Question

Your firm has issued ten-year zero-coupon bonds with a $1,000 face value. If the bonds are currently selling for $514.87. What is the yield to maturity?

Answer 1

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