Question

A 4.30 percent coupon municipal bond has 15 years left to maturity and has a price quote of 97.85. 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.)

a) Compute the bond’s current yield.

b) Compute the yield to maturity.

c) Compute the taxable equivalent yield (for an investor in the 30 percent marginal tax bracket).

d) Compute the yield to call.

Round your final answer to two decimal places.

Answer 1

Part a)

The bond's current yield is calculated as below:

Bond's Current Yield = Annual Coupon Payment/Current Bond Price*100

Substituting values in the above formula, we get,

Bond's Current Yield = (100*4.30%)/97.85*100 = 4.39%

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Part b)

The yield to maturity can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Payment (here, Coupon Payment), PV = Present Value (here, Current Bond Price) and FV = Future Value (here, Face Value of Bonds).

Here, Nper = 15*2 = 30, PMT = 5,000*4.30%*1/2 = $107.50, PV = 5,000*97.85% = $4,892.50 and FV = $5,000 [we use 2 since the bond is semi-annual]

Using these values in the above function/formula for Rate, we get,

Yield to Maturity = Rate(30,107.50,-4892.50,5000)*2 = 4.50%

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Part c)

The value of taxable equivalent yield is determined as follows:

Taxable Equivalent Yield = Yield to Maturity/(1-Tax Rate) = 4.50%/(1-30%) = 6.43%

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Part d)

The yield to call can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period (here Callable Period), PMT = Payment (here, Coupon Payment), PV = Present Value (here, Current Bond Price) and FV = Future Value (here, Call Value of Bonds).

Here, Nper = 4*2 = 8, PMT = 5,000*4.30%*1/2 = $107.50, PV = 5,000*97.85% = $4,892.50 and FV = 5,000 + 215 = $5,215 [we use 2 since the bond is semi-annual]

Using these values in the above function/formula for Rate, we get,

Yield to Call = Rate(8,107.50,-4892.50,5215)*2 = 5.88%