Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $

Question

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $91.20, while a 2-year zero sells at $82.48. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 6% per year.

What is the yield to maturity of the 2-year zero? The 2-year coupon bond? (Do not round intermediate calculations. Round your answers to 3 decimal places. Omit the "%" sign in your response.)

What is the forward rate for the second year? (Do not round intermediate calculations and rounded to whole number. Omit the "%" sign in your response.)

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $91.20, while a 2-year zero sells at $82.48. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 6% per year.

Explanation / Answer

(a) Computation of yield-to-maturity of the 2 years zero coupon bond.We have,

Yield to maturity = (Face Value/Current price)(1/ years to maturity) - 1

Yield to maturity = (100 / 82.48)(1/2) -1

Yield to maturity = 10.11%

Hence, yield to maturity of 2-year Zero coupon bond is 10.11%.

(ii) Computation of yield to maturity.We have,

YTM= [Coupon rate +(face value - issue price)/ number of years] / (Face value + market value)/2

YTM= [ 6 + ( 100 - 82.48) / 2 ] / ( 100 + 82.48) / 2

YTM = [ 14.76 ] / 91.24 = 16.18%

The YTM of the bond is 16.18%.

(b) Computation of forward rate for zero -Coupon bond.We have,

Forward rate = 1 - 0.1011 = 0.8989 %

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