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Towson University Department of Finance Fin331 Dr. M. Rhee 2010 Spring
1. If APR = 10%, what is the EAR (effective annual rate) for quarterly compounding? a. 10.00% b. 10.38% c. 12.36% d. 13.36% e. 15.52% Answer: b APR = Nominal rate 10.00% Periods/yr 4 EFF% =(1+(r_{NOM}/N))^{N − 1} = 10.38% 2. If the current one year CD rate is 3% and the best estimate of one year CD which will be available one year from today is 5%, what is the current two year CD rate with 1% liquidity premium?
Answer: C (1 + _{0}R_{2} – 0.01)^{2} = (1.03)^{1} × (1.05)^{1} _{0}R_{2} = {(1.03) × (1.05)}^{1/2} + 0.01 – 1 = 4.9952% ≈ 5.00% 3. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? a. The present value of a 5year, $250 annuity due will be lower than the PV of a similar ordinary annuity. b. A 30year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20year mortgage. c. A bank loan's nominal interest rate will always be equal to or greater than its effective annual rate. d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%. e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit. Answer: d 4. You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. $1,412.84 b. $1,487.20 c. $1,565.48 d. $1,643.75 e. $1,725.94 Answer: c BEGIN Mode N 3 I/YR 5.5% PMT $550 FV $0.00 PV $1,565.48 Therefore, to receive $550 at the beginning of each year for 3 years at 5.5%, the fair value you should pay is $1,565.48 5. Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end? a. 15.05 b. 16.36 c. 17.22 d. 18.08 e. 18.99 Answer: a BEGIN Mode 6. How much do you need to save each year from two years from today and onward so that you can have $1,000 six years from today at 10% interest rate?
Answer: b N=5, I/Y=10, FV=1,000 => PMT = 163.80 7. Jennifer can make a 100,000 down payment to buy a house. The house is $380,000 and she was offered 30year mortgage and 15year mortgage at a market rate of 12%. How much more interest would Jennifer pay if she took out a 30year mortgage instead 15year mortgage?
Answer: c For 30 years: N=30*12=360, I=1%, PV= (380,000100,000) => PMT=2,880.12 INT = (2,880.12*360) – 280,000 = 756,843.20 For 15 years: N=15*12=180, I=1%, PV= (380,000100,000) => PMT=3,360.47 INT = (3,360.47*180) – 280,000 = 324,884.60 Therefore, the difference in the interests is 756,843.20  324,884.60 = 431,958.60 8. How long will it take for you to pay off $1,500 charged on your credit card, if you plan to make the minimum payment of $15 per month and the credit card charges 24% per annum?
Answer: e I = 2, PV = 1500, PMT = 15 ⇨ N = ? Error 5 is “No solution exists” in the Texas Instrument BA II Plus 9. 5year Treasury bonds yield 5.5%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5year Tbonds is 0.4%. There is no liquidity premium on these bonds. What is the real riskfree rate, r*? a. 2.59% b. 2.88% c. 3.20% d. 3.52% e. 3.87% Answer: c Basic equation: r = r* + IP + MRP + DRP + LP r_{Tbond} 5.50% IP 1.90% MRP 0.40% LP and DRP 0.00% r* = r_{Tbond} – IP – MRP 3.20% 10. Suppose the interest rate on a 1year Tbond is 5.0% and that on a 2year Tbond is 7.0%. Assuming the pure expectations theory is correct, what is the market's forecast for 1year rates 1 year from now? a. 7.36% b. 7.75% c. 8.16% d. 8.59% e. 9.04% Answer: e 1year rate today 5.00% 2year rate today 7.00% Maturity of longer bond 2 Ending return if buy the 2year bond = needed return on series of 1year bonds 1.1449 Rate of return, or yield, on a 1year bond 1 year from now: X in this equation: (1.05)(1 + X) = 1.1449 X = 1.1449/1.05 − 1 = 9.04% 11. Which of the following statements is CORRECT? a. The yield on a 2 year corporate bond should always exceed the yield on a 2 year Treasury bond. b. The yield on a 3 year corporate bond should always exceed the yield on a 2 year corporate bond. c. The yield on a 2 year Treasury bond should always exceed the yield on a 2 year Treasury bond. d. If inflation is expected to increase, then the yield on a 2 year bond should exceed that on a 3 year bond. e. The real riskfree rate should increase if people expect inflation to increase. Answer: a 12. 