate,
those taxes are worth
like 1/3 of what they are
if I pay them today.
So basically by deferring
taxes, we are wealthier.
Just like by deferring payments,
we're poorer.
We don't have the table here.
AUDIENCE: [INAUDIBLE PHRASE].
PROFESSOR: What?
No.
That's OK.
Let me just sort of explain
an example.
Let me just do an example
here and explain that.
So imagine you've got an
individual who's a
70-year-old, so someone
about to retire.
They are a 70-year-old, and
he earns $100 on his job.
And he wants to save it for
1 year and then spend it.
And he has two choices.
He can put it in the bank or he
can have his employer hold
it aside as a pension payment,
and he can get it next year.
And let's say the interest
rate is 10%.
And let's say his
tax rate is 25%.
So the bank route,
what happens?
First of all, $100 he gets
is going to get taxed.
So he's going to have $75
to put in the bank.
He's going to put that
in the bank.
And that's going to
yield $7.50 in
interest after one year.
But that will also be taxed.
That $7.50 of interest
will also be taxed.
He has to pay $1.88 in taxes
on that $7.50 of interest.
So on net, he's going
to end up with $75,
$82.50 minus $1.88.
So he's going to end
up with $80.32.
Is that right?
$80.22.
So he's going to end
up with $80.22.
Now, if instead he asks his
employer to hold it aside as a
pension, then he gets the whole
$100, and that gets
saved at 10%.
So he earns $10 of interest. So
at the end of the year when
he gets the pension
payment from the
employer, he gets $110.
That is then taxed at 25%, and
he ends up with $82.50.
He ends up with more money.
Even though it's just paying
taxes one year later, he ends
up with more money.
And the reason is because he
got to earn the interest on
the taxes instead of the
government earning the
interest on the taxes.
Here, he pays taxes up front.
So he has less to save. So
he ends up with less.
Here, by paying taxes later, he
gets to earn the interest
on that extra money.
And he ends up with more.
So by deferring taxes, he's
effectively richer.
And this is a very
simple example.
If you did the same example,
and instead of making it 1
year, you made it 30 years, then
you'd end up with twice
as much money if you go the
pension then if you go the
regular savings route, twice
as much money just from
deferring taxation
for 30 years.
You get taxed either way.
It's just that you get to earn
the interest instead of the
government earning the
interest. Yeah.
AUDIENCE: Can you earn interest
on a pension?
PROFESSOR: OK.
So let's come to that.
Let me make sure people
understand the math here and
why it's a better deal.
OK.
Do you earn interest
on a pension.
It's a good question.
There is three ways that you
can have tax subsidized
retirement savings.
And let me go through
them clearly now.
One route is the pension.
Under a pension, your employer
takes money out of your
salary, saves it in some account
with your name on it,
but they invest it.
And then you get the money
when you retire.
An alternative, which firms
are slowly moving to, is
401(k) accounts, which you've
all heard of by now.
401(k) accounts are just like
pensions, except you control
the investment of the
money, not the firm.
So under a pension account, your
employer takes money out
of your salary, puts it aside,
and invests it as he likes,
and you get the return
when you retire.
A 401(k) account is the same
thing except you decide how
much to take or the employer
decide how much to take, and
you decide how to invest it.
And then you get the return
at the end of the day.
But the tax treatment
is the same.
Yeah.
AUDIENCE: Isn't it also one's
defined benefits and one's
defined contribution.
PROFESSOR: Well, within this,
within pensions, there's two
kinds of pensions.
There's defined benefits and
defined contributions.
We can think of this as old
style and new style.
Defined benefits is what the
auto companies and the steel
companies had.
It's dying away.
A defined benefit pension is one
where you don't actually
get an account from
your employer.
They just take money
out of your salary.
And then when you retire, they
pay you some amount which is
unrelated to what
you put away.
It's related to something like
how long you worked at the
company and what your
wages were.
So defined benefit pension is
they literally define the
pension benefit you get.
And it's got no direct relation
to how much money
they took away on your behalf.
It's related, instead, to what
you earned and how long you
worked there.
A defined contribution pension
is what I described.
It's literally an account
with your name on it.
And that's what most
pensions are now.
Almost any firm you guys will
work for will have a defined
contribution pension, which is
one where there's literally an
account with your name on it.
And most of you will have
401(k)s where you actually
control the investment.
And then finally, the
last option is IRAs.
That's not the Ireland
thing, but
individual retirement accounts.
These are accounts which
operate outside
the employment setting.
You can literally set up your
own pension, effectively, by
taking money, putting
it in the bank, and
calling it an IRA.
The thing about IRAs
is IRAs are not
special investment vehicles.
They're just a label for
savings that you do.
Any kind of savings
can be an IRA.
You can have gold in your IRA.
You can have cash in your IRA.
You can have whatever you
want in your IRA.
Any kind of investment
is an IRA.
What an IRA means is you say to
the government, this money,
up to $5,000 a year, don't
tax me on now.
I'm going to put it in a
specially labelled bank
account, and you'll tax me
on it when I retire.
So it's just like a pension, but
you set it up on your own.
And the firm is not involved.
Let me just say something
on the IRA.
If you're not wealthy, if your
income is below about $75,000
a year, it operates just
like I described.
If you are wealthy, if your
income is above about $75,000
a year, then you can't get
the tax break on the IRA.
So the IRAs are really more
focused towards lower income
populations.
