A 3.30 percent coupon municipal bond has 11 years left to maturity and has a pri

Question

A 3.30 percent coupon municipal bond has 11 years left to maturity and has a price quote of 97.15. The bond can be called in four years. The call premium is one year of coupon payments (Assume interest payments are semiannual and a par value of $5,000.) Compute the bond's current yield. (Round your answer to 2 decimal places.) Current yield Compute the yield to maturity. (Round your answer to 2 decimal places.) Viekd to maturity Compute the taxable equivalent yield (for an investor percent marginal tax bracket). (Round your answer to 2 decimal places.) in the 36 Equivalent taxable yield Compute the yield to call. (Round your answer to 2 decimal places.) Yield to call

Explanation / Answer

Par Value =$5000

Coupon Rate= 3.30% or 1.65% semi-annually

Time to Maturiry = 11 years or 22 semi-annual periods

a.) Current Yield = Annual Interest Payment/Current Price = 5000x0.033/(97.15/100x5000) =165/4857.50=3.39%

b.) Let y be the YTM of the bond.

97.15/100x5000 = 0.0165x5000x{(1-(1+y)-22)/y} + 5000/(1+y)22

0.9715 = 0.0165x{(1-(1+y)-22)/y} + 1/(1+y)22

Using Trial and Error Method to solve the equation for y,

For y =0.01, RHS=1.12

For y =0.02, RHS=0.938

For y =0.0175, RHS=0.982

For y =0.0180, RHS=0.9729

For y =0.01808, RHS=0.9715

Hence the annual YTM = 0.01808x2 =3.62%

c.) Equivalent Taxable Yield = Tax-Free Yield/(1-T)

                                        = 3.62/(1-0.36)

                                        = 5.65%

d.) Since the bonds are callable in 4 years,

Call Premium = $0.033x5000 =$165

97.15/100x5000 = 0.0165x5000x{(1-(1+y)-8)/y} + (5000+165)/(1+y)8

4857.50 = 82.50x{(1-(1+y)-22)/y} + 5165/(1+y)22

Using Trial and Error Method to solve the equation for y,

For y =0.01, RHS=5771

For y =0.02, RHS=4798

For y =0.0175, RHS=5022

For y =0.0190, RHS=4886

For y =0.01932, RHS=4857.5

Hence the annual YTM = 0.01932x2 =3.86%

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