Question

Corporate Finance

Assume zero-coupon yields on default-free securities are as summarized in the following table:

              Maturity (years)                  1                  2                  3                  4                 5

              Zero-coupon YTM_n         4.00%          4.30%          4.50%         4.70%        4.80%

1. What is the price of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium?

2. What is the price of a five-year, zero-coupon, default-free security with a face value of $1000?

assume zero-coupon yields on default-free securities are as summarized in the following table:

              Maturity (years)                  1                  2                  3                  4                 5

              Zero-coupon YTM_n         4.00%          4.30%          4.50%         4.70%        4.80%

1. What is the price of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium?

2. What is the price of a five-year, zero-coupon, default-free security with a face value of $1000?

Answer 1

1)

Coupon amount=C=1000*6%=$60 per year

Face Value of security=FV=$1000

Price of two year default free security=C/(1+YTM₁)+(C+FV)/(1+YTM₂)²

Price of two year default free security=60/(1+4%)+(60+1000)/(1+4.3%)²=$1032.09

Price is higher than face value, it means that it sells at premium.

2)

In absence of coupon,

Price of five year default free security=FV/(1+YTM₅)⁵

Price of five year default free security=1000/(1+4.8%)⁵=$791.03