Bonds and YTM - Confused

I'm having a little trouble understanding the reason why cash flows derived from a bond's coupon rate are divided by (1 + YTM)^(Year Number). I understand the YTM to be an annualized rate of return that produces a yield that will generally exceed the realized yield due to the assumed reinvestment income at the same YTM. Is the reason the YTM is used as a discount rate simply because it is seen as type of opportunity cost? And what is the math that explains why dividing by this compounded rate of return equals the bond price?

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