Question

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.

Answer 1

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:

$\mathbf{r=\dfrac{i-f}{1+f}}$

where;

r = inflation free rate of return

so;

For the inflation free rate of return of the nontaxable municipal bond $r_M$; we have;

${\mathbf{r_M=\dfrac{0.09-0.06}{1+0.06}}}$

${\mathbf{r_M=\dfrac{0.03}{1.06}}}$

$\mathbf{r_{M }= 0.028}$

$\mathbf{r_{M }= 2.8 \%}$

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:

${\mathbf{r_C=\dfrac{0.12(1-0.06)-0.06}{1+0.06}}}$

${\mathbf{r_C=\dfrac{0.12(0.94)-0.06}{1.06}}}$

${\mathbf{r_C=\dfrac{0.1128-0.06}{1.06}}}$

${\mathbf{r_C=\dfrac{0.0528}{1.06}}}$

${\mathbf{r_C=0.050}$

${\mathbf{r_C=5.0 \% }$

Thus; the inflation free rate of return of the taxable corporate  bond is 5.0%