Exam 2 (Ch.4-6) - Optional Extra Credit Due Date: 4/25/2016 Rule: Complete the f

Question

Exam 2 (Ch.4-6) - Optional Extra Credit Due Date: 4/25/2016 Rule: Complete the following 4 problems and each one is worth 50 points. The adjusted points will be the average of your extra credit and your original total scores if any improvement score exists. 1. Suppose you purchase 2,000 shares of a closed-end mutual fund at its initial public offering; the offer price is $15 per share. The offering prospectus discloses that the fund promoter gets a 7.5 percent fee from the offering. If this fund sells at a 5 per cent discount to NAV the day after the initial public offering, what is the value of your investment? 2. Suppose the following three defense stocks are to be combined into a stock index in January 2013 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance): a. Calculate the initial value of the index if a price-weighting scheme is used. b. What is the rate of return on this index for the year ending December 31, 2013? For the year ending December 31, 2015? 3. The dividend for Douglas, Inc., is currently $1.25 per share. It is expected to grow at 20 percent next year and then decline linearly to a 5 percent perpetual rate beginning in four years. If you require a 16 percent return on the stock, what is the most you would pay per share? 4. Mid-American stock has a sustainable growth rate of 8 percent, ROE of 15 percent, and dividends per share of $1.65. If the P/E ratio is 20, what is the value of a share of stock?

Explanation / Answer

Part 1)

The value of investment is calculated as follows:

The NAV at the time of IPO = 15*(1-7.5%) = $13.875

We need to get the value per share as follows:

-5% = (P-13.875)/13.875

P = 13.875 - .069375 = $13.18125

Value of the Investment = 2,000*13.18125 = $26,362.50

_________

Part 2)

Incomplete question. Information on 3 defense stocks is not available.

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Part 3)

The stock price can be calculated with the use of following formula:

Stock Price = D1/(1+Required Return)^1 + D2/(1+Required Return)^2 + D3/(1+Required Return)^3 + D4/(1+Required Return)^3*(Required Return)^3

D1 = 1.25*(1+20%) = 1.50

D2 = 1.50*(1+15%) = 1.725

D3 = 1.725*(1+10%) = 1.8975

D4 = 1.8975*(1+5%) = 1.992375

Using these values in the above formula, we get,

Stock Price Today = 1.50/(1+16%)^1 + 1.725/(1+16%)^2 + 1.8975/(1+16%)^3 + 1.992375/(1+16%)^3*(16% - 5%) = $15.39

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Part 4)

Step 1: Calculate Dividend Payout Ratio

The dividend payout ratio can be calculated with the use of formula for Sustainable Growth Rate given below:

Sustainable Growth Rate = ROE*(1-Dividend Payout Ratio)

Substituting the information provided in the question, we get,

8% = 15%*(1-Dividend Payout Ratio)

Dividend Payout Ratio = 1- 8%/15% = 46.67%

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Step 2: Calculate Earnings Per Share

The earnings per share can be calculated as follows:

Dividend Per Share = EPS*Dividend Payout Ratio

or

EPS = Dividend Per Share/Dividend Payout Ratio = 1.65/46.67% = $3.53

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Step 3: Calculate the Value of the Stock

The value of the stock can be calculated as follows:

PE Ratio = Market Price Per Share/Earnings Per Share

or

Value of the Stock (Market Price Per Share) = PE Ratio*EPS = 20*3.53 = $70.71

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