A $1,000 corporate bond with 20 years to maturity pays a coupon of 7% (semi-annual) and the market required rate of return is 13%. What is the selling price?
Bond price is given by:
Price = C x (1-1/x)/i + M/x; where C = coupon return, i = interest, x = (1+i)^n, n = number of coupon payments and M = the face value of the bond.
So, remembering to halve the percentage yields (7% and 13%) since we're compounding semi-annually:
M = 1000
n = 40 (20 years, twice per year)
C = coupon return = 35 (7% of $1000, halved since it's semi-annual)
i = 13%/2 = 0.065; (so x = 1.065^40 = 12.416)
Selling price = 35 * (1-1/12.416)/0.065 + 1000/12.416 = 575.63.
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