Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. -1. d. 0.5. By definition, the beta of the market portfolio is 1. 2. The risk-free rate and the expected market rate of return are 0.06 and 0.12, respectively. According to the capital asset pricing model (CAPM), the expected rate of return on security X with a beta of 1.2 is equal to a. 0.06. b. 0.144. c. 0.12. *d. 0.132 e. 0.18 E(R) = 6% + 1.2(12-6) = 13.2%. 3. According to the Capital Asset Pricing Model (CAPM), fairly priced securities a. have positive betas. *b. have zero alphas. c. have negative betas. d. have positive alphas.. A zero alpha results when the security is in equilibrium (fairly priced for the level of risk). 4. According to the Capital Asset Pricing Model (CAPM), a. a security with a positive alpha is considered overpriced. b. a security with a zero alpha is considered to be a good buy. c. a security with a negative alpha is considered to be a good buy. *d. a security with a positive alpha is consider to be underpriced.. A security with a positive alpha is one that is expected to yield an abnormal rate of return, based on the perceived risk of the security, and thus is underpriced. 5. Security X has an expected rate of return of 0.11 and a beta of 1.5. The risk-free rate is 0.05 and the market expected rate of return is 0.09. According to the Capital Asset Pricing Model, this security is a. underpriced. b. overpriced. *c. fairly priced.
d. cannot be determined from data provided.. 11% = 5% + 1.5(9% - 5%) = 11.0%; therefore, the security is fairly priced. 6. What is the expected return of a zero-beta security? a. The market rate of return. b. Zero rate of return. c. A negative rate of return. *d. The risk-free rate. e. None of the above. E(R S ) = r f + 0(R M - r f ) = r f. 7. A coupon bond that pays interest annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10%. The intrinsic value of the bond today will be if the coupon rate is 7%. a. $712.99 b. $620.92 c. $1,123.01 *d. $886.27 e. $1,000.00 FV = 1000, PMT = 70, n = 5, i = 10, PV = 886.27 8. A coupon bond that pays interest semi-annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10%. The intrinsic value of the bond today will be if the coupon rate is 8%. *a. $922.78 b. $924.16 c. $1,075.80 d. $1,077.20 FV = 1000, PMT = 40, n = 10, i = 5, PV = 922.78 9. A coupon bond that pays interest of $100 annually has a par value of $1,000, matures in 5 years, and is selling today at a $72 discount from par value. The yield to maturity on this bond is. a. 6.00% b. 8.33% *c. 12.00% d. 60.00% FV = 1000, PMT = 100, n = 5, PV = -928, i = 11.997% 10. You purchased an annual interest coupon bond one year ago that had 6 years remaining to maturity at that time. The coupon interest rate was 10% and the par value was $1,000. At the time you purchased the bond, the yield to maturity was 8%. If you sold the bond after receiving the first
interest payment and the yield to maturity continued to be 8%, your annual total rate of return on holding the bond for that year would have been. a. 7.00% b. 7.82% *c. 8.00% d. 11.95% FV = 1000, PMT = 100, n = 6, i = 8, PV = 1092.46 FV = 1000, PMT = 100, n = 5, i = 8, PV = 1079.85 HPR = (1079.85 1092.46 + 100) / 1092.46 = 8% 11. A coupon bond pays annual interest, has a par value of $1,000, matures in 4 years, has a coupon rate of 10%, and has a yield to maturity of 12%. The current yield on this bond is. a. 9.39% b. 10.00% *c. 10.65% d. 12.00% FV = 1000, n = 4, PMT = 100, i = 12, PV= 939.25 $100 / $939.25 = 10.65%. 12. A zero-coupon bond has a yield to maturity of 9% and a par value of $1,000. If the bond matures in 8 years, the bond should sell for a price of today. a. 422.41 *b. $501.87 c. $513.16 d. $483.49 $1,000/(1.09) 8 = $501.87 13. The yield to maturity on a bond is. a. below the coupon rate when the bond sells at a discount, and equal to the coupon rate when the bond sells at a premium. *b. the discount rate that will set the present value of the payments equal to the bond price. c. based on the assumption that any payments received are reinvested at the coupon rate. d. none of the above. e. a, b, and c. The reverse of a is true; for c to be true payments must be reinvested at the yield to maturity. 14. A bond will sell at a discount when. a. the coupon rate is greater than the current yield and the current yield is greater than yield to maturity b. the coupon rate is greater than yield to maturity c. the coupon rate is less than the current yield and the current yield is greater than the yield to maturity
