Chapter 2, Problem 4CP

a.

Summary Introduction

To state: The highest after tax yield between the short-term municipal bonds and comparable taxable bonds when the tax bracket is zero.

Introduction:

Short Term Municipal Bonds: − When government accepts investment from the public, the interest given on the investments will be tax free. The interest is given in the form of Municipal bonds to the investors. Normally local government uses this sort of investment for development activities related to the common public. They are also called as “Muni Bonds”. The bonds which are supposed to mature within a period less than 5 years, these bonds are called short term municipal bonds.

After-Tax Yield: Sometimes, it will become very necessary to increase the returns. In such a case, the rate of return on any investment has to be calculated after considering all the taxes payable for other Investments. This is also called as “Tax Equivalent Yield”.

Explanation of Solution

Given information: Short-term municipal bonds offer yields of 4%

Comparable taxable bonds pay 5%

Tax bracket is zero

Yield on Short-term Municipal bond = 4%

Yield on Taxable bond = 5%

tax rate ‘t’ = 0%

tax yield as ‘r’ and

after-tax yield as ‘r_m’ To find the after-tax field, we need to use the following formula:

  $\begin{array}{l}{r}_m=r\times \left(1-t\right)\\ r_m=5\%\times \left(1-0\right)\\ r_m=5\%\end{array}$

Therefore, after-tax yield of the taxable bond in case of 0% tax bracket is 5%. So, after-tax yield on the taxable bond is highest when both the bonds are compared.

Conclusion

After comparing both short-term municipal bonds and comparable taxable bonds, it is found that after-tax yield of the taxable bond in case of 0% tax bracket is 5%.

b.

Summary Introduction

To state: The highest after tax yield between the short-term municipal bonds and comparable taxable bonds when the tax bracket is 10%.

Introduction:

Short Term Municipal Bonds: − When a Government accepts any investment from the common public, the interest given on the investments made will be tax free. The interest is given in the form of Municipal bonds to the investors. Normally a local Government uses this sort of investment for development activities related to the common public. There are also called as “Muni Bonds”. The bonds which are supposed to mature within a period less than 5 years, these bonds are called short term municipal bonds.

After-Tax Yield: Sometimes, it will become very necessary to increase the returns. In such a case, the rate of return on any investment has to be calculated after considering all the taxes payable for other Investments. This is also called as “Tax Equivalent Yield”.

Explanation of Solution

Given information: Short-term municipal bonds offer yields of 4%

Comparable taxable bonds pay 5%

Tax bracket is 10%

We have been given the yields earned on both short-term municipal bond as well as taxable bonds. Let us summarize the information given to us as below:

Yield on Short-term Municipal bond = 4%

Yield on Taxable bond = 5%

The tax rate = 10% (Let us consider this as t)

Now to make our calculation simpler, let us denote before tax yield as ‘r’ and after-tax yield as r_m.

To find the after-tax field, we need to use the following formula:

  $r_m=r\times \left(1-t\right)$

We can further simply the tax rate 10% as $\frac{10}{100}=0.10$ .

  $\begin{array}{l}{r}_m=5\%\times \left(1-0.10\right)\\ r_m=5\%\times 0.90\\ r_m=4.50\%\end{array}$

Therefore, after-tax yield of the taxable bond in case of 10% tax bracket is 4.50%. So, after-tax yield on the taxable bond is highest when both the bonds are compared.

Conclusion

After comparing both short-term municipal bonds and comparable taxable bonds,

After-tax yield of the taxable bond in case of 10% tax bracket is 4.50%.

c.

Summary Introduction

To state: The highest after tax yield between the short-term municipal bonds and comparable taxable bonds when the tax bracket is 20%.

Introduction:

Short Term Municipal Bonds: − When a Government accepts any investment from the common public, the interest given on the investments made will be tax free. The interest is given in the form of Municipal bonds to the investors. Normally a local Government uses this sort of investment for development activities related to the common public. There are also called as “Muni Bonds”. The bonds which are supposed to mature within a period less than 5 years, these bonds are called short term municipal bonds.

After-Tax Yield: Sometimes, it will become very necessary to increase the returns. In such a case, the rate of return on any investment has to be calculated after considering all the taxes payable for other Investments. This is also called as “Tax Equivalent Yield”.

Explanation of Solution

Given information: Short-term municipal bonds offer yields of 4%

Comparable taxable bonds pay 5%

Tax bracket is 20%

We have been given the yields earned on both short-term municipal bond as well as taxable bonds. Let us summarize the information given to us as below:

Yield on Short-term Municipal bond = 4%

Yield on Taxable bond = 5%

The tax rate = 20% (Let us consider this as t)

Now to make our calculation simpler, let us denote before tax yield as ‘r’ and after-tax yield as r_m.

To find the after-tax field, we need to use the following formula:

  $r_m=r\times \left(1-t\right)$

We can further simply the tax rate 20% as $\frac{20}{100}=0.20$ .

  $\begin{array}{l}{r}_m=5\%\times \left(1-0.20\right)\\ r_m=5\%\times 0.80\\ r_m=4\%\end{array}$

Therefore, after-tax yield of the taxable bond in case of 20% tax bracket is 4%. So, when both the bonds are compared. After-tax yield on the taxable bond and Short-term Municipal bonds are equal.

Conclusion

After comparing both short-term municipal bonds and comparable taxable bonds, it is found that after-tax yield of the taxable bond in case of 20% tax bracket is 4% which is equal to that of short-term municipal bonds.

d.

Summary Introduction

To state: The highest after tax yield between the short-term municipal bonds and comparable taxable bonds when the tax bracket is 30%.

Introduction:

Short Term Municipal Bonds: − When a Government accepts any investment from the common public, the interest given on the investments made will be tax free. The interest is given in the form of Municipal bonds to the investors. Normally a local Government uses this sort of investment for development activities related to the common public. There are also called as “Muni Bonds”. The bonds which are supposed to mature within a period less than 5 years, these bonds are called short term municipal bonds.

After-Tax Yield: Sometimes, it will become very necessary to increase the returns. In such a case, the rate of return on any investment has to be calculated after considering all the taxes payable for other Investments. This is also called as “Tax Equivalent Yield”.

Explanation of Solution

Given information: Short-term municipal bonds offer yields of 4%

Comparable taxable bonds pay 5%

Tax bracket is 30%

We have been given the yields earned on both short-term municipal bond as well as taxable bonds. Let us summarize the information given to us as below:

Yield on Short-term Municipal bond = 4%

Yield on Taxable bond = 5%

The tax rate = 30% (Let us consider this as t)

Now to make our calculation simpler, let us denote before tax yield as ‘r’ and after-tax yield as r_m.

To find the after-tax field, following formula is used:

  $r_m=r\times \left(1-t\right)$

We can further simply the tax rate 30% as $\frac{30}{100}=0.30$ .

  $\begin{array}{l}{r}_m=5\%\times \left(1-0.30\right)\\ r_m=5\%\times 0.70\\ r_m=3.5\%\end{array}$

Therefore, after-tax yield of the taxable bond in case of 30% tax bracket is 3.5%. So, when both the bonds are compared, we find that the after-tax yield on Short-term Municipal bonds is the highest.

Conclusion

After comparing both short-term municipal bonds and comparable taxable bonds, it is found that after-tax yield of the taxable bond in case of 30% tax bracket is 3.5%.