The yeild-to-maturity is the Internal Rate of Return on a coupon paying bond, if you held the bond to maturity and all the coupons were re-invested as soon as they were received.
The bond typically has two cash flows:
- Cashflow from coupon
- Cashflow from repayment from principal
\[ PV(PMT) = \sum_{t=1}^{N} \frac{C}{(1+y)^t} \]
and
\[ PV(FV) = \frac{FV}{(1+y)^N} \]
Therefore, the total PV is:
\[ PV = \sum_{t=1}^{T} \frac{C}{(1+y)^t} + \frac{FV}{(1+y)^N} \]
Now solve for \(y\) to get the yield from maturity.