In: Finance
A zero-coupon bond with face value $1,000 and maturity of four years sells for $756.22. |
a. | What is its yield to maturity? (Round your answer to 2 decimal places.) |
Yield to maturity | % |
b. |
What will the yield to maturity be if the price falls to $740? (Round your answer to 2 decimal places.) |
Yield to maturity | % |
Solution a :
The Yield to Maturity of a zero coupon bond can be calculated using the following formula
YTM = (Face value / Current Price)(1/ Years to maturity ) - 1
As per the Information given in the question we have
Face value of the bond = $ 1000
Current price of the bond = $ 756.22
Years to maturity = 4 years
Applying the above values in the formula we have
= ( 1000 / 756.22 ) ( 1/ 4) – 1
= ( 1.3224 ) ( 0.25 ) – 1
= 1.0724 – 1 = 0.0724
Thus the YTM of the zero coupon bond = 7.24 %
Note : ( 1.3224 ) ( 0.25) = 1.0724 is calculated using the excel formula =POWER(Number,Power)
=POWER(1.3224,0.25)
Solution b :
The Yield to maturity of a zero coupon bond can be calculated using the following formula
YTM = (Face value / Current Price)(1/ Years to maturity ) - 1
As per the Information given in the question we have
Face value of the bond = $ 1000
Current price of the bond = $ 740
Years to maturity = 4 years
Applying the above values in the formula we have
= ( 1000 / 740 ) ( 1/ 4 ) – 1
= ( 1.3514 ) ( 0.25 ) – 1
= 1.0782 – 1 = 0.0782
Thus the YTM of the zero coupon bond = 7.82 %
Note : ( 1.3514 ) ( 0.25) = 1.0782 is calculated using the excel formula =POWER(Number,Power)
=POWER(1.3514,0.25)