ABC Ltd have issued a bond with a $1,000 face value and 8%pa coupons paid semian
ID: 2702574 • Letter: A
Question
ABC Ltd have issued a bond with a $1,000 face value and 8%pa coupons paid semiannually (ie 4% each 6 months) and three years to maturity. XYZ Ltd has also issued a bond with $1,000 face value and 8%pa coupons paid semi-annually, but with a maturity of twenty years. Yields are currently at 8% with both bonds selling at par.
(i) What is the current value of both these bonds?
(ii) What is the value of each of these bonds if yields rise to 10%?
(iii) What is the percentage change in value for each of these bonds if yields rise rom 8% to 10%?
(iv) What is the value of each of these bonds if yields fall to 6%?
(v) What is the percentage change in value for each of these bonds if yields fall from 8% to 6%?
Explanation / Answer
value of ABC bond
= 40 * PVIFA(4%,6) + 1000 * PVIF(4%,6)
= 999.984
value of XYZ bond
= 40 * PVIFA(4%,40) + 1000 * PVIF(4%,40)
= 1000.012
ii)
value of ABC bond
= 40 * PVIFA(5%,6) + 1000 * PVIF(5%,6)
= 949.228
value of XYZ bond
= 40 * PVIFA(5%,40) + 1000 * PVIF(5%,40)
= 828.364
iii) percentage change of ABC bond
= 949.228 - 999.984/999.984 = -5.076%
percentage change in XYZ bond
= 828.364 - 1000.012 /1000.012 = - 17.17%
iv)
value of ABC bond
= 40 * PVIFA(3%,6) + 1000 * PVIF(3%,6)
= 1054.188
value of XYZ bond
= 40 * PVIFA(3%,40) + 1000 * PVIF(3%,40)
= 1231.192
v)
percentage change of ABC bond
= 1054.188 - 999.984/999.984 = 5.42%
percentage change in XYZ bond
= 1231.192 - 1000.012 /1000.012 = 23.11%