Question

A 10-year 8% bond issued by Holiday Shipping sells for $679.40 on January 1, 2011. The bond matures on December 31, 2017. Assume that the bond is held until it’s maturity, and determine the IRR. The bond’s face value is $1000, and interest is paid semiannually. (Answer: 16.3%)

Please show work. Mainly I don't understand the terminology of bonds maturing and what a face value is.

Answer 1

Face value of the bond is the original value of the bond i.e. the stated value. It is the value which the bonds will be paid at the end of the tenure. It is the value based on which the interest paid is calculated. Bonds maturity is when the bonds will be paid i.e. after certain years.

Interest paid = 1000 * 8% *6/12 = $40

No of periods = 7* 2 = 14

Let's try a discount rate of 6%:

P _6% = 679.4 - 40( P/A, 6% , 14, ) - 1000 (P/F,6% ,14) = 679.4 - 40* 9.29498 - 1000 *0.44230 = -134.6992

Lets try discount rate of 8%

P _8%= 679.4 - 40( P/A, 8% , 14, ) - 1000 (P/F,8% ,14) = 679.4 - 40* 8.24424 - 1000 *0.34046 = 9.1704

Interpolating 6 month IRR:

IRR = 6% + 2% * 134.6992 / ( 134.6992 + 9.1704) = 7.87%

Effective annual IRR = ( 1+ 7.87%)² -1 = 16.36%