Now, here's an interesting
question that you all face.
You're going to get jobs
in a couple of years.
And your employers are going
to offer you pensions, or a
401(k), and you can
set up an IRA.
And you're going to have
to decide, do I want
to do that or not?
Now, what are the
considerations?
Well one consideration is what
I mentioned last time, which
is that savings earlier in
your career is a lot more
beneficial than savings
later in your career.
The second advantage, of course,
is that there's the
tax break which, of course,
the earlier you do it, the
more valuable it is than
the later you do
it by the same logic.
On the other hand, there's a
huge disadvantage to these
forms of savings.
You can't get them
until you retire.
If you take them out before
you retire, you pay a tax
penalty on them.
So this trade-off when you think
about setting these up
is you only want to put in money
you're sure you're not
going to need until
you retire.
So it's a good idea
to set these up.
It's a good idea to take
advantage of this tax breaks.
But, in doing so, you have
to remember that there's
different kinds of savings, and
there's different needs
for savings.
You can't put savings for
a house in these.
You don't put savings in case
you lose your job in these.
These are for savings which you
can honestly say I won't
need for 30 years.
And that's the trade-off.
You should do it early and
as much as you can.
But you should also recognize
that you don't want to leave
yourself with no money in
the bank to do this.
Because then, if you lose
your job, there's
nothing to draw on.
And that's how one sort of
thinks about these things.
Yeah.
AUDIENCE: So you said there
was a tax penalty if you
[INTERPOSING VOICES] early.
Is that greater than the tax
rate that you would normally
pay on them?
Because then, even with
that penalty--
PROFESSOR: It depends on how
long you have the money in.
If you have it in for 20 plus
years, even with the tax
penalty, it's a good
idea to do it.
But if you're going to have
it for five years,
it's not worth it.
AUDIENCE: So it's bigger than
a tax [INAUDIBLE PHRASE].
PROFESSOR: Yes.
It's 10% of the balance.
You pay 10% of the balance
for the tax.
So, basically, whether that's a
good thing or not depends on
how long the money's been in
there and what the forgone
interest rate is.
But for a short investment, it's
going to be a bad idea.
If you have an IRA for 20 years
and then have to take it
out, it's still a better
deal then having
not put it in there.
One last point about a 401(k)
that's very interesting.
Basically, in the theory I've
taught you in the last two
lectures, what determines your
savings is the interest rate.
If the interest goes up and
substitution effects dominate,
you save more.
If it goes down,
you save less.
But, in fact, in the real world,
savings is determined
by lots of other factors that
economists are just starting
to think about and model.
One which you've know for a
long time, of course, is
precaution.
The bigger risk you face in
your life, the more you'll
want to save. So, for a given
interest rate, we've found
that individuals who face
greater risk in
their lives save more.
Likewise, we found that
government programs which
protect you from risk cause
you to save less.
So this is another tricky
thing with government
programs. On the one hand, we
like government programs like
unemployment insurance or social
health insurance that
protect us in case we lose
our job or get sick.
We have to recognize the social
costs of those programs
is people save less.
And that's less savings equals
less investment.
So precaution is one reason
why people save.
But there's other factors which
fall in the realm of
behavioral economics, which I've
mentioned earlier in this
course, which drive why people
save. And this is one of the
most important economic
findings in the
last couple of decades.
Studies of firms that change the
structure of their 401(k)s
in a particular way
that shouldn't
matter but does a lot.
So for most firms, when you go
decide to join the firm,
they'll say, here's a
benefits package.
You can sign up.
You can sign up for
health insurance.
You can sign up for
life insurance.
You can sign up for a 401(k).
And that's the way
it usually goes.
And we typically see, as a
typical large firm, is with
new employees there's about a
25% sign-up rate for 401(k)s.
And over the next 10 years,
that grows to about 70%.
So people don't join
right away.
They join slowly.
Some firms experimented with
changing the contract in a
very small way that should not
matter in this course.
They've instead said,
welcome to our firm.
You are now signed up for the
401k unless you tell us you
don't want that.
Now, that's the same thing.
I can sign up or I can tell them
I don't want to be in.
Those are identical things.
It's just a question
of the default.
It's just a question of the
default that I have to say
affirmatively yes or I have
to say affirmatively no.
What they found when they
switched, is the initial
sign-up rate from 401(k)s went
from 25% to 75% simply by this
relabeling.
Simply by shifting the default,
you've got an
incredible change in
people's behavior.
And what this says is that
economics is about more than
things like interest rates.
It's about more than prices.
In this course, economics
is all about prices.
I talked about it in
the first lecture.
But in the real world, we bring
psychology into it.
Economics is about more
than just price.
It's about important
behavioral factors.
And this says that important
policies that there may be a
much more significant policy
than spending all this money
on tax subsidies and raising
the government deficit.
These tax subsidies, by the way,
add up to on the order of
$200 billion a year that
we spend on these.
So that's $200 billiion a year
that we're increasing the
deficit by to have these
tax subsidies.
What if, instead, we got rid of
them all and just defaulted
everyone to 401(k)s.
We'd probably raise savings more
and potentially save the
government a lot of money.
So, basically, the point is that
we have a lot of tools at
our disposal besides prices.
And our government policy makers
have to be thinking
about those.
OK so let me stop there.
Thank you all for coming.
Have a great Thanksgiving.
And we'll come back after
Thanksgiving and talk about
equity and efficiency.
