Question

A $1000 bond, redeemable at par, with annual coupons at 10% is purchased for $1050. If the write-down in the book value is $20 at the end of the 1st year, what is the write-down at the end of the 4th year

Answer 1

As per the information given in the question,

$20 was written down at the end of 1st Year.

Hence, the Book Value of the Bond at the end of 1st Year = $1,050 - $20 = $1,030.

Now, We can use the following Bond valuation formula,

Here,

              B₀= $1,050 ; INT = $100;       B_n=$1,030;       n = 1

Putting these values in the above mentioned equaitions we get K_d i.e. Yield to Maturity (YTM) value.

              K_d = 7.62%

Now to derive the Bond Value at the end of 4th Year the below mentioned formula should be used.

Bond Value = Present value of Interest + Present value of Maturity value

Here,

              B₀= $1,050 ; INT = $100;       K_d = 7.62%;       n = 4

Hence, putting these values in the above mentioned equaitions we get B_n i.e. Bond Maturity value at the end of 4th Year.

              B_n = 960.43

Hence, The Book Value of the Bond at the end of 4th Year is = $ 960.43

              The write-down at the end of 4th year is = $1,050 - $960.43 = $89.57