Saddam Husin 1301026226 Page 1 1. Stock A and B have the following historical returns :
Year Stock A’s Returns, rA(%) Stock B’s Returns, rB(%)
2006 (18) (24)
2007 44 24
2008 (22) (4)
2009 22 8
2010 34 56
a. Calculate the average rate of return for ech stock during 5 year period. Assume that someone held a portfolio of 50 percent of Stock A and 50 percent of Stock B. What would have been the realized rate of return on the portfolio in each year ? What would have been the average return on the portfolio during this period ?
b. Now calculate the standard deviation of return for each stock and for the potfolio. Use Equation 4-3a.
c. Looking at the annual returns data in the two stocks, would you guess that the correlation coefficient between returns on the, two stocks is closer to 0.8 or to -0.8 ? d. If you added more stock at random to the portfolio, which of the following nis the most accurate statement of what would happen to standard deviation p
(1) standard deviation p remain constant
Saddam Husin 1301026226 Page 2 2. ECRI Corp. Is a holding company with four main subsidiaries. The percentage of its business coming each of the subsidiaries, and their respective betas are as follows :
Subsidiary Percentage of Business Beta
Electric utility 60% 0.70
Cable company 25 0.90
Real Estate 10 1.30
International/secial project 5 1.50
a.What is holding company’s beta ?
b. Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent. What is the holding company’s required rate of return ?
c. ECRI is considering a change in its strategic focus : it will reduce its reliance on the electic utility subsidiary, so the percentage of its business from this subsidiary will be 50%. At the same time, ECRI will increase its reliance on the internationl/specia project division, so the percentage of its business from taht subsidiary wi rise to 15 percent. Will be the shareholders; required rate return if they adopt these changes ? 3. You are palnning to invest $200,000. Two securities, A and B, are available, and you
can invest in either of them or in a portfolio with some each. You estimate that the following probability distribution of returns are aplicable for A and B.
Security A Security B
PA rA PB RB
0.1 -10% 0.1 -30%
0.2 5 0.2 0
0.4 15 0.4 20
0.2 25 0.2 40
0.1 40 0.1 70
a. The expected return for security B is rA = 20% an = 25.7%. Find rA and b. Use the equation in footnote 3 to find the value of WA thah produces the minimum
Saddam Husin 1301026226 Page 3 c. Construct a table giving rp and for portfolio with WA = 1.0000, 0.75, 0.50, 0.25, 0.0, minimum risk value of WA. (Hint: For WA = 0.75, rp = 16.25%, and = 8,5 %; for WA = 0.5, rA = 17.5% and = 11.1%; for wa = 0.25%, rp = 18.75% and = 17.9%)
d. Graph the feasible set of portfolio and identify the efficient frontier of the feasible set. e. Suppose your risk/return trade-off function, or indiference curve, is tangent to the efficient set at the point where rp = 18%. Use this information, plus the graph constructed in part d to locate (approximately) your optimal portfolio. Draw in a reasonable indifference curve, indicate the percentage of your funds invested in each security, and determine the optimal portfolio’s and rp. (Hint : Estimate and rp graphically, and then use the equation for rp tp determine WA.)
f. Now suppose a riskless asset with a return rRF = 10% becomes available. How would this change the investment opportunity set ? explain why the efficeint frontier become linear.
g. Given the indifference curve in part e, would you change your potfolio ? If so, how ? (Hint : Assume the indifernce curves are parallel)
h. What are the beta coefficients of Sticks Aand B ? (Hints : (1) Recognize that ri = rRF + bi (rM + rRF) and solve for bi and(2) assume that your preferences match those of most other investors.)
4. Peenington Corp. Issued a new series of bonds on January 1, 1981. The bonds were sold at par ($1000), have a 12 percent coupun, and mature in 30 years, on December 31, 2010. Coupon payments are made semiannually (on June 30 and December 31) a. What was the YTM of Pennington’s bonds on Jauary 1, 1981 ?
b. What was the price of the bond on January 1, 1986, five years later, assuming that the level of interest rates had fallen to 10% ?
c. Find the curent yild and capital gains yield on the bond on January, 1, 1986, given the price as determined in part b ?
d. On July 1, 2004, Pennington’s bond sold for $916.42. Wahat was the YTM at that date ?
