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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.

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Duration: 7 minutes and 44 seconds
Country: Andorra
Language: English
License: Dotsub - Standard License
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Posted by: christineward on Feb 29, 2016

Time value of money calculations using the TI BAII Plus calculator - part 2

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