Yield to maturity (YTM) for a bond - definition

Question

In "Principles of corporate finance" (Brealey, Myers, Allen) the YTM corresponding to a currently priced bond is the "y" unknown from the formula:

(present value of a 8.5% coupon bond - sold at a premium to face value of 100)
This takes into account the actual "equivalent" discount rate that justifies the present value (PV) of the security.
Looking in Investopedia for yield to maturity article I see the following addition though "YTM assumes that all coupon payments are reinvested at a yield equal to the YTM and that the bond is held to maturity"
I wonder what is the proper definition though. In the cash flow model if you want to take into account reinvesting coupons it becomes interesting as you need to solve for "y" considering that at every cash flow point you reinvest with the same yield. (curios also with the math that involves investing coupons).

D Stanley · Accepted Answer

The definitions are both correct. The reason for the assumption is to make the bond equivalent in value to just investing the market price at the YTM compounded continuously. So the coupons received are cancelled out by investing that cash in something else with the same yield.
If you don't reinvest the coupons, you'll have a different ending value - you'll just have the face value of the bond plus the coupons. So the initial coupons just sit as cash until the bond matures, when in reality, investors will take the coupons cash and reinvest it somewhere.
In other words, a 5-year bond with a YTM of 5% that costs $97 is equivalent to (cash flow wise) putting $97 in a 2% savings account for 5 years. Reinvesting the coupons cancels out the cash flows, and you'll have the same enging value in cash at the maturity of the bond.

Yield to maturity (YTM) for a bond - definition

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