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# Bond reinvestment of coupons; Yield to call; IRR for a 20 ye

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a- What is the total future value dollar difference between reinvestment of coupons at the YTM of a bond selling at 98-5/8 with a coupon of 7% (paid semiannually) and a maturity of 12 years and the same bond with a reinvestment assumption of 6%?

b- What is the yield-to-call (YTC) for a bond with three years remaining to first call, a remaining maturity of 17 years, coupon of 10% (paid semiannually), par value of \$1,000, 110% call premium, and selling for \$1,008.50

c- Assume a 20-year bond, 12% coupon (paid semiannually), \$1,000 face, callable after five years at \$1,120, and currently selling at par. Calculate the IRR for the 20-year period if the bond is held for five years and then called since market rates have fallen to 8%. How does the IRR of the called bond compare to the original 12% YTM?

#### Solution Preview

PV = -98.625
FV= 100
PMT = 3.5
n= 12*2= 24

compute i = 3.586 -> semi annual i
convert to annually rate (1.03586)^2 - 1= 7.3% = YTM without reinvestment

YTM with reinvestment
for FV of ...

\$2.19