a. A taxpayer is considering buying a fully taxable corporate bond. The bond has

Question

a. A taxpayer is considering buying a fully taxable corporate bond. The bond has a remaining maturity of 5 years, promises to pay 6% interest annually (assume the coupon interest is payable annually), and has a face value of $1,000. the taxpayer faces a 31% tax rate on the interest income and requires a pretax rate of return of 6% to invest. What price is the taxpayer willing to pay for this bond?

b. The same taxpayer is also considering buying a tax-exempt municipal bond.   The municipal bond has a remaining maturity of 5 years, also promises to pay 6% intererst annually (again the coupon interest is payable annually), and has a face value of $1,000. Assume the corporate and municipal bonds are equally risky. At what price is the taxpayer indifferent between the corporate and municipla bond? (Alternately stated, what price is the taxpayer willing to pay for the municipal bond assuming he requires a pretax rate of return of 6% and faces a marignal tax rate of 31%?)

Explanation / Answer

1. interest = 6%;

face value = $1000;

rate of return after 1 year = 6% ;

return = $60 ;

tax rate 31% ; so tax = $18.6;

earnings = $41.4;

but for 6% i.e 604 return investment = ?;

for 41.4 investment = $1000;

for 60 the investment = 1000*60/41.4;

$1449;

2. Municipal bond

interest = 6%;

face value = $1000;

rate of return after 1 year = 6% ;

return = $60 ;

tax exempt bond so interest earned

= 60$ per year for every 1000$ invested ;

so different in investment = 1449-1000;

= $449

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