It should be obvious now that the value of a dollar delivered in the future,
even if it comes from the US government is worth less than a real dollar
right now.
A real dollar right now is worth $1.
If I promise to give you a dollar in the future it's not worth as much.
So how should we estimate or
think about the value of dollars delivered in the future?
I think we've also agreed that the United States government,
promising to give you a dollar in the future, is worth a bit more,
than the promise of Tucker Balch giving you a dollar in the future.
But having a real dollar in your hand right now, this one, is worth the most.
Why is that?
You know intuitively why that is.
The deeper reason is there's a chance that I won't deliver on that guarantee
whereas we can be pretty sure that the U.S.
government will deliver on that guarantee.
So it amounts to risk.
And it all boils down to interest rate.
We're trying to figure out the present value,
or PV of a dollar that will be delivered in the future.
So it's worth some fraction of this future value.
Present value is worth some fraction of the future value.
So here's the formula in it's entirety.
Present value is equal to future value divided by 1 plus
interest rate raised to the i.
So the i is how far into the future this payment is going to be delivered.
So for instance, if it's going to be delivered right now i is equal to 0 this
whole component becomes 1 and present value is equal simply to future value.
In other words, if we're going to pay a $1, present value is worth $1,
if in the future that future is going to be 1 year from now.
It's 1 plus the interest rate, raised to the 1th power.
And that is what the future value of that dollar is.
So, let's work out an example.
Suppose with the United States government, because they're so
trustworthy, you can negotiate a 1% interest rate.
Actually, as of today, which is 2015,
this 1 year interest rate is only one-quarter of a percent.
In order words, interest rates are very, very low.
If you work it out, the value of a $1 bill paid to you in the future,
1 year from now, at a 1% interest rate is $0.99.
In other words, today, it's worthwhile for you to pay $0.99 to
the US government for the promise that they'll give you a dollar in a year.
Okay, consider now the Balch Bond.
So it's hard for me to sell you this asset right now for the same
price as the US government because if you had to choose between me and
the US government for a 1% return, why wouldn't you choose the US government?
You should go with the US
government because they're more trustworthy than I am.
So, how can I attract you?
Well, I can offer you a higher interest rate.
Let's say 5%.
And that works out to a value of about $0.95.
In other words, in order for me to attract you to buy my promise for
$1 in the future, I could only charge you $0.95.
So let's consider this in a chart form.
So how much is $1 worth if I promise to give it to you today.
Well, in that case, this i is equal to 0, so
the present value is equal to the future value of all this divided by 1.
So in all cases, if the number of years we're going to wait for
the delivery of that dollar is 0, the value is $1.
But what if we talk about promising you that dollar in the future.
If we look at this for the US bond, in 1 year we see it's worth $0.99.
If we carry that forward,
it's sort of this exponentially decreasing value like that.
If you look at the Balch Bond, which is, of course, not as worthwhile
as the US government, you see one that decreases at an even faster rate.
So in other words, at each year in the future, this $1 is worth less.
In other words, if I promise to give you $1 in two years, it's worth less than,
if I promise to give you $1 in a year,
it's worth even less than if I promise to give you $1 right now,
and these charts are different depending on what the interest rate is.
In other words, for the higher interest rate assets,
they decrease further into the future.
In other words, a dollar delivered in the future is worth less now
than the lower interest rate assets.