5year Tbonds yield 4.75%. The real riskfree rate is r* = 3.60%, and the maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t = number of years to maturity. What inflation premium (IP) is built into 5year bond yields using 5year Tbonds? a. 0.68% b. 0.75% c. 0.83% d. 0.91% e. 1.00% Answer: b Using 5year Tbonds Basic equation: r = r* + IP + MRP r_{Tbond} Required data 4.75% r* Required data 3.60% Years to maturity Required data 5 MRP = (t – 1) × (0.1) = 0.40% IP = r_{Tbond} − r* − MRP 0.75% 13. Suppose the real riskfree rate is 3.50%, the average future inflation rate is 2.50%, a maturity premium of 0.2% per year to maturity applies, i.e., MRP = 0.20%(t), where t is the years to maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of 1.35% applies to Arated corporate bonds. What is the difference in the yields on a 5year Arated corporate bond and on a 10year Treasury bond? Here we assume that the pure expectations theory is NOT valid, and disregard any crossproduct terms, i.e., if averaging is required, use the arithmetic average. a. 0.77% b. 0.81% c. 0.85% d. 0.89% e. 0.94% Answer: c Real riskfree rate, r* 3.50% IP 2.50% MRP, 10year Tbond Per year: 0.20% Years: 10 2.00% MRP, 5year corporate Per year: 0.20% Years: 5 1.00% LP 0.50% DRP 1.35% Tbond yield r_{Tbond} = r* + IP + MRP + A bond yield r_{Corp} = r* + IP + MRP + DRP + LP 8.85% Difference 0.85% 14 What is the relationship between PVIFA(r%, N) and PVIF(r%, N)? a. PVIFA is greater than or equal to PVIF b. PVIF is a sum of PVIFA from n=1 to n=N c. PVIF is an inverse of PVIFA d. PVIF is used for an annuity e. None of the above Answer: a PVIFA is a sum of present values of payments. Therefore, a 15. Ryngaert Inc. recently issued noncallable bonds that mature in 15 years. They have a par value of $1,000 and an annual coupon of 5.7%. If the current market interest rate is 7.0%, at what price should the bonds sell? a. $817.12 b. $838.07 c. $859.56 d. $881.60 e. $903.64 Answer: d Coupon rate 5.70% PMT $57.00 N 15 I/YR 7.00% FV $1,000 PV $881.60 16. Sadik Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $105 annual coupon and have a 15year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)? a. 6.63% b. 6.98% c. 7.35% d. 7.74% e. 8.12% Answer: d N 5 PV $1,180 PMT $105 FV $1,100 I/YR = YTC 7.74% 17. In calculating the current price of a bond paying semiannual coupons, one needs to a. Use double the number of payments. b. Use half the annual coupon. c. Use double the annual market rate as the discount rate. d. All of the above need to be done. e. Only a and b are true. Answer: e 18. Bonds sell at a premium from par value when market rates for similar bonds are a. Less than the bond’s coupon rate. b. Greater than the bond’s coupon rate. c. Equal to the bond’s coupon rate. d. Both lower than and equal to the bond’s coupon rate. e. Market rates are irrelevant in determining a bond’s price. Answer: a 19. Assume that all interest rates in the economy decline from 10% to 9%. Which of the following bonds would have the largest percentage increase in price? a. An 8year bond with a 9% coupon. b. A 1year bond with a 15% coupon. c. A 3year bond with a 10% coupon. d. A 10year zero coupon bond. e. A 10year bond with a 10% coupon. Answer: d 20. A portfolio with a level of systematic risk less than that of the market has a beta that is a. equal to zero. b. greater than zero but less than one. c. less than the beta of the riskfree asset. d. less than zero. e. equal to infinity. Answer: b 21. Cooley Company's stock has a beta of 1.40, the riskfree rate is 4.25%, and the market risk premium is 5.50%. What is the firm's required rate of return? a. 11.36% b. 11.65% c. 11.95% d. 12.25% e. 12.55% Answer: c Beta 1.40 Riskfree rate 4.25% Market risk premium 5.50% Required return 11.95% 22. Consider the following information and then calculate the required rate of return for the Global Investment Fund, which holds 4 stocks. The market’s required rate of return is 13.25%, the riskfree rate is 7.00%, and the Fund's assets are as follows: Stock Investment Beta A $200,000 1.50 B $300,000 0.50 C $500,000 1.25 D $1,000,000 0.75 a. 9.58% b. 10.09% c. 10.62% d. 11.18% e. 11.77% Answer: e r_{M} 13.25% r_{RF} 7.00% Find portfolio beta: Weight Beta Product $200,000 0.100 1.50 0.1500 $300,000 0.150 0.50 0.0750 $500,000 0.250 1.25 0.3125 $1,000,000 0.500 0.75 0.3750 $2,000,000 1.000 0.7625 = portfolio beta Find RP_{M} = r_{M} − r_{RF} = 6.25% r_{s} = r_{RF} + b(RP_{M}) = 11.77% 23. Stock A has a beta of 0.8 and Stock B has a beta of 1.2. 50% of Portfolio P is invested in Stock A and 50% is invested in Stock B. If the market risk premium (r_{M} − r_{RF}) were to increase but the riskfree rate (r_{RF}) remained constant, which of the following would occur? a. The required return would increase for both stocks but the increase would be greater for Stock B than for Stock A. b. The required return would decrease by the same amount for both Stock A and Stock B. c. The required return would increase for Stock A but decrease for Stock B. d. The required return on Portfolio P would remain unchanged. e. The required return would increase for Stock B but decrease for Stock A. Answer: a 24. Consider the following information and then calculate the projected expected rate of return for the Global Investment Fund, which holds 3 stocks. Stock Investment Projected Expected Return for Each Security A $200,000 15% B $300,000 5% C $500,000 10% a. 5.9% b. 6.5% c. 7.8% d. 8.7% e. 9.5% Answer: b 25. What is the coefficient of variation for security b?
Answer: a 