Question 1 - Bond Valuation
Assume the following information for bonds A and B. Both bonds have the same YTM and have semi-annual coupon payments. Bond B is currently selling at par.
Face Value Maturity Coupon Rate
Bond A 1000 30 yrs 8% Bond B 1000 20 yrs 10%
a) What is the price for Bond B (2 pts)? What is the current yield for Bond B (2 pts)? Bond A is selling at a ________(discount /par/ premium) (2 pts).
b) Suddenly interest rates rise by 2%. The price of bond A will go________ (up/down) (2 pts).
c) The percentage change in the price of Bond B (in absolute value) will be _________ (smaller/bigger) than that of Bond A (in absolute value) (3 pts).
d) Assuming interest rates remain unchanged (after the initial 2% increase took place), what is the price of Bond B after 5 years (7 pts)?
a) Price = 1000 since it sells at par. Current yield = Annual coupon payment / Price = 100 / 1000 = 10%. Bond A is selling at a discount. b) down , down
d) 50/0.06*(1 – 1/1.06^30) + 1000/1.06^30 = $862.3517
Question 2 - Stock Valuation
XYZ Corp. sells toothpicks. The company currently has earnings per share of $8.25. The company has no growth and pays out all earnings as dividends. It has a new project which will require an investment of $1.60 per share today (at time zero). The project will increase the earnings by $0.40 per share indefinitely starting one year after the investment. Investors require a 10 percent return on XYZ stock. Assume the firm just paid the dividend of $8.25 yesterday.
a) What is the value per share of the company’s stock assuming the firm does not undertake the investment opportunity? (5 pts)
b) If the company does undertake the investment what is the value per share now? (10 pts)
c) What will the value per share be 3 years from now? (5 pts)
a) P = Dividend / R = 8.25 / 0.1 = $ 82.5
b) NPVGO = (-1.60 + 0.40 / 0.1) = $ 2.40
So the stock price will be: 82.5 + 2.40 = 84.90
c) (8.25 + 0.40) / 0.1 = 86.5
Question 3 – Portfolio Variance
Suppose the expected returns and standard deviation of stocks A and B are E(Ra) = 0.13, E(Rb) = 0.19, σa = 0.38, σb = 0.62 respectively. a) Calculate the expected return and standard deviation for a portfolio that is composed of 45 percent A and 55 percent B when the correlation coefficient between the returns on A and B is 0.5 (10 pts) b) How does the correlation coefficient between the returns on A and B affect the standard deviation of the portfolio? (3 pts) c) Provide a range for the correlation coefficient where we obtain diversification benefits. (i.e, The portfolio standard deviation is less than the weighted average of the individual standard deviations of the stocks?) Provide a range where we don’t have diversification benefits. (3 + 2 pts) d) For some values of correlation coefficient, we can achieve a portfolio standard deviation of almost zero. TRUE or FALSE? ( 2 pts)
Solution: a) The expected return of the portfolio is the sum of the weight of each asset times the expected return of each asset, so:
E(RP) = wAE(RA) + wBE(RB)
E(RP) = .45(.13) + .55(.19)
E(RP) = .1630 or 16.30%
The variance of a portfolio of two assets can be expressed as:
([pic] = w[pic]([pic] + w[pic]([pic] + 2wAwB(A(B(A,B
([pic] = .452(.382) + .552(.622) + 2(.45)(.55)(.38)(.62)(.50)
([pic] = .20383
So, the standard deviation is:
(P = (.20383)1/2 = .4515 or 45.15%
b) As Stock A and Stock B become less correlated, or more negatively correlated, the standard deviation of the portfolio decreases. c) corr < 1 (strictly less), corr = 1
Question 4 – CAPM and SML
Suppose that you observe the following information. Assume these securities are correctly priced.
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