In: Finance
Yield to maturity of Zero coupon bond
YTM is rate of return you will earn if you buy a bond and hold it to maturity
Here the firm issue a
ten - year zero-coupon bonds with a $1,000 face value.
If the bonds are currently selling for $514.87
here,
The $ 1000 is thee futur value and the $ 514.87 is the present value. So the YTM is the rate to convert the future value of the bond to its present value
What is the yield to maturity? 9.71%
calculation is below)
equation for present value
PV = F V / (1 + YTM )n or present value = face (future ) value / ( 1 + YTM)n
Here,
FV = future value = face value = $ 1000 ( it is the redemption amount after 10 years )
PV = present value = $ 514.87
N = years to maturity = 10
and calculate YTM (yield to maturity)
For YTM the equation we can rewrit
YTM = ( FV / PV ) 1 / n - 1
Here,
FV = future value = face value = $ 1000 ( it is the redemption amount after 10 years )
PV = present value = $ 514.87
N = years to maturity = 10
Put the values in the formula
YTM = ( 1000 / 514.87 ) 1 / 10 - 1
YTM = ( 1000 / 514.87 ) 0.100 - 1
YTM = 1.06864 - 1 = 0.6864 = 6.864%
**( 1000 / 514.87 ) 0.100 for solve this use calculator