Originally Posted by
ArcSine
The YTM is the discount rate which makes the PV of all your cash flows net to zero.
First, get a good handle on all your cash flows, both as to their amounts and their exact timing. At time t = 0 you have a cash outflow equal to the 110 puchase price, plus the accrued interest. Subsequently, you have cash inflows of $4 on each of the remaining coupon dates, and then the final maturity payoff of $104 (including the final coupon).
Having scheduled out your cash flows, you'll then go through the usual PV exercise of discounting all the cash inflows by some discount rate. The objective is to identify a discount rate such that the sum of the inflows' PV is exactly equal to your total immediate outflow (which is equivalent to saying that the sum of all the cash flows' PV is zero, since the t = 0 outflow has a negative PV equal to its actual amount). Once identified, that particular discount rate is your bond's Yield To Maturity.
Very roughly, if you have more than two CFs (as you do here), it amounts to trial-and-error. If you're familiar with the algebraic rendering of the PV of a cash-flow series, you'll see that it's really just a polynomial. With two cash flows, you've got a quadratic, whose roots are easily determined by your favorite weapon of choice. Three or four cash flows, and you're dealing with a cubic or quartic--roots are 'findable' but difficult. Five or more CFs, and it's off to trial-and-error land.
That's the bad news. The good news is that many tools, such as Excel, can blaze through the trial-and-error iterations for you in a blink. Having laid your bond's cash flow amounts and timing, try hitting them with Excel's Goal Seek or Solver tools, or its IRR function.
Go through the foregoing procedure and you'll have the bond's YTM in no time. Best of luck!
...it was early and I was full of no coffee...