Saddam Husin 1301026226 Page 4 f. Now, assume that you purchased an outstanding Pennington bond on March 1, 2004, when the going rate of interest was 15.5%. How large a check mustyou have written to complete transaction ? This is hard question !
5. Ewald Company’s current stock price is $36, and its last dividend was $2.40. In view of Edwald’s strong financial position and its consequent low risk, its required rate of return is only 12%. If dividends are expected to grow at a constant rate, gm in future, and if the required rate of return on the stock is 12%, what is Ewald’s expected stock price 5 from now ?
6. Snyder Computer Chips Inc. is experiencing a period of rapid growth. Earnings and dividend are expected to grow at a rate of 15 percent during the next 2 years, at 13 percent in the third year, and a constant rate of 6 percent thereafter. Snyder’s last divident was %1.15 and the required rate of return on the stock is 12%
a. Calculate the value of the stock today b. Calculate P1 and P2
c. Calculate the dividend yield and capital gains yield for years 1, 2 and 3
7. A call option on the stock of Bedrock Boulders has a market price of 7$ The stock sells for $30 a share and the option has an exercise price of %25 a share.
a. What is the exercise value of the call option ? b. What is the premium on the option ?
8. Which of the following events are likely to increase the market value of a call option on a common stock ? explain
a. An increase in the stock ? explain b. An increase in the stock’s price
Saddam Husin 1301026226 Page 5 9. Longstreet Coomunication Inc. (LCI) has the following capital structure, which it consider to be optimal : debt 25%, PS =15%, and CS = 60%. LCI’s tax rate is 40% and investors expect earnings and dividens to grow a constant rate is 40% and investors ecxpect earnings and dividends to grow a constant rate of 6% in the future. LCI paid a dividend of $3.70 per share last year (D0), and its stock currently sells ata price of $60 per share. Treasury bonds yield 6 percent the market risk premium is 5%, and LCI’s. Preferred : New preferred could be sold to the public at a price $100 per share, with a dividend of 9%. Flotation costs of 5% per share would be, Debt could be sold at an interest rate of 9%
Saddam Husin 1301026226 Page 6
c. Correlation Coefficient 0.8
d. Jika kita menambahkan saham secara acak di portofolio maka yang akan terjadi adalah standar deviasi akan turun sekitar 20% dari titik semula.
Subsidiary Percentage Of Business Beta
Electric 60% 0.7 0.42
b. Holding Company'S Rate of return 10.25
Subsidiary Percentage Of Business Beta
Electric 50 % 0.7 0.35
Cable Company 25 % 0.9 0.225
Rale Estate 10 % 1.3 0.13
Project 15 % 1.5 0.225
Holding Companys Beta 0.93
Holding Company'S Rate of return 10.65
Saddam Husin 1301026226 Page 8
c. Current yield and Capital gains:
Current Yield = Annual Coupon / PV
e. Current yield and Capital gains:
Saddam Husin 1301026226 Page 10 6) Calculate the PV of dividend paid during the supernormal growth period :
a. = $ 1,15 (1,15) = $ 1,3225
Find the PV of Snyder’s stock price of the end year 3 :
Now sum the two components to find the value of the stock today : = $ 3,62 + $ 21,61
c. Calculate the dividend yield and capital gains yield for Years 1, 2. And 3 :
Saddam Husin 1301026226 Page 11
7) Opinions :
a. The exercise value of the call option is $ 25 + $ 7 = $ 32. It’s the value to stock must rise to, in order to make a profit.
b. The current intrinsic value of the option is $ 30 - $ 25 = $ 5. It’s the worth of the opinion if it would expire “today”. As the market price is $ 7, the difference $ 7 - $5 = $ 2 represents the opition’s time value.
9) Dik :
Dit : Cost of debt, preffered stock, and commond stock ? Jawab : Cost of Preffered Stock : Dividend = $ 9 Price = $ 100 KPS =
= 9 %
Cost of commond stock : F = $ 5 (flotation cost)
= $ 3,6
Saddam Husin 1301026226 Page 12
Div 1 =
KE = + 9
KE = + 9