# FIN500 Mod03 P3b Time value of money calculations using the TI BAII Plus calculator - part 2

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Now the only other thing that we need to
do to - well two more things - the present value of mixed streams.
Say you have (uh) cash flows
of $100 dollars the first year, $200
the next two years, and $400
the 3rd year [should be 4th year]. We're going to place those
and we have an investment that will earn a
required rate of return of 10% - and we want to know the present value of those.
Now for mixed streams, present value of mixed streams
we do not use the 5 time value of money button;
we use a button above the interest rate button
the CF or cash flow button. So we hit CF
and that shows CF0. So what, how much do we have now to put in the account?
Or how much are we going to pay? We will use this later on
when we calculate NPV and IRR but
for projects, but we're not going to use it right now, so we will leave it 0 (zero).
And the buttons we're going to use, we're going to use the enter and the down arrow
to enter in our numbers. The BAII Plus works similarly to a spreadsheet
and that as you put in the numbers in the cells you can toggle back
and see what you've entered. So our first cash flow, we said, was $100 dollars
so we had a 100 and then enter, and then the down button.
Now F01 means frequency,
the first how many times does the cash flow occur in a row?
On this example we had a 100 the first year,
two hundred dollars for years 2&3, and four hundred dollars for year four.
So the hundred dollars only happens once so we just leave that at 1.
Arrow down to cash flow 2 or CO2.
Now again this one there was $200 dollars so we're going to have $200 dollars,
for years 2&3 so hit 200,
enter, hit the down arrow,
and then frequency since that 200 happens two years in a row
we hit 2 enter. And so that takes care of
cash flows for years 2&3. Then we hit
down arrow again, and enter our last cash flow of 400
enter - and there we've got all our cash flows. We can toggle back
up by hitting the up arrow, to see we don't have anything in the first one
(again we will leave that 0 until we get to a later chapter)
$100 dollars for the next cash flow and that happens once.
$200 dollars for the next cash flow
and that happens twice, and then $400 dollars for the last cash flow;
and that happens once. And if you keep going down you'll see the other cash flows
are zero. Now to calculate the present value, we're going to use the NPV button;
meaning net present value. You hit NPV and it says I equals
- that the interest rate that is used to compound these cash flows -
or discount these cash flows. So we'll say that was 10%;
so 10 enter,
and then we hit the down arrow
and it says NPV equals.
And then we hit compute and it says the present value of that stream of cash flows
is 67967. Now to calculate the future value
of a mixed stream you have to do it one at a time. Alright so I will not display that
now, it's just basically if we had that $100 dollars,
$200 dollars for two years, and 400 we'd have to calculate each one individually
to some time point in the future, and then add them up.
The only other thing I need to show you is say if we're doing
a semi-annual compound, or quarterly compound -
in that case, instead of changing the periods per year I would suggest
just changing the number of periods in the interest rate.
So we've got a $100 dollars we're going to put in for two years
at 10% interest,
then we're going to - but it's compound it's semi-annually -
we're going to increase or up the number periods by two
and divide the interest rate by 2.
Right so instead of - so it's in there for two years
instead of 2 we're going to put 4 because it's semi-annual compounding.
So I put 4 in, the interest rate was 10% annually,
and note that interest rates are always quoted in annual rates,
but since it's semi-annual compounding we're going to take 10% divided by 2
or 5% would be our interest rate.
100 as a present value, again we have 0 payment,
and then we're going to compute future value
to get an answer of 12155.
Now just a couple more things to show you on when you're
on the cash flow button, for the cash
mixed stream present value, for example, in order to get rid of
what you have entered in there, you have to hit the second
clear button - which says clear work -
while you're in the cash flow. So first you have to hit cash flow,
second clear work, and then after you do that
you can see that everything is back to zero.
One more thing with compounding that I almost forgot to mention
was continuous compounding. Say for example we're
putting money in an account that compounds continuously,
which is every microsecond.
What we have to do instead of using the time value of money buttons,
we have to use a button, LN, which actually second LN,
see above that is E to the x, E is the base
of the natural logarithm. And so in order to
do continuous compounding say we're $100 dollars
in an account for 2 years
continuously compounded at 7%.
The first you have to do is convert the 7% to a decimal,
so you take .07 multiply it by the number of years, in this case 2.
So times 2 equals .14.
And then you hit 2nd and then E to the x
and it gives 1.1503. That is your future value interest factor
that you then multiply -
so times the deposit a $100 dollars
so you can see your money - your $100 dollars -
has grown in 2 years at 7% compounded continuously
has grown to 115.03 rounding.
Now say if you just wanted an effective rate -
an effective rate at continually compounding,
say 7% that's the nominal rate,
what's the effective rate if you compound continuously?
Just hit .07 2nd E to the x, and it gives you 1.0725.
So we subtract 1,
so the effective rate is 7.25% (.0725)
So continuously compounded,
that's what the effective rate would be.