Chapter 14, Problem 11PA

Summary Introduction

(a)

To determine:

the total ending investment value.

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,

Initial purchase amount is $10,000.

Initial purchase date is 1^stJanuary.

Initial purchase price is $19.30 per share.

Annual capital gains distribution rate is 1.5%.

Annual distribution rate is 0.6%.

Investment horizon is 5 years.

Annual price appreciation rate is 7.4%.

Formula to calculate the number of shares,

$\text{Number}\text{of}\text{shares}=\frac{\text{Purchase}\text{amount}}{\text{Initial}\text{price}}$

Substitute $10,000 as the purchase amount and $19.30 as the initial price,

$\begin{array}{c}\text{Number}\text{of}\text{shares}=\frac{\$10,000}{\$19.3}\\ =518\end{array}$

Number of shares are 518.

Formula to calculate the new appreciated price,

$\text{New}\text{appreciated}\text{price}=\left(\text{Rate}\text{of}\text{appreciation}\times \text{Initial}\text{value}\right)+\text{Initial}\text{value}$

Substitute 7.4% for Annual price appreciation rate and $19.3 for initial value.

$\begin{array}{c}\text{New}\text{appreciated}\text{price}=\left(0.074\times \$19.3\right)\\ =\$20.7\end{array}$

Hence, the new appreciated price is $20.7.

Formula to calculate the ending investment value,

$\text{Ending}\text{investment}\text{value}=\text{Number}\text{of}\text{shares}\times \text{Price}\text{of}\text{shares}$

Substitute 518 for the number of shares and $27.5 for the price of shares,

$\begin{array}{c}\text{Ending}\text{investment}\text{value}=518\times \$27.5\\ =\$14,245\end{array}$

Hence, the ending investment value is $14,245.

Computation of table showing capital gain

Years	Share price ($) (A)	Number of shares purchased (B)	Value of investment ($) $\left(\text{A}\times \text{B}\right)$	Capital gain ($)	Dividend ($)
1	20.7	518	10,722	161	64
2	22.2	518	11,500	173	69
3	23.8	518	12,328	185	74
4	25.6	518	13,261	199	80
5	27.5	518	14,245	214	85
Total				932	372

Table (1)

Formula to calculate ending value of fund,

$\text{Ending}\text{value}\text{of}\text{fund}=\text{Ending}\text{value}\text{of}\text{investment}+\text{Dividend}+\text{Capital}\text{gain}$

Substitute 14,245 for ending value, $372 for the dividend and $932 for capital gain.

$\begin{array}{c}\text{Ending}\text{value}\text{of}\text{fund}=\$14,245+\$372+\$932\\ =\$15,549\end{array}$

The ending investment value is $15,549.

Working notes:

Given,

Initial purchase amount is $10,000.

Initial purchase date is 1^stJanuary.

Initial purchase price is $19.30 per share.

Annual capital gains distribution rate is 1.5%.

Annual distribution rate is 0.6%.

Investment horizon is 5 years.

Annual price appreciation rate is 7.4%.

Year 1

Computation of capital gain,

$\begin{array}{c}\text{Capital}\text{gain}=1.5\%\times \text{Value}\text{of}\text{investment}\\ =1.5\%\times \$10,722\\ =\$161\end{array}$

Hence, the capital gain in year 1 is $161.

Computation of dividend,

$\begin{array}{c}\text{Dividend}=\text{Dividend}\text{rate}\times \text{Value}\text{of}\text{investment}\\ =0.6\%\times \$10,722\\ =\$64.\end{array}$

Hence, the dividend is $64.

Year 2

Computation of new appreciated price,

$\begin{array}{c}\text{New}\text{appreciated}\text{price}=\left(\text{Rate}\text{of}\text{appreciation}\times \text{Initial}\text{value}\right)+\text{Initial}\text{value}\\ =\left(0.074\times \$20.7\right)+\$20.7\\ =\$22.2\end{array}$

Hence, the new appreciated price is $22.2

Computation of capital gain,

$\begin{array}{c}\text{Capital}\text{gain}=1.5\%\times \text{Value}\text{of}\text{investment}\\ =1.5\%\times \$11,500\\ =\$173\end{array}$

Hence, the capital gain in year 1 is $173.

Computation of dividend,

$\begin{array}{c}\text{Dividend}=\text{Dividend}\text{rate}\times \text{Value}\text{of}\text{investment}\\ =0.6\%\times \$11,500\\ =\$69\end{array}$

Hence, the dividend is $69.

