Exam-Type Questions for Midterm 2

FIN303 Exam-type questions For Midterm 2 Chapter 2 1. Suppose you have $2,000 and plan to purchase a 3-year certificate of deposit (CD) that pays 4% interest, compounded annually. How much will you have when the CD matures? a. b. c. d. $2,324.89 $2,591.45 $2,249.73 * $2,011.87 PV= -2,000; I=4%;N=3 PMT=0; FV=? 2. Suppose a U.S. government bond promises to pay $2,249.73 three years from now. If the going interest rate on 3-year government bonds is 6%, how much is the bond worth today? a. b. c. d. $2,011.87 $2,591.45 $2,324.89 $1,888.92 * PV=?; I=6%; N=3; PMT=0; FV=2,249.73 3. What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. b. c. d. $ 670.44 $ 842.91 $1,169.56 $1,348.48 * Financial calculator solution: Inputs: N = 5; I = 15; PV = 0; PMT = -200. $1,348.48. 4. Output: FV = What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. b. c. d. $ 670.43 * $ 842.91 $1,169.56 $1,348.48 Financial calculator solution: Inputs: N = 5; I = 15; PMT = -200; FV = 0. Output: PV = 1 $670.43. 5. A real estate investment has the following expected cash flows: Year 1 2 3 4 Cash Flows $10,000 25,000 50,000 35,000 The discount rate is 8 percent. What is the investment’s present value? a. b. c. d. $103,799 $ 96,110 * $ 95,353 $120,000 PV = $10,000/1.08 + $25,000/(1.08)2 + $50,000/(1.08)3 + $35,000/(1.08)4 = $9,259.26 + $21,433.47 + $39,691.61 + $25,726.04 = $96,110.38 ≈ $96,110. 6. If $100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years? a. b. c. d. $122.02 * $105.10 $135.41 $120.90 Financial calculator solution: Inputs: N = 20; I = 1; PV = -100; PMT = 0. $122.02. 7. Output: FV = In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the 30-year period? a. 12% b. 9% c. 6% d. 7% * Financial calculator solution: Inputs: N = 30; PV = -1800; PMT = 0; FV = 13700. 7.0%. 8. Output: I = At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4 percent? a. b. c. d. 12 years 15 years 18 years * 20 years 2 Financial calculator solution: Inputs: I = 4; PV = -1; PMT = 0; FV = 0.50. Output: N = -17.67 ≈ 18 years. 9. South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying? a. 7% b. 8% * c. 9% d. 10% Financial calculator solution: Inputs: N = 5; PV = 10000; PMT = -2504.56; FV = 0. 8%. 10. Output: I = Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan in which interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks? a. b. c. d. 0.25% 0.50% 0.70% * 1.00% Bank A: 8%, monthly. m k   EARA = 1 + Nom  − 1 m   12 0.08   = 1 +  12   Bank B: − 1 = 8.30%. 9%, interest due at end of year EARB = 9%. 9.00% - 8.30% = 0.70%. 11. You recently received a letter from Cut-to-the-Chase National Bank that offers you a new credit card that has no annual fee. It states that the annual percentage rate (APR) is 18 percent on outstanding balances. What is the effective annual interest rate? (Hint: Remember these companies bill you monthly.) a. b. c. d. 18.81% 19.56% * 19.25% 20.00% Use the formula for rates as follows: calculating effective rates from nominal EAR = (1 + 0.18/12)12 - l = 0.1956 or 19.56%. 3 12. Jill currently has $300,000 in a brokerage account. The account pays a 10 percent annual interest rate. Assuming that Jill makes no additional contributions to the account, how many years will it take for her to have $1,000,000 in the account? a. 23.33 years b. 3.03 years c. 16.66 years d. 12.63 years * Enter the data given in your financial calculator: I = 10; PV = -300000; PMT = 0; FV = 1000000. Then solve for N = 12.63 years. 13. You are considering buying a new car. The sticker price is $15,000 and you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 10 percent and you wish to pay for the car over a 5-year period, what are your monthly car payments? a. b. c. d. $216.67 $252.34 $276.21 * $285.78 First, find the monthly interest rate = 0.10/12 = 0.8333%/month. Now, enter in your calculator N = 60; I/YR = 0.8333; PV = -13000; FV = 0; and then solve for PMT = $276.21. 