Question

A 4.70 percent coupon municipal bond has 19 years left to maturity and has a price quote of 107.00. The bond can be called in eight 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.) Yield to maturity %

Compute the taxable equivalent yield (for an investor in the 35 percent marginal tax bracket). (Round your answer to 2 decimal places.) Equivalent taxable yield %

Compute the yield to call. (Round your answer to 2 decimal places.) Yield to call %

Answer 1

Calculation of current yield:

Price of Bond = 107

Semi annual interest payment on Bond = 100*4.70%*1/2 = 2.35

Current yield = Semi annual interest payment on Bond /Price of Bond *100

= (2.35/107) *100 = 2.20%

Calculation of yield to maturity:

Semi annual interest payment on Bond = 100*4.70%*1/2 = 2.35

Par value = 100

Price of bond = 107

Maturity = 19 years = 19*2 = 38 semi annual periods

Yield to maturity = [Interest amount + (Price - Par value)/n] / (Price + Par value)/2

= [2.35 + (107 - 100)/38] / (107 + 100)/2 = (2.53/103.5) *100 = 2.44%

Annual yield = 2.44%*2 = 4.89%

Calculation of taxable equivalent yield:

Semi annual interest payment on Bond = 100*4.70%*1/2 = 2.35

Par value = 100

Price of bond = 107

Maturity = 19 years = 19*2 = 38 semi annual periods

Tax rate = 0.35 i.e. 35%

Yield to maturity = [Interest amount + (Price - Par value)/n] / (Price + Par value)/2

= [2.35*(1-0.35) + (107 - 100)/38] / (107 + 100)/2 = (2.53/103.5) *100 = (1.5275 + 0.1842) / 103.5 = 1.653%

Taxable equivalent yield = 1.653%*2 = 3.31%

Calculation of yield to call:

Semi annual interest payment on Bond = 100*4.70%*1/2 = 2.35

Call amount = 100 + 2.35*2 = 100 + 4.7 = 104.7

Price of bond = 107

Call periods = 8 years i.e. 16 periods

Yield to call = [Interest amount + (Call amount - Par value)/n] / (Price + Par value)/2

= [2.35 + (104.7 - 100)/16] / (107 + 100)/2 = (2.64375/103.5) *100 = 2.554%

Annual yield to call = 2.554%*2 = 5.11%