Current Yield = Annual Coupon/Current Bond Price
Yield to maturity (YTM) is the average annual internal rate of return on a bond’s cash flows that will be earned if it is bought now and held to maturity, which is the implied market discount rate at which the sum of all its expected future cash flows (coupons and principal) equal to the bond’s current market price. YTM takes into account the timing of the cash flows and any capital gain or loss to be realized by holding the bond to maturity. The formula for an approximation of YTM is, where C is annual coupon, F is face value, P is price, and n is number of coupon payment periods remaining to maturity:
YTM ≈ [C + ((F − P)/n)]/[(F + P)/2]
Also called approximate promised yield, the accurate YTM is found through trial and error by adjusting each estimated discount rate until the present value (PV) in the present value formula equals the bond’s price. YTM measures the potential return on a bond that will be realized only if (1) the bond is held to maturity, and (2) the coupons are reinvested at the YTM. If neither (1) nor (2) occurs, the actual yield will most likely be greater or less than the YTM.
For a zero-coupon bond, which is an original-issue discount (OID) bond having no coupon payment and only one cash flow equal to its face value (F), the YTM equation is as follows:
YTM = (F/P)1/n – 1
A zero-coupon bond’s yield to maturity is equals to the normal rate of return (yield) on the bond. The formula for calculating the yield to maturity (YTM) on a zero-coupon bond is, where N is the number of years to maturity:
YTMZero= (F/P)(1/N) – 1
It is customary to express zeros in terms of bond equivalent yield (BEY), using the following formula, where the number of years to maturity (N) and the semiannual effective yield (SAEY) are doubled:
BEYZero= [(F/P)[1/(N x 2)] – 1] x 2