Question

1. A 4.55 percent coupon municipal bond has 16 years left to maturity and has a price quote of 103.40. 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.)

a) Compute the bond’s current yield. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b) Compute the yield to maturity.

c) Compute the taxable equivalent yield (for an investor in the 35 percent marginal tax bracket).

d) Compute the yield to call.

Answer 1

a]

current yield = annual coupon payment / price of bond

annual coupon payment = face value * coupon rate = $5,000 * 4.55% = $227.50

price of bond = price as % of par * par value = 103.40% * $5,000 = $5,170

current yield = $227.50 / $5,170 = 4.40%

b]

YTM is calculated using RATE function in Excel with these inputs :

nper = 16*2 (16 years to maturity with 2 semiannual coupon payments each year)

pmt = 5000 * 4.55% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -5170 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 5000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 2.13%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 4.25%

c]

Taxable equivalent yield = YTM / (1 - tax rate)

Taxable equivalent yield = 4.25% / (1 - 35%) = 6.55%

d]

YTC is calculated using RATE function in Excel with these inputs :

nper = 8*2 (8 years to call date with 2 semiannual coupon payments each year)

pmt = 5000 * 4.55% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -5170 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 5227.50 (call price of the bond receivable on call date = face value + annual coupon payment = $5,000 + $227.50 = $5,227.50. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 2.26%. This is the semiannual YTC. To calculate the annual YTC, we multiply by 2. Annual YTC is 4.52%