Question

Assume that the City of Rockwall sold an issue of $1,000 maturity value, tax-exempt (municipal bond), 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 10 percent, but with semiannual compounding. The bonds are now callable at a premium of 10 percent 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?

Answer 1

This question requires application of time value of money concept, according to which FV = PV * (1 + r)ⁿ

Now, when bond is issued, FV = $1000, n = 25 * 2 = 50 periods, r = 10%/2 = 5% (semi-annual)

So issue price, PV = 1000/(1 + 0.05)⁵⁰ = 1000/11.4674 = 87.2037

Now, after 5 years, bond is to be called at 10% over the accrued value.

First let us calculate the accrued value over 5 years,

FV = 87.2037 * (1 + 5%)¹⁰

FV = 142.0457

So, the bond is callable at: 142.0457 * (1 + 10%) = $156.25

So, effective annual rate can be calculted using the same TVM formula,

156.25 = 87.2037 * (1 + r)⁵

1.7918 = (1 + r)⁵

1.1237 = 1 + r

r = 0.1237

r = 12.37% --> Effective rate