The missing part of the question is shown in bold format.
You have $10,000 cash which you want to invest. Your alternatives are either a nontaxable municipal bond paying 9% or a taxable corporate bond paying 12%. Your marginal tax rate is 30% for both ordinary income and capital gains. You expect the rate of inflation to be 6% during the investment period. You can buy a high grade municipal bond costing $10,000 which pays interest of 9% per year. This interest is not taxable. A comparable high grade corporate bond is also available that is just as safe as the municipal bond paying interest rate of 12% per year. This interest is taxable as ordinary income. Both bonds mature at the end of year 5.
Determine the real (inflation - free ) rate of return of each bond
Answer:
the inflation free rate of return of the nontaxable municipal bond is 2.8%
the inflation free rate of return of the taxable corporate bond is 5.0%
Explanation:
Given that :
A nontaxable municipal bond pays an interest of 9% annually
A taxable corporate bond pays an interest of 12% annually
The marginal tax rate = 30% for both ordinary income and capital gains
The rate of inflation f = 6%
Determine the real (inflation - free ) rate of return of each bond
The inflation free rate of return can be determined by using the formula:
[tex]\mathbf{r=\dfrac{i-f}{1+f}}[/tex]
where;
r = inflation free rate of return
so;
For the inflation free rate of return of the nontaxable municipal bond [tex]r_M[/tex]; we have;
[tex]{\mathbf{r_M=\dfrac{0.09-0.06}{1+0.06}}}[/tex]
[tex]{\mathbf{r_M=\dfrac{0.03}{1.06}}}[/tex]
[tex]\mathbf{r_{M }= 0.028}[/tex]
[tex]\mathbf{r_{M }= 2.8 \%}[/tex]
Thus; the inflation free rate of return of the nontaxable municipal bond is 2.8%
The inflation free rate of return of the taxable corporate bond is as follows:
[tex]{\mathbf{r_C=\dfrac{0.12(1-0.06)-0.06}{1+0.06}}}[/tex]
[tex]{\mathbf{r_C=\dfrac{0.12(0.94)-0.06}{1.06}}}[/tex]
[tex]{\mathbf{r_C=\dfrac{0.1128-0.06}{1.06}}}[/tex]
[tex]{\mathbf{r_C=\dfrac{0.0528}{1.06}}}[/tex]
[tex]{\mathbf{r_C=0.050}[/tex]
[tex]{\mathbf{r_C=5.0 \% }[/tex]
Thus; the inflation free rate of return of the taxable corporate bond is 5.0%
