ShmoopTube

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principles of finance a la shmoop present value another twist all right

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well you've just won a mini lottery it pays $10,000 a year for five years it's [hand scratching lottery ticket]

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backed by Jeff Bezos founder of Amazon so if you attribute no risk to the money

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not being paid you buy into the 10% of your stock market appreciation thing

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meaning that you actually believe the market will go up on average about ten

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percent a year for the next few decades and you'd love to just put your money in

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an index fund and well forget about it and go play some golf [man hits golf ball]

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so the question what price buys you out of this annuity and yeah forget taxes

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because well in most structures it's way better to leave the money coming in in

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small payments over long periods of time if you take a lot of money out in year [stacks of money falling]

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one well if you'd likely be taxed at a much higher rate than otherwise but

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that's a separate issue from this problems fine illustration here well

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here's the discount rate and this is what the math looks like so you got your

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one you're gonna take out ten thousand bucks

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you're gonna divide it by the interest rate there it's it's one plus point one

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at point one for ten percent of your compounding notice it's to the first

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power because it's after one year of compounding and you get to nine grand

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and change and then a year two you take out another ten grand the present value

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of it you have to discount by two iterations of that ten percent of your

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thing you can you get eighty two hundred bucks

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then we scoop all the way down to year five that's ten thousand dollars given

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to you five years from now with no risk associated on the premium on top of it

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and you're gonna guess that ten percent a year is about your opportunity cost of

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compounding in the market that's one plus 0.1 there so you get one point one

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to the fifth power and if you divide that into ten thousand will you get

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sixty two hundred bucks and change okay so then you just add up this column this

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stuff over here the nine grand plus eighty two hundred plus seventy got and

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so on and you get about thirty eight grand so using the discount rate of 10%

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a year ie the opportunity cost of what you could do with the money deploying it

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elsewhere while the dough today is worth yeah about thirty eight grand

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steep discount from the fifty thousand dollars you thought you'd won great

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marketers those lottery people well the exercise here is really

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important to understand professionals use present value technique

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to value companies in the stock market and these flows don't just apply to

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bonds or promise series of payments they apply to companies and all kinds of [people handling money]

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other investing things that are coming your way in the meantime keep cursing

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Bezos name to the heavens for tricking you because as long as you're near a [man is angry at computer]

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computer microphone well he's probably listening or trying to sell you

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something

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