In this screencast, I'm going to show you how we can use some of the things that you have learned in the past couple of screencasts in order to compare alternatives. So these are investment alternatives. The first example that we're going to look at is would you rather have $15,000 cash now today, or a car in 10 years at the selling price of $25,000? So essentially a $25,000 value in 10 years from now or $15,000 today. We're going to assume an interest rate at 5% interest that's compounded semi-annually, which means twice a year. The second example, we're going to compare three Alternatives. Which would you rather have a b or c, we're going to assume a pretty high interest rate here of 0.09 and that's annual compounding. Would you rather have a $1,000 today right now or $1500 in four years from now or $350 now plus $200 at the end of the next four years? And then we're going to consider is your answer the same if the interest rate is 0.04 compared to 0.09. I've got this Stata file called comparing alternatives. So let's go ahead and work the first one. The two options, we have $15,000 cash now that's a present value. So we don't really have to do anything if we're converting everything to present value. Often times what you do is you take any future payments and you want to kind of discount them into today's terms. And we've talked about that quite a bit already in this course. So the present value of $15,000 cash is just 15,000. The car in 10 years we can use the present value function. So this is going to be present value, I've named cell B5 the variable i, this interest is compounded semi-annually. So I'm going to divide by 2. The number of periods in 10 years is going to be 20 because again interest is compounded twice a year. We aren't making any payments so that's 0, and the future value though is $25,000 that's a future value. In 10 years we have a car that we can sell at $25,000. So when I press Enter that tells us that $15,000 invested today, that's why it's negative in this function. If we invested $15,256, then that would be equivalent to 25,000. So the car in 10 years the present value 15,256 is slightly more at this interest rate than the $15,000 cash today. However, you got to be really careful because if the interest rate is a little bit more. So if I change this 2.06 you see that the present value of $25,000, 10 years from now is not quite as much as it was. So this is very sensitive to the interest rate. In other words, if we took $15,000 and invested it at 6% that would be more than $25,000. And so you have to be careful because what happens in the next 10 years if interest rates change slightly. The second example we're going to compare three options. The first option is a present value of $1,000 option B, we get $1,500 in four years from now. We're going to assume an interest rate for this example of 0.09. I've named cell C22 int for interest to differentiate between the interest here and example one. And then option C is we get $350 now plus $200 at the end of the next four years. Let's go ahead and calculate the present value of option B, we can again use the present value function. The rate is going to be our interest rate, we're compounding annually, so we don't need to divide by anything. The number of periods is going to be n, so I've named cell C21 n, and then the next argument is going to be our payment. We aren't making any payments on this particular scenario, but the future value is $1,500. That's a cash flow in the future, that's going to be a positive cash flow. So when I press Enter this means if we invested $1,062 today, we would get $1,500 back. This is a positive value, let me actually make that a currency and you see that option B is slightly more than option A here at an interest rate of 0.09. If the interest rate is less .05, then the present value of $1,500 in the future is actually more. So as the interest rate goes down, the present value of future investment will go up. Now let's take a look at option C, there's a couple ways we can do this. The easiest way is just to use the Net Present Value function NPV. Remember the Net Present Value function doesn't, you don't include anything that you get today or the the zeroth period, this is just future values. So I'm going to put in the rate that's our interest rate up here, and our values. Now I've already named cell C21 A, so we're going to be getting A, that's our payment next year. So year one, year two, year three, and year four. And so then if I press Enter that's only taking into account the four payments, but we have to add outside the function. We have to add in the present value of anything. So we get $350 now and what this means is that has a present value and net present value of $1,059. Actually let me go back to 0.09. So I got 0.09 and interest rate of 0.09 has a present value of 997, which is a little bit less than a present value of $1,000 cash today. So right now of these three, the best option is option B getting $1,500 in four years from now at the interest rate of 0.09. Another way to solve this that I like to do. I like to set this up as a table where I calculate the present values of each of our cash flows for each of the periods. And I just like to discount present values. I always remember that's a future value divided by 1 plus the interest rate raised to the year. So, this is our zeroth year, the zeroth year is not going to do anything to a present value, of already 350. But when I drag this down or discounting future cash flows to today's terms. What this means is $200 given to us four years from now is only worth a $141 today. Another way of looking at this is we can take $141.69 today invest it at 9% and in four years from now we would get $200. And then I can sum this, equals the sum of all the present values and that's exactly the same thing that you get using Net Present Value function. I like to do this way over here, call me old-fashioned, but I just like to kind of see an itemized present value for each year. By the way you can also use if you forget that formula you can use the present value function. The rate is our interest rate, you can put in the number of periods. So this is the number of periods that we have invested. We're not making any payments, but the fourth argument is where you can put the future value. And when I press Enter this is negative, which you kind of have to realize you have to flip that around, but we get the exact same things. So of these three options, it looks like option B is the best, but if we change this down to something like 4% we see again that option B is the best. Let's actually increase this to, what if we could get 12% interest? Then it looks like the best option would be to have cash today, because we could take that $1,000 today invest it at 12% and it would be better than either of these other two options. Hopefully this screencast give you a better idea of how you can compare financial alternatives.