14. Today, Bruce and Brenda each have $150,000 in an investment account. No other contributions will be made to their investment accounts. Both have the same goal: They each want their account to reach $1 million, at which time each will retire. Bruce has his money invested in risk-free securities with an expected annual return of 5 percent. Brenda has her money invested in a stock fund with an expected annual return of 10 percent. How many years after Brenda retires will Bruce retire? a. 12.6 b. 19.0 * c. 19.9 d. 29.4 Step 1: Find the number of years it will take for each $150,000 investment to grow to $1,000,000. BRUCE: I/YR = 5; PV = -150000; PMT = 0; FV = 1000000; and then solve for N = 38.88. BRENDA: I/YR = 10; PV = -150000; PMT = 0; FV = 1000000; and then solve for N = 19.90. Step 2: Calculate the difference in the length of time for the accounts to reach $1 million: Bruce will be able to retire in 38.88 years, or 38.88 – 19.90 = 19.0 years after Brenda does. 4 Chapter 7 15. One of the basic relationships in interest rate theory is that, other things held constant, for a given change in the required rate of return, the the time to maturity, the the change in price. a. b. c. d. 16. longer; smaller. longer; greater. shorter; smaller. Statements b and c are correct. * Which of the following statements is most correct? a. All else equal, long-term bonds have more interest rate risk than short-term bonds. b. All else equal, high-coupon bonds have more reinvestment rate risk than lowcoupon bonds. c. All else equal, short-term bonds have more reinvestment rate risk than do long-term bonds. d. All of the statements above are correct. * 17. Which of the following bonds will have the greatest percentage increase in value if all interest rates decrease by 1 percent? a. b. c. d. 20-year, zero coupon bond. * 10-year, zero coupon bond. 20-year, 10 percent coupon bond. 20-year, 5 percent coupon bond. The longer the maturity of a bond, the more of an effect a change in interest rates will have on it. The reason for this is that the price change is compounded into the bond price for more periods. Therefore, you can rule out statements b and e. A bond that pays coupons will be less affected by interest rate changes than one that doesn’t pay coupons. The bond price is the NPV of all the future cash flows, both the coupon payments and the par value paid at maturity. The first coupon payment is only discounted one period. The second coupon is discounted two periods, and so on. The par value is discounted for the full life of the bond. Thus, statements c and d can be eliminated. Since a zero coupon bond’s price today is determined just by the NPV of its par value, all of its payment is discounted for the maximum amount of time, whereas a coupon bond has many payments discounted for less than the maximum amount of time. Therefore, a zero coupon bond is most affected by interest rate changes. So, the longest zero coupon bond is the correct answer, which is statement a. 5 18. Which of the following events would make it more likely that a company would choose to call its outstanding callable bonds? a. b. c. d. A reduction in market interest rates. * The company’s bonds are downgraded. An increase in the call premium. Statements a and b are correct. Statement a is correct; the other statements are false. A bond down-grade generally raises the cost of issuing new debt. Therefore, the callable bonds would not be called. If the call premium (the cost paid in excess of par) increases, the cost of calling debt increases; therefore, callable bonds would not be called. 19. All of the following may serve to reduce the coupon rate that would otherwise be required on a bond issued at par, except a a. b. c. d. 20. Sinking fund. Restrictive covenant. Call provision. * Change in rating from Aa to Aaa. A 10-year corporate bond has an annual coupon payment of 9 percent. The bond is currently selling at par ($1,000). Which of the following statements is most correct? a. The bond’s yield to maturity is 9 percent. b. The bond’s current yield is 9 percent. c. If the bond’s yield to maturity remains constant, the bond’s price will remain at par. d. All of the statements above are correct. * All the statements are true; therefore, the correct choice is statement e. Since the bond is selling at par, its YTM = coupon rate. The current yield is calculated as $90/$1,000 = 