Effective Yield

finance a la shmoop what is yield to maturity yield it's the dough you get

back from your investment in a bond here's a thousand-dollar bond here's the [pigeons sitting on a line]

coupon of 7% so the yield is 7% while the bond lasts for 10 years and then

after paying you 70 bucks a year for a fat and happy decade of sitting on your

Duff collecting your interest you get your grand back and well that's it right [check changes hands]

um no well what happens if you bought that bond for nine hundred bucks or

twelve hundred bucks or some other random amount yeah way more complex well

there are two ways you make money from investing in a bond first there's the

interest as we just outlined 70 bucks a year the semi annual festival of dances [people dancing together]

when the interest payment is made right it's 35 bucks twice a year easy but then

there's the appreciation of the principle of the bond and yeah it could [flying crow starts inflating]

be depreciation of it - all right you bought a 6% yielding bond at a discount

to its thousand-dollar par value like say you paid 92 cents on the dollar nine

hundred twenty bucks for a thousand dollar par value bond well over ten

years you hold that bond until it matures it will appreciate in value I

call it - eight bucks a year and then it will pay to investors that thousand [check change hands]

dollar par value well yield to maturity which doesn't apply to shmoop writers

takes into account both sets of cash flows into your wallet the interest

yield plus the appreciation of the principle of the bond so in this case

the bond was paying interest of 60 bucks a year but then it also had appreciation

of eight bucks a year for a total of 6.8%

or 68 bucks a year in appreciation all right is this all there is to it you

just throw in a straight line number therefore the annual appreciation eight

bucks every year smoothly that's of the principle until it hits par and then

you're done no not at all life is never that simple all kinds of curveballs will

be thrown at you all over your head there and you think about you to [flying bird dodging balls]

maturity okay here's one for starters what about the time value of money

remember that thing ie the cash that you get twice a year in bond interest well

couldn't you reinvest that money elsewhere like it

moment the moment you collected 10 years earlier before bond matures and make

more money well sure you could and what about the application of straight-line

depreciation to the gain of 80 bucks over 10 years like why does the bond

depreciate exactly eight dollars a year in value instead of Raoh maybe less in

the early years and more in the later or or vice versa

yeah lots of curveballs and some of these are just accounting decisions or [businessman studying papers]

the way things are done and the way things are done in bond land is usually

driven largely by the way the IRS wants to tax you got it so that whole [Uncle Sam walking down the street]

straight-line depreciation thing and that's largely an IRS driver and here's

another some bonds are callable early so what if this bond was callable after

five years but at 102 or a $20.00 premium per bond or a thousand twenty

well then yeah the yield calculation is different and it's normally called out

as a quote yield to worst unquote or rather yield to the worst possible

outcome of the bond other than it going bankrupt or you know not paying on time [coins dropping]

in this case the yield to worst would be an appreciation from nine twenty two a

thousand twenty or a gain of a hundred bucks then over just five years so you'd

add twenty bucks a year to the dividends of sixty bucks a year and you'd get a

well at least a notional yield here then of eight percent right if the bonds were

in fact called at ten twenty thousand twenty bucks each got at eight percent

or does that yield to worst is that the worst you knuth know it's not the worst

at all the normal trajectory of this bond has it maturing in a decade and at

par not at a premium to par that ten twenty thing so it isn't bad to be a

yield to Wurster in this case it's just that if the bond is called early well [crow flying]

that would be the worst it would do other than like you know not pay off or

go bust and obviously this is all about appreciation when you buy it

depreciation you know works the same so just relist into this video in Reverse

and sometimes worst ain't so bad you [two birds on a line]