Year 3

Computation of the new appreciated price,

$\begin{array}{c}\text{New}\text{appreciated}\text{price}=\left(\text{Rate}\text{of}\text{appreciation}\times \text{Initial}\text{value}\right)+\text{Initial}\text{value}\\ =\left(0.074\times \$22.2\right)+\$22.2\\ =\$23.8\end{array}$

Hence, the new appreciated price is $23.8.

Computation of capital gain,

$\begin{array}{c}\text{Capital}\text{gain}=1.5\%\times \text{Value}\text{of}\text{investment}\\ =1.5\%\times \$12,328\\ =\$185\end{array}$

Hence, the capital gain in year 1 is $185.

Computation of dividend,

$\begin{array}{c}\text{Dividend}=\text{Dividend}\text{rate}\times \text{Value}\text{of}\text{investment}\\ =0.6\%\times \$12,328\\ =\$74\end{array}$

Hence, the dividend is $74.

Year 4

Formula to calculate the new appreciated price,

$\begin{array}{c}\text{New}\text{appreciated}\text{price}=\left(\text{Rate}\text{of}\text{appreciation}\times \text{Initial}\text{value}\right)+\text{Initial}\text{value}\\ =\left(0.074\times \$23.8\right)+\$23.8\\ =\$25.6\end{array}$

Hence, the new appreciated price is $25.6.

Computation of capital gain,

$\begin{array}{c}\text{Capital}\text{gain}=1.5\%\times \text{Value}\text{of}\text{investment}\\ =1.5\%\times \$13,261\\ =\$199\end{array}$

Hence, the capital gain in year 1 is $199.

Computation of dividend,

$\begin{array}{c}\text{Dividend}=\text{Dividend}\text{rate}\times \text{Value}\text{of}\text{investment}\\ =0.6\%\times \$13,261\\ =\$80\end{array}$

Hence, the dividend is $80.

Year 5

Computation of new appreciated price,

$\begin{array}{c}\text{New}\text{appreciated}\text{price}=\left(\text{Rate}\text{of}\text{appreciation}\times \text{Initial}\text{value}\right)+\text{Initial}\text{value}\\ =\left(0.074\times \$25.6\right)+\$25.6\\ =\$27.5\end{array}$

Hence, the new appreciated price is $27.5.

Computation of capital gain,

$\begin{array}{c}\text{Capital}\text{gain}=1.5\%\times \text{Value}\text{of}\text{investment}\\ =1.5\%\times \$14,245\\ =\$214\end{array}$

Hence, the capital gain in year 1 is $214.

Computation of dividend,

$\begin{array}{c}\text{Dividend}=\text{Dividend}\text{rate}\times \text{Value}\text{of}\text{investment}\\ =0.6\%\times \$14,245\\ =\$85\end{array}$

Hence, the dividend is $85.

Conclusion

The ending value of the investment is $15,549.

Summary Introduction

(b)

To determine:

The ending investment value if the capital gain and dividend are reinvested.

Explanation of Solution

Computation of capital gain and dividend reinvested.

Year	Share price ($) (A)	Number of shares purchased (B)	Value of investment ($) $\left(\text{A}\times \text{B}\right)$	Capital gain ($) C	Dividend ($) D	Reinvested Amount ($) $\left(\text{C}+\text{D}\right)$	Number of new shares purchased
1	20.7	518	10,722	161	64	225	11
2	22.2	529	11,744	173	69	246	11
3	23.8	529	12,590	185	74	265	11
4	25.6	529	13,542	199	80	284	11
5	27.5	529	14,547	214	85	305	11
Total				932	372

Table (2)

Formula to calculate ending value of investment,

$\text{Ending}\text{value}\text{of}\text{investment}=\text{Ending}\text{value}+\text{Last}\text{distribution}\text{amount}$

Substitute 14,547 for ending value of investment and 305 for reinvested amount,

$\begin{array}{c}\text{Ending}\text{value}\text{of}\text{investment}=\$14,547+\$305\\ =\$14,825\end{array}$

Hence, the ending value of investment is $14,825.

Conclusion

Hence, the ending value of investment is $14,825.

Summary Introduction

(c)

To discuss:

The difference in the reinvested values.

Explanation of Solution

Due to low rate of appreciation the reinvestment cannot be that much effective and the differences are there in reinvested distributions.

Conclusion

The reinvestment cannot be much effective.