Chapter 11, Problem 1P

You are considering how to invest part of your retirement savings. You have decided to put $200,000 into three stocks: 50% of the money in Goldfinger (currently $25/share). 25% of the money in Moosehead (currently $80/share). and the remainder in Venture Associates (currently $2/share). If Goldfinger stock goes up to $30/share. Moosehead stock drops to $60/share, and Venture Associates stock rises to $3 per share.

1. a. What is the new value of the portfolio?
2. b. What return did the portfolio earn?
3. c. If you don’t buy or sell shares after the price change, what are your new portfolio weights?

Summary Introduction

To determine: The new value of the portfolio.

Introduction:

Portfolio refers to a set of financial investments owned by an investor. The portfolio of investments includes debentures, stocks, bonds, and mutual funds.

Answer to Problem 1P

The new value of the portfolio is $232,500.

Explanation of Solution

Given information:

Person X has decided to investment $200,000 in three stocks. He decided to put 50 percent of $200,000 in GF Company, 25 percent of $200,000 in MH Company, and the remaining 25 percent of $200,000 in VT Associates.

The current share price of GF Company is $25 per share, the current share price of MH Company is $80 per share, and the current share price of VT Associates is $2 per share. Assume that GF Company’s stock rises by $30 per share, VT Associates’ stock even goes up to $3 per share, and MH Company’s stock falls by $60 per share.

The formula to calculate the number of shares in a particular stock:

$\begin{array}{l}\text{Number of shares }\\ \text{in a particular stock}\end{array}\}=\frac{\left(\text{Total value of investment}\times \text{Percentage of shares invested}\right)}{\text{Current share price of a particular stock}}$

The formula to calculate the new value of the portfolio:

$\text{New value of the portfolio}=\left(\begin{array}{l}\text{Stock market rise or fall in a particular stock}\\ \times \text{Number of shares of a particular stock}\end{array}\right)$

Calculate the number of shares of GF Company:

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{of GF}\text{}\text{ Company}\end{array}\}=\frac{\left(\begin{array}{l}\text{Total value of investment}\\ \times \text{}\text{ Percentage of shares invested in GF }\text{}\text{Company}\end{array}\right)}{\text{Current share price of GF}\text{}\text{ Company}}\\ =\frac{\left(\$200,000\times 0.50\right)}{\$25}\\ =\frac{\$100,000}{\$25}\\ =4,000\end{array}$

Hence, the number of shares of GF Company is 4,000.

Calculate the number of shares of MH Company:

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{of MH}\text{}\text{ Company}\end{array}\}=\frac{\left(\begin{array}{l}\text{Total value of investment}\\ \times \text{}\text{ Percentage of shares invested in MH }\text{}\text{Company}\end{array}\right)}{\text{Current share price of MH}\text{}\text{ Company}}\\ =\frac{\left(\$200,000\times 0.25\right)}{\$80}\\ =\frac{\$50,000}{\$80}\\ =625\end{array}$

Hence, the number of shares of MH Company is 625.

Calculate the number of shares of VT Associates:

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{of VT Associates}\end{array}\}=\frac{\left(\begin{array}{l}\text{Total value of investment}\\ \times \text{ Percentage of shares invested in VT Associates}\end{array}\right)}{\text{Current share price of VT Associates}}\\ =\frac{\left(\$200,000\times 0.25\right)}{\$2}\\ =\frac{\$50,000}{\$2}\\ =25,000\end{array}$

Hence, the number of shares of VT Associates is 25,000.

Compute the new value of the portfolio:

$\begin{array}{c}\text{New value of the portfolio}=\left[\begin{array}{c}\left(\begin{array}{l}\text{Amount of increase in GF Company's }\text{}\text{stock}\\ \times \text{Number of shares of GF}\text{}\text{ Company}\end{array}\right)\\ +\left(\begin{array}{l}\text{Amount of decrease in MH Company's }\text{}\text{stock}\\ \times \text{Number of shares of MH}\text{}\text{ Company}\end{array}\right)\\ +\left(\begin{array}{l}\text{Amount of increase in VT Associates' }\text{}\text{stock}\\ \times \text{Number of shares of VT Associate}\end{array}\right)\end{array}\right]\\ =\left(\$30\times 4,000\right)+\left(\$60\times 625\right)+\left(\$3\times 25,000\right)\\ =\$120,000+\$37,500+\$75,000\\ =\$232,500\end{array}$

Hence, the new value of the portfolio is $232,500.

