00:01
So here we're looking at the present value.
00:03
And the whole idea of present value is that future cost and benefits are not the same as present cost and benefits, right? if i offered you $10 ,000 today or $10 ,000 through years from now, $10 ,000 to $1 ,000 today is obviously better because you could do more things, right? you could invest it, you could buy something as opposed to just having to wait.
00:21
So what we do is we want to convert future costs and benefits, future dollars to present dollars through the process of discounting, right? so the present value here is based on the five things, right? 50 ,000, also 60 ,000, also 75 ,000 in year three, and 90 ,000 in years four and five.
00:54
So we want to add these together because these are the cost savings, right? but we can't add them together because dollars five years from now are not the same dollars of today.
01:09
So here we're contemplating, look, after the first year of operating the machine, we're going to get $50 ,000 back.
01:18
But those $50 ,000 have to be adjusted by the rate of interest, right? when you divide x over one plus r, you are bringing it back one year, right? because the idea is that if you had x times 1 plus r a year ago, you could invest it at the rate of interest and end up with the actual value x, right? so every year you don't have something, you're giving up the rate of interest.
01:46
And that's why future things are worth less proportional to the rate of interest.
01:51
So in two years, we're going to have this squared.
01:56
Then we're going to have 1 .08 cubed, 1 .08 to the fourth, and 1 .08 to the 5, right? this is the present value or the process of discounting these futures cost savings to convert them back to current day dollars.
02:17
Now all we've got is simply an ugly calculator question.
02:21
And when i put this into the calculator, i get 284 ,000.
02:30
$679 .22...