*d. the coupon rate is less than the current yield and the current yield is less than yield to maturity are true. In order for the investor to earn more than the current yield the bond must be selling for a discount. Yield to maturity will be greater than current yield as investor will have purchased the bond at discount and will be receiving the coupon payments over the life of the bond. 15. Consider a 5-year bond with a 10% coupon that has a present yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be. a. higher *b. lower c. the same d. cannot be determined e. $1,000 This bond is a premium bond as interest rates have declined since the bond was issued. If interest rates remain constant, the price of a premium bond declines as the bond approaches maturity. 16. A 1% decline in yield will have the greatest effect on the price of the bond with a a. 10-year maturity, selling at 80 b. 10-year maturity, selling at 100 *c. 20-year maturity, selling at 80 d. 20-year maturity, selling at 100 e. all bonds will be affected equally The longer the maturity the more an interest rate changes the price of the bond. Bonds selling at discount are affected more than bonds selling at par. 17. Using semiannual compounding, a 15-year zero coupon bond that has a par value of $1,000 and a required return of 8% would be priced at. *a. 308 b. $315 c. $464 d. $555 FV = 1000, n = 30, I = 4, PV = 308.32 18. The yield curve shows at any point in time: a. The relationship between the yield on a bond and the duration of the bond. b. the relationship between the coupon rate on a bond and time to maturity of the bond. *c. The relationship between yield on a bond and the time to maturity on the bond. d. All of the above. e. None of the above. Use the following information to answer questions 19 through 21. Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year Forward Interest Rate 0 (today) 5% 1 7% 2 9% 3 10% 19. What is the price of 3-year zero coupon bond with a par value of $1,000? a. $863.83 *b. $816.58 c. $772.18 d. $765.55 $1,000 ) (1.05)(1.07)(1.09) = $816.58 20. What is the price of a 2-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000) a. $1,092.97 b. $1,054.24 c. $1,000.00 *d. $1,073.34 [(1.05)(1.07)] 1/2-1 = 6%. FV = 1000, n = 2, PMT = 100, i = 6, PV = $1,073.34 21. What is the yield to maturity of a 3-year zero coupon bond? a. 7.00% b. 9.00% *c. 6.99% d. 7.49% [(1.05)(1.07)(1.09)] 1/3-1 = 6.99. Use the following information to answer question 22. Given the following pattern of forward rates: Year Forward Rate 1 5% 2 6% 3 6.5% 22. If one year from now the term structure of interest rates changes so that it looks exactly the same as it does today, what would be your holding period return if you purchased a 3-year zero coupon bond today and held it for one year? a. 6% *b. 8% c. 9% d. 7%
$1,000 / (1.06)(1.065) = $885.82 (selling price) $1,000 / (1.05)(1.06)(1.065) = $843.64 (purchase price) ($885.82 - $843.64) / $843.64 = 5% 23. Given the time to maturity, the duration of a zero coupon bond is higher when the discount rate is a. higher. b. lower. c. equal to the risk free rate. *d. independent of the discount rate.. The duration of a zero coupon bond is equal to the maturity of the bond. 24. Which of the following two bonds is more price sensitive to changes in interest rates? 1. A par value bond, X, with a 5-year-to-maturity and a 10% coupon rate. 2. A zero coupon bond, Y, with a 5-year-to-maturity and a 10% yield-to-maturity. a. Bond X because of the higher yield to maturity. b. Bond X because of the longer time to maturity. *c. Bond Y because of the longer duration. d. Both have the same sensitivity because both have the same yield to maturity. e. None of the above Duration is the best measure of bond price sensitivity; the longer the duration the higher the price sensitivity. 25. Which of the following is not true? a. Holding other things constant, the duration of a bond increases with time to maturity. *b. Given time to maturity, the duration of a zero coupon decreases with yield to maturity. c. Given time to maturity and yield to maturity, the duration of a bond is higher when the coupon rate is lower. d. Duration is a better measure of price sensitivity to interest rate changes than is time to maturity. e. All of the above. The duration of a zero coupon bond is equal to time to maturity, and is independent of yield to maturity. 26. Par value bond XYZ has a modified duration of 6. Which one of the following statements regarding the bond is true? *a. If the market yield increases by 1% the bond's price will decrease by $60. b. If the market yield increases by 1% the bond's price will increase by $50. c. If the market yield increases by 1% the bond's price will decrease by $50. d. If the market yield decreases by 1% the bond's price will increase by $60. e. None of the above. P/P = -D* y -$60 = -6(0.01) X $1,000 27. Which of the following bonds has the longest duration?
