Question

Ye Yuan is in retirement and is considering investing in one of the following two money market securities: A Bank CD offering a quoted yield of 7.32% A Massachusetts Municipal bond offering a quoted yield of 4.78% Ye pays federal tax at the rate of 28% and tax to the state of Massachusetts (his state residency) of 7%. Ye estimates that the Massachusetts municipal bond has a 1% chance of default, and that the bank CD has a 2% chance of default. Because the quoted yield is before tax and credit risk adjustments, Ye is interested in determining which of these two bonds is best. How much more or less) in yield does the Bank CD offer after adjusting for tax and credit risk? If the believe that the CD is best, then enter the differential as a positive number. If you believe the municipal is best, then enter the differential as a negative number. Difference in yield = Place your answer as a percent without the percentage sign. For example, if your answer is zero point six three percent, then enter your answer as 0.63

Answer 1

Given,

Before tax quoted yield of bank CD = 7.32%

Before tax quoted yield of Massachusetts Municipal bond = 4.78%

Federal tax rate (T_f) = 28% or 0.28

Massachusetts tax rate (T_m) = 7% or 0.07

Chance of default of bank CD (D_b) = 2% or 0.02

Chance of default of Massachusetts Municipal bond (D_m) = 1% or 0.01

Solution :-

Bank CD's yield = Before tax quoted yield of bank CD ( 1-T_f ) ( 1-D_b)

= 7.32% ( 1 - 0.28 ) ( 1 - 0.02 )

= 7.32% ( 0.72 ) ( 0.98 )

= 5.16%

Massachusetts Municipal bond's yield = Before tax quoted yield of Massachusetts Municipal bond ( 1 - T_m ) ( 1 - D_m )

= 4.78% ( 1 - 0.07 ) ( 1 - 0.01 )

= 4.78% ( 0.93 ) ( 1 - 0.99 )

= 4.40%

Difference in yield = bank CD's yield - Massachusetts Municipal bond's yield

= 5.16% - 4.40% = 0.76%