Consider the decision to purchase either a 5-year corporate bond or a 5-year municipal bond. The corporate bond is a 12% annual coupon bond with a par value of $1,000. It is currently yielding 11.5%. The municipal bond has an 8.5% annual coupon and a par value of $1,000. It is currently yielding 7%. Assume that your marginal tax rate is 35%. What is the after tax yield to maturity (YT

MUNICPAL BOND YTM;   r= 7.00%

CORPORATE BOND YTM; r= 7.35%

Explanation:

Given the data in the question;

To get the after tax yield to maturity (YTM)

MUNICPAL BOND

Purchase price                          PV of coupons + PV of Face value at maturity

                                                   [(1000×8.5%) × (1 - 1.07⁻⁵] / 0.07) + (1000/1.07⁵)

                                                    348.516 + 712.98 =  1061.5

After-tax coupon payment       1000 × 8.5% = 85

                                                        COUPONS RECORD ON MUNICIPAL ARE

                                                         TAX-EXCEMPT.

Par value                                       1000

Calculated YTM                        1061.5 = (85× (1-(1+r)⁻⁵)/r) + (1000/(1+r)⁵)

                                                      r= 7.00%

CORPORATE BOND

Purchase price                         PV of coupons +PV of Face value at maturity

                                                ((1000×12%) × (1-1.115⁻⁵)/0.115) +(1000/1.115⁵)

                                                      437.985 + 580.264 =  1018.25

After-tax coupon payment       1000 × 12% × (1 - 35%) =  78

Par value                                    1000

Calculated YTM                     1018.25 = (78× (1-(1+r)⁻⁵)/r) + (1000/(1+r)⁵)

                                                   r= 7.35%  

MUNICPAL BOND YTM;   r= 7.00%

CORPORATE BOND YTM; r= 7.35%  

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