Question

A 3.60 percent coupon municipal bond has 14 years left to maturity and has a price quote of 95.45. 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. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Compute the yield to maturity. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Compute the taxable equivalent yield (for an investor in the 36 percent marginal tax bracket). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Compute the yield to call. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Coupon Rate = 3.6 % payable semi-annually, Par Value = $ 5000, Remaining Tenure = 14 years or (14 x 2) = 28 half-years, Price Quoute = 95.45 % of Par Value, Market Price = 0.9545 x 5000 = $ 4772.5

Semi-Annual Coupon = 0.036 x 5000 x 0.5 = $ 90

Current Yield = 90 / 4772.5 = 0.018858 or 1.8858 % ~ 1.89 %

Let the yield to maturity be 2R

Therefore, 4772.5 = 90 x (1/R) x [1-{1/(1+R)^(28)}] + 5000 / (1+R)^(28)

Using EXCEL's Goal Seek Function/ A financial calculator/ trial and error method to solve the above equation, we get:

R = 0.020142 or 2.0142 %

Yield to Maturity = 2.0142 x 2 = 4.0284 % ~ 4.03 %

Investor Tax Bracket = 36 %

Taxable Equivalent Yield = YTM / (1-Tax Rate) = 4.03 / (1-0.36) = 6.2944 % ~ 6.29 %

Call Premium = Annual Interest Rate = 3.6 % of Par Value = $ 90

Call Price = Par Value + Call Premium = 5000 + 90 = $ 5090

Time to Call = 4 years or 8 half-years

Let the yield to call be 2Rc

Therefore, 4772.5 = 90 x (1/Rc) x [1-{1/(1+Rc)^(8)}] + 5090 / (1+Rc)^(8)

Using EXCEL's Goal Seek Function/ A financial calculator/ trial and error method to solve the above equation, we get:

Rc = 0.026435 or 2.6435 %

Yield to Call = 2.6435 x 2 = 5.287 % ~ 5.29 %