# 1. BP has come out with a new product. As a result, the firm projects ROE will equal 12%, and that t

1. BP has come out with a new product. As a result, the firm projects ROE will equal 12%, and that the plowback ratio will equal .70. Its earnings today (time 0) are \$1.40 per share. Investors expect a 10% rate of return on the stock.

(a) Find the intrinsic value of the stock P (show your work and remember to use D1)

(b) Find the PVGO

(c) Find the P/E ratio

2. Find a publicly traded stock that pays a dividend. Find an estimate of cash flow (you can use EBITDA or Levered Cash flow – but make sure it is adjusted to be a per share calculation), and

(a) estimate the intrinsic value of the stock using dividends assuming a six percent constant growth rate and that the discount rate is 8% for year 1, 9% for year 2 and 10% in year 3 and after.

(b) estimate the intrinsic value of the stock using cash flows assuming a six percent constant growth rate and that the discount rate is 8% for year 1, 9% for year 2 and 10% in year 3 and after.

(c) compare your results with the actual stock price. Which is closer to the actual price?

3. You are bullish on Telecom stock. The current market price is \$40 per share, and you have \$10,000 to invest. If the margin limit is 50% and you borrow the maximum from your broker at 4% interest, and invest everything in Telecom,

(a) what will your return be if you hold the stock for a year and the price goes up to \$50? Show your calculation including the cost of interest

(b) how far does the price have to fall for you to have a margin call if the maintenance margin is 30%? Show your calculation.

4. You have decided PhoneCo stock is overpriced at \$120 and you want to sell short the stock,

(a) what is the maximum number of shares you can sell if you have \$10,000 to invest and the initial margin is 50% for short sales? Show your calculation.

(b) what is the first price that results in a margin call if the maintenance margin on       short positions is 30%? Show your calculation.

5. The risk-free rate is 1% and there are three stocks that you can invest in with the following E(r) and ?:

E(r)                 ?

Stock A           .11                   .29

Stock B           .09                   .21

Stock C           .13                   .32

The pair-wise correlation coefficients are ?AB = .25, ?BC = .35, ?AC = .40

In addition to the stocks A,B,C you can also invest in the following portfolios as follows:

Portfolio Weights

A                    B                   C

Portfolio 1:      50%                50%                0%

Portfolio 2:    50%                 0%                  50%

Portfolio 3:     0%                   50%                 50%

Portfolio 4:     331/3%             331/3%                         331/3%

(a) Construct a table showing the E(r) and ? for each of the seven investments.

(b) Carefully graph the seven investment choices from questions on a plot with E(r) as the y axis and ? as the x axis.

(c) Draw on your graph (approximately) the Efficient Frontier and the Capital Allocation Line for the minimum variance portfolio.

(d) Would risk averse investors invest in a combination of the minimum variance portfolio and the risk-free rate? Explain.

(e) Using the approximate results from your graph, calculate the exact investment you would make to earn an E(r)=20%.