9%. If YTM = coupon rate, the bond will sell at par. So, if the bond’s YTM remains constant the bond’s price will remain at par. 21. Which of the following statements is most correct? a. Junk bonds typically have a lower yield to maturity relative to investment grade bonds. b. A debenture is a secured bond that is backed by some or all of the firm’s fixed assets. c. Subordinated debt has less default risk than senior debt. d. None of the statements above is correct. * Statement d is correct; the others are false. Junk bonds have a higher yield to maturity relative to investment grade bonds. A debenture is an unsecured bond, while subordinated debt has greater default risk than senior debt. 6 22. Which of the following Treasury bonds will have the largest amount of interest rate risk (price risk)? a. b. c. d. A 7 percent coupon bond that matures in 12 years. * A 9 percent coupon bond that matures in 10 years. A 12 percent coupon bond that matures in 7 years. A 7 percent coupon bond that matures in 9 years. Statement a is correct. The longer the maturity and the lower the coupon of a bond, the more sensitive it is to interest rate (price) risk. The bond in answer a has a maturity greater than or equal to and a coupon less than or equal to all the other bonds. 23. You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond? a. b. c. d. $ 826.31 $1,086.15 $ 957.50 $1,124.62 * Financial calculator solution: Inputs: N = 20; I = 5; PMT = 60; FV = 1000. Output: PV = -$1,124.62; VB = $1,124.62. 24. Consider a $1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent? a. 10.00% b. 8.46% * c. 7.00% d. 8.52% Current yield = Annual coupon payment/Current price. Step 1: Find the price of the bond: N = 9; I/YR = 10; PMT = 70; FV = 1000; and then solve for PV = -$827.23. VB = $827.23. Step 2: Calculate the current yield: CY = $70/$827.23 = 8.46%. Chapter 8 25. You observe the following information regarding Company X and Company Y: • • • Company X has a higher expected mean return than Company Y. Company X has a lower standard deviation than Company Y. Company X has a higher beta than Company Y. Given this information, which of the following statements is most correct? 7 a. b. c. d. Company X has a lower coefficient of variation than Company Y * Company X has more company-specific risk than Company Y. Company X is a better stock to buy than Company Y. Statements a and b are correct. Statement a is correct, since the coefficient of variation is equal to the standard deviation divided by the mean. 26. Which of the following statements is most correct? the risk-free rate remains constant.) (Assume that a. If the market risk premium increases by 1 percentage point, then the required return on all stocks will rise by 1 percentage point. b. If the market risk premium increases by 1 percentage point, then the required return will increase for stocks that have a beta greater than 1.0, but it will decrease for stocks that have a beta less than 1.0. c. If the market risk premium increases by 1 percentage point, then the required return will increase by 1 percentage point for a stock that has a beta equal to 1.0. * d. Statements a and c are correct. CAPM equation: ks = kRF + (kM - kRF)b If the market risk premium (measured by kM - kRF) goes up by 1.0, then the required return for each stock will change by its beta times 1.0. Therefore, a stock with a beta of 0.5 will see its required return go up by 0.5 percentage point. Therefore, statement a is false. As just shown in statement a, a stock with a beta of 0.5 will see its required return increase by 0.5 percentage point. All stocks with positive betas will see their required returns increase. Therefore, statement b is false. If the market risk premium increases by 1 percentage point, then the required return increases by 1.0 times the stock’s beta. Therefore, the required return of a stock with a beta coefficient equal to 1.0 will increase by 1 percentage point, and statement c is correct. 