Question 8.2: Bigbie Corp. issued a five-year bond one year ago with a cou...

Fundamentals of Corporate Finance

Bigbie Corp. issued a five-year bond one year ago with a coupon of 8 percent. The bond pays interest semiannually. If the yield to maturity on this bond is 9 percent, what is the price of the bond?

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We can find the price of Bigbie Corp.’s bond as follows:

P_B=\frac{C/m}{1+i/m}+\frac{C/m}{(1+i/m)^2}+\frac{C/m}{(1+i/m)^3}+…+\frac{C/m+F_8}{(1+i/m)^8}

=\frac{\$40}{1.045}+\frac{\$40}{(1.045)^2}+\frac{\$40}{(1.045)^3}+…+\frac{(\$40+\$1,000)}{(1.045)^8}

=\$38.28+\$36.63+\$35.05+\$33.54+\$32.10+\$30.72+\$29.39+\$731.31

=\$967.02

Alternatively, we can use the present value annuity factor from Chapter 6 (Equation 6.1) and the present value equation from Chapter 5 (Equation 5.4) to solve for the price of the bond.

PVA_n=\frac{CF}{i}\times\left[1-\frac{1}{(1+i)^n}\right]

$=CF\times\frac{1-1/(1+i)^n}{i^2}$ 6.1

$PV=\frac{FV_n}{(1+i)^n}$ 5.4

P_B=C\times\left[\frac{1-\frac{1}{(1+i/m)^{mn}}}{i/m}\right]+\frac{F_n}{(1+i/m)^{mn}}=\$40\times\left[\frac{1-\frac{1}{(1+0.045)^8}}{0.045}\right]+\frac{\$1,000}{(1.045)^8}

=\$263.84+\$703.19=\$967.03

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