Chapter 14, Problem 9PA

Summary Introduction

To discuss:

The increase or decrease of the fund and the type of fund that is recommended.

Introduction:

Mutual fund refers to the fund that consists of the pool of money from various different investors and is done by trained professionals who has a great experience in the field in order to purchase different and various securities that can provide good returns to the investors.

Explanation of Solution

Given,

Shares worth is $10,000.

Return before fee is 12%.

Class A

Initial commission paid to A is 5.75%.

Back end load is 0%.

Management fee is 0.55%.

12b-1 fee is 0.25%.

Formula to calculate annual percentage expense,

$\text{Annual}\text{percentage}\text{expense}=\left(\begin{array}{l}\text{Initial}\text{commission}+\text{Back}\text{end}\text{load}\\ +\text{Management}\text{fee}+12\text{b}-1\end{array}\right)$

Substitute 5.75% for initial commission, 0% for back end load, 0.55% for management fee and 0.25% for 12b-1 fee.

$\begin{array}{c}\text{Annual}\text{percentage}\text{expense}=5.75\%+0\%+0.55\%+0.25\%\\ =6.55\%\end{array}$

Hence, the annual percentage expense is 6.55%.

Formula to calculate net annual earnings,

$\text{Net}\text{annual}\text{earnings}=\text{Return}\text{before}\text{fee}+\text{Annual}\text{percentage}\text{expense}$

Substitute 12% for return before fee and 6.55% for annual percentage expense.

$\begin{array}{c}\text{Net}\text{annual}\text{earnings}=12\%-6.55\%\\ =5.45\%\end{array}$

Formula to calculate the future value,

$\text{Future}\text{value}=\text{Present}\text{value}\times {\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}$

Substitute $10,000 for present value, 5.45% for the interest rate and 5 for number of years.

$\begin{array}{c}\text{Future}\text{value}=\$10,000\times {\left(1+0.0545\right)}^5\\ =\$13,038\end{array}$

Hence, the future value of class A is $13,038.

Class B

Initial commission paid to A is 0.0%.

Back end load is 0%.

Management fee is 0.9%.

12b-1 fee is 0.5%.

Formula to calculate annual percentage expense,

$\text{Annual}\text{percentage}\text{expense}=\left(\begin{array}{l}\text{Initial}\text{commission}+\text{Back}\text{end}\text{load}\\ +\text{Management}\text{fee}+12\text{b}-1\end{array}\right)$

Substitute 0% for initial commission, 0% for back end load, 0.9% for management fee and 0.55% for 12b-1 fee.

$\begin{array}{c}\text{Annual}\text{percentage}\text{expense}=0.0\%+0\%+0.9\%+0.5\%\\ =1.4\%\end{array}$

Hence, the annual percentage expense is 1.4%.

Formula to calculate net annual earnings,

$\text{Net}\text{annual}\text{earnings}=\text{Return}\text{before}\text{fee}+\text{Annual}\text{percentage}\text{expense}$

Substitute 12% for return before fee and 6.55% for annual percentage expense.

$\begin{array}{c}\text{Net}\text{annual}\text{earnings}=12\%-1.4\%\\ =10.6\%\end{array}$

Formula to calculate the future value,

$\text{Future}\text{value}=\text{Present}\text{value}\times {\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}$

Substitute $10,000 for present value, 5.45% for the interest rate and 5 for number of years.

$\begin{array}{c}\text{Future}\text{value}=\$10,000\times {\left(1+0.106\right)}^5\\ =\$16,549\end{array}$

Hence, the future value of class A is $16,548.

Working note:

Back end load is 5%.

Declining value per year is 1%.

Declining value for 5 years is 5%.

Computation of total back end load,

$\begin{array}{c}\text{Total}\text{back}\text{end}\text{load}=\text{Back end load}-\text{Declining value for }5\text{ years}\\ =5\%-5\%\\ =0\%\end{array}$

Hence, total back load is 0%.

Class C

Initial commission paid to C is 0.0%.

Back end load is 0%.

Management fee is 1.0%.

12b-1 fee is 1.0%.

Formula to calculate annual percentage expense,

$\text{Annual}\text{percentage}\text{expense}=\left(\begin{array}{l}\text{Initial}\text{commission}+\text{Back}\text{end}\text{load}\\ +\text{Management}\text{fee}+12\text{b}-1\end{array}\right)$

Substitute 0% for initial commission, 0% for back end load, 1.0% for management fee and 1.0% for 12b-1 fee.

$\begin{array}{c}\text{Annual}\text{percentage}\text{expense}=0.0\%+0\%+1.0\%+1.0\%\\ =2.0\%\end{array}$

Hence, the annual percentage expense is 2.0%.

Formula to calculate net annual earnings,

$\text{Net}\text{annual}\text{earnings}=\text{Return}\text{before}\text{fee}+\text{Annual}\text{percentage}\text{expense}$

Substitute 12% for return before fee and 2.0% for annual percentage expense.

$\begin{array}{c}\text{Net}\text{annual}\text{earnings}=12\%-2.0\%\\ =10.0\%\end{array}$

Formula to calculate the future value,

$\text{Future}\text{value}=\text{Present}\text{value}\times {\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}$

Substitute $10,000 for present value, 10.0% for the interest rate and 5 for number of years,

$\begin{array}{c}\text{Future}\text{value}=\$10,000\times {\left(1+0.10\right)}^5\\ =\$16,105\end{array}$

Hence, the future value of class A is $16,105.

Hence, the class B has the least fee among all the class so it should be preferred.

Conclusion

Hence, the class B is the best investment as it has the least fee among all the classes.