a. An 8-year maturity, 0% coupon bond. b. An 8-year maturity, 5% coupon bond. c. A 10-year maturity, 5% coupon bond. *d. A 10-year maturity, 0% coupon bond. e. Cannot tell from the information given. The longer the maturity and the lower the coupon, the greater the duration 28. Which one of the following par value 12% coupon bonds experiences a price change of $23 when the market yield changes by 50 basis points? a. The bond with a duration of 6 years. b. The bond with a duration of 5 years. c. The bond with a duration of 2.7 years. *d. The bond with a duration of 5.15 years. e. None of the above. P/P = -D X [ (1+y) / (1+y)]; -.023 = -D X [.005 / 1.12]; D = 5.15 29. An 8%, 15-year bond has a yield to maturity of 10% and a duration of 8.05 years. If the market yield changes by 25 basis points, how much change will there be in the bond's price? *a. 1.85% b. 2.01% c. 3.27% d. 6.44% P/P = (-8.05 X 0.0025)/1.1 = 1.85% 30. Each of two stocks, A and B, are expected to pay a dividend of $5 in the upcoming year. The expected growth rate of dividends is 10% for both stocks. You require a rate of return of 11% on stock A and a return of 20% on stock B. The intrinsic value of stock A. *a. will be greater than the intrinsic value of stock B b. will be the same as the intrinsic value of stock B c. will be less than the intrinsic value of stock B d. cannot be calculated without knowing the market rate of return. d. none of the above are true. PV 0 = D 1 /(k-g); given that dividends are equal, the stock with the larger required return will have the lower value. Use the following information to answer questions 31-33. Dominion Tool Company is expected to pay a dividend of $2 in the upcoming year. The risk-free rate of return is 4% and the expected return on the market portfolio is 14%. Analysts expect the price of Dominion Tool Company shares to be $22 a year from now. The beta of Dominion Tool Company's stock is 1.25. 31. The market s required rate of return on Dominion s stock is. a. 14.0% b. 17.5%
*c. 16.5% d. 15.25% 4% + 1.25(14% - 4%) = 16.5%. 32. What is the intrinsic value of Dominion s stock today? *a. $20.60 b. $20.00 c. $12.12 d. $22.00 k =.04 + 1.25 (.14 -.04) ; k =.165.165 = (22 P + 2) / P.165P = 24 P 1.165P = 24 ; P = 20.60 33. If Dominion s intrinsic value is $21.00 today, what must be its growth rate? a. 0.0% b. 10% c. 4% d. 6% *e. 7% k =.04 + 1.25 (.14 -.04) ; k =.165.165 = 2/21 + g; g =.07 Use the following information for questions 34-35. Civil Engineering Corporation is expected to pay a dividend of $1.00 in the upcoming year. Dividends are expected to grow at the rate of 6% per year. The risk-free rate of return is 5% and the expected return on the market portfolio is 13%. The stock of Civil Engineering Corporation has a beta of 1.2. 34. What is the return you should require on Civil Engineering s stock? a. 12.0% *b. 14.6% c. 15.6% d. 20% 5% + 1.2(13% - 5%) = 14.6%. 35. What is the intrinsic value of Civil Engineering s stock? a. $14.29 b. $14.60 c. $12.33 *d. $11.62
k = 5% + 1.2(13% - 5%) = 14.6% P = 1 / (.146 -.06) = $11.62. 36. High Fly Airline is expected to pay a dividend of $7 in the coming year. Dividends are expected to grow at the rate of 15% per year. The risk-free rate of return is 6% and the expected return on the market portfolio is 14%. The stock of High Fly Airline has a beta of 3.00. The return you should require on the stock is. a. 10% b. 18% *c. 30% d. 42% 6% + 3(14% - 6%) = 30%. 37. High Fly Airline is expected to pay a dividend of $7 in the coming year. Dividends are expected to grow at the rate of 15% per year. The risk-free rate of return is 6% and the expected return on the market portfolio is 14%. The stock of High Fly Airline has a beta of 3.00. The intrinsic value of the stock is. *a. $46.67 b. $50.00 c. $56.00 d. $62.50 6% + 3(14% - 6%) = 30%; P = 7 / (.30 -.15) = $46.67 38. Sunshine Corporation is expected to pay a dividend of $1.50 in the upcoming year. Dividends are expected to grow at the rate of 6% per year. The risk-free rate of return is 6% and the expected return on the market portfolio is 14%. The stock of Sunshine Corporation has a beta of 0.75. The intrinsic value of the stock is. a. $10.71 b. $15.00 c. $17.75 *d. $25.00 6% + 0.75(14% - 6%) = 12%; P = 1.50 / (.12 -.06) = $25. 39. Mature Products Corporation produces goods that are very mature in their product life cycles. Mature Products Corporation is expected to pay a dividend in year 1 of $2.00, a dividend of $1.50 in year 2, and a dividend of $1.00 in year 3. After year 3, dividends are expected to decline at a rate of 1% per year. An appropriate required rate of return for the stock is 10%. The stock should be worth a. $9.00 *b. $10.57 c. $20.00 d. $22.22
Yr. Div. PV of Div. @ 10% 1 $2.00 $2.00/1.10 = $1.82 2 $1.50 $1.50/(1.10) 2 = $1.24 3 $1.00 $1.00/(1.10) 3 = $0.75 $3.81 P 3 = 1.00 (.99) / [.10 (-.01)] = $9.00 PV of P 3 = $9/(1.10) 3 = $6.76; P O = $6.76 + $3.81 = $10.57. 40. Assume that at the end of the next year, Company A will pay a $2.00 dividend per share, an increase from the current dividend of $1.50 per share. After that, the dividend is expected to increase at a constant rate of 5%. If you require a 12% return on the stock, the value of the stock is. *a. $28.57 b. $28.79 c. $30.00 d. $31.78 P 1 = 2 (1.05) / (.12 -.05) = $30.00 PV of P 1 = $30/1.12 = $26.78; PV of D 1 = 2/1.12 = 1.79 P O = $26.78 + $1.79 = $28.57.