Quinn Electric Company has outstanding a bond issue that will mature to its $1,000 par value in 12 years. The bond has a coupon rate of 15% and pays the interest annually.
a) Find the value of the bond if the required return is (1) 10 percent, (2) 15 percent and (3) 17 percent.
b) Use your findings in part a) to discuss the relationship between coupon interest rate on a bond and the required return and the market value of the bond relative to its par value.
c) What two reasons cause the required return to differ from the coupon interest rate?
Annual coupon payment is 15% of $1,000 = $150.
Present value of an $x annuity at an interest rate of r lasting n years = x/r - x/[r*((1+r)^n)]
In this case x = 150, n = 12 years and r is 0.10, 0.15 or 0.17.
Required return is 10% or 0.10:
Value of bond = 150/0.10 - 150/[0.10*(1.10^12)] + 1,000/(1.10^12) = $1,340.68
Where 150/0.10 - 150/[0.10*(1.10^12)] ...
This solution calculates the valuation of a bond based on different returns and discusses the relationship between the coupon rate, required return and market value of the bond.