27. A highly risk-averse investor is considering the addition of an asset to a 10-stock portfolio. The two securities under consideration both have an expected return, k , equal to 15 percent. However, the distribution of possible returns associated with Asset A has a standard deviation of 12 percent, while Asset B’s standard deviation is 8 percent. Both assets are correlated with the market with r equal to 0.75. Which asset should the riskaverse investor add to his/her portfolio? a. b. c. d. 28. Asset A. Asset B. * Both A and B. Neither A nor B. Stock A has a beta of 1.5 and Stock B has a beta of 0.5. Which of the following statements must be true about these securities? (Assume the market is in equilibrium.) a. When held in isolation, Stock A has greater risk than Stock B. b. Stock B would be a more desirable addition to a portfolio than 8 Stock A. c. Stock A would be a more desirable addition to a portfolio than Stock B. d. The expected return on Stock A will be greater than that on Stock B. * 29. Over the past 75 years, we have observed that investments with higher average annual returns also tend to have the highest standard deviations in their annual returns. This observation supports the notion that there is a positive correlation between risk and return. Which of the following lists correctly ranks investments from having the highest returns and risk to those with the lowest returns and risk? a. Small-company stocks, large-company stocks, long-term corporate bonds, long-term government bonds, U.S. Treasury bills. * b. Small-company stocks, long-term corporate bonds, large-company stocks, long-term government bonds, U.S. Treasury bills. c. Large-company stocks, small-company stocks, long-term corporate bonds, U.S. Treasury bills, long-term government bonds. d. U.S. Treasury bills, long-term government bonds, long-term corporate bonds, small-company stocks, large-company stocks. The correct answer is statement a. Stocks are riskier than bonds, with stocks in small companies being riskier than stocks in larger companies. From there, corporate bonds are riskier than government bonds, and longer-term government bonds are riskier than shorter-term ones. 30. The risk-free rate is 6 percent. Stock A has a beta of 1.0, while Stock B has a beta of 2.0. The market risk premium (kM – kRF) is positive. Which of the following statements is most correct? a. Stock B’s required rate of return is twice that of Stock A. b. If Stock A’s required return is 11 percent, the market risk premium is 5 percent. * c. If the risk-free rate increases (but the market risk premium stays unchanged), Stock B’s required return will increase by more than Stock A’s. d. Statements b and c are correct. The CAPM is written as: ks = kRF + (kM – kRF)b. Statement a is false based on the CAPM equation. Statement b is correct on the basis of the CAPM equation. Statement c is false; the required returns will increase by the same amount. 31. Assume that the risk-free rate is 5 percent. Which of the following statements is most correct? a. If a stock’s beta doubles, the stock’s required return will also double. b. If a stock’s beta is less than 1.0, the stock’s required return is less than 5 percent. c. If a stock has a negative beta, the stock’s required return is less than 5 percent. * d. All of the statements above are correct. 9 The correct answer is statement c. Here, the required rate is ks = 5% + b × RPM. If a stock’s beta doubles, b becomes 2b. So, ks = 5% + 2b × RPM. But doubling its required return would require the equation to be 2(5% + b × RPM) = 10% + 2b × RPM. So, statement a is incorrect. Statement b would be correct only if the beta coefficient were Statement c is negative. Therefore, statement b is incorrect. correct. If b < 0 and RPM > 0, then (b × RPM) < 0. So, ks < 5%. 32. The risk-free rate of interest, kRF, is 6 percent. The overall stock market has an expected return of 12 percent. Hazlett, Inc. has a beta of 1.2. What is the required return of Hazlett, Inc. stock? a. b. c. d. 12.0% 12.2% 12.8% 13.2% * ks = kRF + (kM - kRF)b = 6% + (12% - 6%)1.2 = 13.2%. 33. A stock has an expected return of 12.25 percent. The beta of the stock is 1.15 and the risk-free rate is 5 percent. What is the market risk premium? a. 1.30% b. 6.50% c. 15.00% d. 6.30% * 12.25% = 5% + (RPM)1.15 7.25% = (RPM)1.15 RPM = 6.3043% ≈ 6.30%. 10