Reference no: EM133395615

Introduction to Finance

Question 1. The dividend yield on the S&P 500 index is 2% per year. That is, if you invest $100 in the portfolio of stocks underlying the index, during the next year you will receive dividends that total to $2.

For simplicity, you can think of the index as being a stock with current price of P0 and dividends of D1 = 0.02 × P0.

You expect that dividends will grow in perpetuity at the rate of g = 0.06 or 6% per year. This estimate of a dividend growth rate of 6% is based on a long run inflation rate of 2%, growth in per capita GDP of 2.8926% per year, population growth of 1% per year, and a belief that the growth rate of the dividends on a broad stock market index will be the same as the growth rate of the economy. (Note that 1.02 × 1.028926 × 1.01 = 1.06.)

Given your estimate of the dividend growth rate g = 0.06, what is your estimate of the expected rate of return r on the portfolio of stocks underlying the S&P 500 index?

Hint: What model or formula relates P0, D1, r, and g?

Question 2. The Shanghai Stock Exchange composite index on Jan 1, 2010 was at 3289.75, and has a dividend yield of approximately 1%. For simplicity, treat the index as a stock with P0 = 3289.75 and D1 = 32.8975. The market consensus was that dividends would grow at the rate of g = 0.11 or 11% per year, which is equal to a reasonable estimate of the growth rate of nominal GDP in China. For simplicity, assume that Chinese GDP and dividends on the Shanghai Stock Exchange composite index both grow at this rate in perpetuity. Consistent with the estimated dividend growth rate of 11% per year, analysts estimated that the expected rate of return on Chinese stocks was r = 0.12 or 12% per year.

If the expected rate of return on Chinese stocks remained at 12% per year but the market's estimate of the dividend growth rate decreased to 10% per year, the Shanghai Composite Index will decline. What would have been the new value of the index?

Question 3. Microsoft stock price is currently (Sep 1, 2022) $258 per share with earnings per share over the next year estimated to be $11.94. What is the net present value of its growth opportunities (per share) if the required rate of return is 11 percent?

Note, for this question, you may find information from the live sessionin Module 6 useful.

Question 4. On April 21, 2017, Volkswagen were fined $2.8 billion for rigging vehicles to cheat on emissions tests. However, the stock price returns on the day after the announcement (Mon, April 24) were 3.3% and an additional 1.5% the day after (Tues, April 25). Does this example indicate that markets are not efficient? Explain your answer.

Case Questions
For the next three questions you will have to read the case Warren E. Buffet, 2015. Please use your own words to answer the following questions in well-composed sentences. You may refer to the case and internet, but please do not copy verbatim from the case, internet, or other sources.

Note that this case will form the basis of the material in the Module 7 live session.

Question 5. Please describe the main business of Berkshire Hathaway. (up to 100 words)

Question 6. Based on the data in the case, what do you think of the investment performance of Berkshire Hathaway?(up to 200 words)
Note: Your answer should discuss the performance over
• The long run(from exhibit 3 this would be from 1976 - 2015)
• The most recent five years, 2010-2015
• The final year in the case - 2015.

Question 7. From Yahoo Finance download the monthly adjusted close prices for Berkshire Hathaway Class A shares (Ticker BRK-A) and the S&P 500 Index (Ticker: ^GSPC - you may have to manually copy these) from Dec 1, 2015 until Jan 1, 2023 (note that in the yahoo output thefirst data point will be Dec 1, 2015 and the final data point will be Dec 1, 2022)

a) Reproduce a diagram similar to Exhibit 3in the case but for 2015-2022in that both the Berkshire Hathaway and S&P 500 Index prices are normalized to 100 on Dec 1, 2015.

b) Calculate the 7-year annualized returns for Berkshire Hathaway and the S&P 500 Indexfrom 12/1/2015 to 12/1/2022.

c) What do you think of Berkshire Hathaway's performance in this period?(up to 50 words).