Summary Introduction

To determine: The return from the portfolio.

Introduction:

Return is a loss or gain incurred on the investment made by the investors. It is expressed in terms of percentage.

Answer to Problem 1P

The return from the portfolio is 16.25%.

Explanation of Solution

Given information:

Person X has decided to investment $200,000 in three stocks.

The formula to compute the return from the portfolio:

$\text{Return}=\frac{\text{New value of portfolio}}{\text{Total value of investment}}-1$

Compute the return from the portfolio:

$\begin{array}{c}\text{Return}=\frac{\text{New value of portfolio}}{\text{Total value of investment}}-1\\ =\frac{\$232,500}{\$200,000}-1\\ =1.1625-1\\ =0.1625\text{ or 16}\text{.25\%}\end{array}$

Hence, the return from the portfolio is 16.25%.

Summary Introduction

To determine: The new portfolio weights.

Introduction:

Portfolio weight refers to the share of each financial investment in a portfolio. It refers to a portion of the total value of portfolio that represents a particular asset in the portfolio.

Answer to Problem 1P

The new portfolio weight of GF Company is 51.61%.

The new portfolio weight of MH Company is 16.13%.

The new portfolio weight of VT Associates is 32.26%.

Explanation of Solution

Given information:

Person X has decided to investment $200,000 in three stocks. He decided to put 50 percent of $200,000 in GF Company, 25 percent of $200,000 in MH Company, and the remaining 25 percent of $200,000 in VT Associates.

The current share price of GF Company is $25 per share, the current share price of MH Company is $80 per share, and the current share price of VT Associates is $2 per share. Assume that GF Company’s stock rises by $30 per share, VT Associates’ stock even goes up to $3 per share, and MH Company’s stock falls by $60 per share.

The formula to compute the portfolio weights:

$\text{New portfolio weights}=\frac{\left(\begin{array}{l}\text{Number of shares in a particular stock}\\ \times \text{Price change}\end{array}\right)}{\text{New value of the portfolio}}$

Compute the portfolio weight of GF Company:

$\begin{array}{c}\text{New portfolio weight}=\frac{\left(\begin{array}{l}\text{Number of shares of GF}\text{}\text{ Company}\\ \times \text{Price change}\end{array}\right)}{\text{New value of the portfolio}}\\ =\frac{4,000\times \$30}{\$232,500}\\ =\frac{120,000}{\$232,500}\\ =0.5161\text{ or 51}\text{.61\%}\end{array}$

Hence, the new portfolio weight of GF Company is 51.61%.

Compute the portfolio weight of MH Company:

$\begin{array}{c}\text{New portfolio weight}=\frac{\left(\begin{array}{l}\text{Number of shares of MH}\text{}\text{ Company}\\ \times \text{Price change}\end{array}\right)}{\text{New value of the portfolio}}\\ =\frac{625\times \$60}{\$232,500}\\ =\frac{37,500}{\$232,500}\\ =0.1613\text{ or 16}\text{.13\%}\end{array}$

Hence, the new portfolio weight of MH Company is 16.13%.

Compute the portfolio weight of VT Associates:

$\begin{array}{c}\text{New portfolio weight}=\frac{\left(\begin{array}{l}\text{Number of shares of VT Associates}\\ \times \text{Price change}\end{array}\right)}{\text{New value of the portfolio}}\\ =\frac{25,000\times \$3}{\$232,500}\\ =\frac{75,000}{\$232,500}\\ =0.3226\text{ or 32}\text{.26\%}\end{array}$

Hence, the new portfolio weight of VT Associates is 32.26%.