Question

In: Finance

A zero-coupon bond with face value $1,000 and maturity of four years sells for $756.22. a....

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 %

Solutions

Expert Solution

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)


Related Solutions

A zero-coupon bond with face value $1,000 and maturity of four years sells for $737.22. a....
A zero-coupon bond with face value $1,000 and maturity of four years sells for $737.22. a. What is its yield to maturity? (Round your answer to 2 decimal places.) b. What will the yield to maturity be if the price falls to $721?
A zero-coupon bond with face value $1,000 and maturity of four years sells for $753.22. a....
A zero-coupon bond with face value $1,000 and maturity of four years sells for $753.22. 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 $737? (Round your answer to 2 decimal places.) Yield to maturity             %
A zero coupon bond with a face value of $1,000 that matures in 8 years sells...
A zero coupon bond with a face value of $1,000 that matures in 8 years sells today for $556. What is the yield to maturity? (Use annual compounding.)
(Bonds) A zero-coupon bond has a $1,000 par value, 9 years to maturity, and sells for...
(Bonds) A zero-coupon bond has a $1,000 par value, 9 years to maturity, and sells for $527.82. What is its yield to maturity? Assume annual compounding. Record your answer to the nearest 0.01% (no % symbol). E.g., if your answer is 3.455%, record it as 3.46.
Consider a zero-coupon bond maturing in 2 years with a face value of $1,000 and a...
Consider a zero-coupon bond maturing in 2 years with a face value of $1,000 and a yield to maturity of 2%. Assume the recovery rate is 40%, and that default can only happen exactly at the end of the 2-year period. There is a credit default swap (CDS) available for this bond, and the premium is 0.8%. For both a bondholder and a CDS buyer (with notional value $1,000), compute the cash flows two years from today in the case...
Bond A is a 10% coupon bond with a face value of $1,000 and a maturity...
Bond A is a 10% coupon bond with a face value of $1,000 and a maturity of 3 years. The discount rate (required return, or interest rate) is 8% now or in the future. A. What is the bond price now, in year 1, in year 2, and in year 3      (P0,P1,P2 and P3)? B. If you buy the bond now and hold it for one year, what is the      (expected) rate of return? C. If you buy...
A $1,000 zero-coupon bond makes payment of the face value at maturity. How would you value...
A $1,000 zero-coupon bond makes payment of the face value at maturity. How would you value the price of a zero-coupon bond and decide if you should buy the zero-coupon bond? Is the bond selling at premium, at discount or at par?
A bond with a face value of $1,000 has 8 years until maturity, carries a coupon...
A bond with a face value of $1,000 has 8 years until maturity, carries a coupon rate of 7.0%, and sells for $1,085. a. What is the current yield on the bond? (Enter your answer as a percent rounded to 2 decimal places.) b. What is the yield to maturity if interest is paid once a year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.) c. What is the yield to maturity...
A bond with a face value of $1,000 has 10 years until maturity, carries a coupon...
A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 7.7%, and sells for $1,130. Interest is paid annually. a. If the bond has a yield to maturity of 10.3% 1 year from now, what will its price be at that time? (Do not round intermediate calculations.) b. What will be the annual rate of return on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to...
A bond with a face value of $1,000 has 10 years until maturity, carries a coupon...
A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 7.1%, and sells for $1,190. Interest is paid annually. (Assume a face value of $1,000 and annual coupon payments.) a. If the bond has a yield to maturity of 10.9% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your answer to nearest whole number.) b. What will be the rate of return...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT