Question

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             %

Answer 1

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 = $ 753.22

Years to maturity = 4 years

Applying the above values in the formula we have

= ( 1000 / 753.22 ) ^{( 1/ 4)} – 1

= ( 1.3276 ) ^{( 0.25 )} – 1

= 1.0734 – 1 = 0.0734

Thus the YTM of the zero coupon bond = 7.34 %                                           

Note : ( 1.3276 ) ^{( 0.25)} = 1.0734 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.3276,0.25)

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 = $ 737

Years to maturity = 4 years

Applying the above values in the formula we have

= ( 1000 / 737 ) ^{( 1/ 4 )} – 1

= ( 1.3569 ) ^{( 0.25 )} – 1

= 1.0793 – 1 = 0.0793

Thus the YTM of the zero coupon bond = 7.93 %                                           

Note : ( 1.3569 ) ^{( 0.25)} = 1.0793 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.3569,0.25)