Question

Bill’s salary at the jet-engine manufacturing plant places his household in the 20% tax bracket. Bill is contemplating buying one of two bonds – a Peg City municipal bond or a Government Treasury bond – but is having some trouble deciding which would be the better investment. Both are discount bonds, have a face value of $10,000, mature in one year, and are identical in terms of risk. The current price of the Treasury bond is $9,803.92 and the municipal bond is $9,852.22. Hint: The municipal bond is tax-exempt.

1) What is the yield-to-maturity (YTM) on the Peg City bond? (provide your answer in % with one decimal point of accuracy)

2) What is the yield-to-maturity (YTM) on the Treasury bond? (provide your answer in % with one decimal point of accuracy)

3) Now consider the after tax YTMs. Which bond offers the greater after-tax return for Bill's household? (i.e., municipal or federal?). Briefly justify/explain your answer.

Answer 1

The YTM can be found using RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

1. YTM of Peg City bond=RATE(nper,pmt,pv,fv,type)

nper=1 (maturity=1 year)

pmt=0

pv=9852.22

fv=10000

=RATE(1,0,-9852.22,10000,0)=1.50%

YTM of municipal bond=1.50%

As mentioned in the above question, it is totally exemped from the tax. Hence, YTM=1.50%

2. YTM of Government Treasury bond=RATE(nper,pmt,pv,fv,type)

nper=1 (maturity=1 year)

pmt=0

pv=9803.92

fv=10000

=RATE(1,0,-9803.92,10000)=2.0%

Here, YTM=2.0%

After tax YTM of Treasury bond=2.0%*(1-20%)=1.6%

3. The YTM of Treasury bond is higher than YTM of Municipal bond by 10 basis points (0.1%). Hence, Bill should purchase Treasury bond which can yield 1.6% (after tax) while Municipal bond yields only 1.5%