This was really helpful, thanks. Just to rephrase to make sure I’m clear, the IRR is basically equivalent to the rate I would need to invest my principal at in order to attain future cash flows
That makes sense when I think about just 1 payout (i.e. the IRR just becomes a CAGR). But when I have a schedule of cash flows, then the statement of “future cash flows” doesn’t make sense, because the future value of all cash flows is actually dependent on the IRR
So is it basically solving a system of equations? Two unknowns are the future value of all cash flows for your terminal year (or last year of projection) [call this x], and the IRR [call this y]. For a bond currently trading at $80 that matures in 3 years, and with a coupon of $3, your two equations are:
Equation 1:
3/(1+y)^1 + 3/(1+y)^2 + 3/(1+y)^3 + 100 = x
Equation 2:
(x/80)^(1/3) = y
Is that the intuition? Really helpful, thank you everyone 
(especially busprof, explanation happened to make the most sense to me)