Assume that the City of Tampa sold an issue of $1,000.00 maturity value,tax-exempt (muni),zero coupon bonds 5 years ago.The bonds had a 25-year maturity when they were issued,and the interest rate built into the issue was a nominal 6.00%,but with semiannual compounding.The bonds are now callable at a premium of 10.00% over the accrued value.What effective annual rate of return would an investor who bought the bonds when they were issued and who still owns them earn if they were called today?

Question

Quizplus · Accepted Answer

The first step is to calculate the current accrued value of the bond. Since it is a zero-coupon bond, the accrued value is simply the present value of the bond after 5 years. Using the formula for present value of a lump sum, we get:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value (maturity value) of the bond, r is the semiannual interest rate, and n is the number of semiannual periods (in this case, 5 years = 10 semiannual periods).
Plugging in the values, we get:
PV = 1000 / (1 + 0.03)^10
PV = $744.09
Adding the 10% premium to the accrued value, we get:
Call price = $744.09 x 1.10 = $818.50
The investor would receive $818.50 if the bonds were called today.
To calculate the effective annual rate of return, we use the formula:
EAY = (Call price / Purchase price)^(1/t) - 1
where EAY is the effective annual yield, Call price is the call price of the bond, Purchase price is the price the investor paid for the bond (which is the same as the maturity value), and t is the number of years the bond has been held (in this case, 5).
Plugging in the values, we get:
EAY = ($818.50 / $1000)^(1/5) - 1
EAY = 0.0813 or 8.13%
Therefore, the investor would earn an effective annual rate of return of 8.13% if the bonds were called today. The correct answer is D.

Assume That the City of Tampa Sold an Issue of $1,000.00