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

Part 1)

The bond's current yield is calculated as below:

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

Here, Annual Coupon Payment = 5,000*3.60% = $180 and Current Bond Price = 5,000*95.45% =  $4,772.50

Substituting values in the above formula, we get,

Bond's Current Yield = 180/4,772.50*100 = 3.77%

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Part 2)

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 = 14*2 = 28, PMT = 5,000*3.60%*1/2 = $90, PV = 5,000*95.45% = $4,772.50 and FV = $5,000 [we use 2 since the bond is semi-annual]

Substituting values in the above formula, we get,

Yield to Maturity = Rate(28,90,-4772.50,5000)*2 = 4.03%

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Part 3)

The value of taxable equivalent yield is arrived as follows:

Taxable Equivalent Yield = Yield to Maturity/(1-Tax Rate)

Substituting values in the above formula, we get,

Taxable Equivalent Yield = 4.03%/(1-36%) = 6.29%

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Part 4)

The yield to call can again 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 + 1 Year Coupon Payment).

Here, Nper = 4*2 = 8, PMT = 5,000*3.60%*1/2 = $90, PV = 5,000*95.45% = $4,772.50 and FV = 5,000 + 180 = $5,180 [we use 2 since the bond is semi-annual]

Substituting values in the above formula, we get,

Yield to Call = Rate(8,90,-4772.50,5180)*2 = 5.70%