FIN331-Fall 2010 Extra Credit
1. PVIF(10%, 1)?
2. What is the relationship between FVIF(r%, N) and PVIF(r%, N)?
a. PVIF is greater than FVIF
b. FVIF is a sum of PVIF from n=1 to n=N
c. PVIF is an inverse of FVIF
d. PVIF is used for an annuity
3. You want to buy a $15,000 car. If you borrow money from the dealer, they are willing to give you a 1 year loan and you need to make a single payment one year from today at zero interest. If you borrow money from a bank for the same one year period and make a cash payment to the dealer right now (using the money you borrow from the bank), you can enjoy a $1,000 discount from a dealer. The bank interest rate is 12% and you need to make a single payment one year from today to pay off the debt. Which alternative do you like better. Basically, you need to borrow money, either from the dealer or from the bank. What is the difference between the future payments of these two choices?
a. Loan from the dealer, more than $2,000
b. Bank, more than $2,000
c. Loan from the dealer, less than $2,000
d. Bank, less than $2,000
4. Susie Orman argues that you can have more money by saving $100 each month (starting at the end of this month for 12 deposits) instead of saving $1,200 at the end of each year. To check whether that is true, you are going to compare saving $600 every six months for a year (starting from 6 months from today for 2 deposits) vis-à-vis $1,200 at the end of the year. What is the future value of $600 saved every six months for a year at the end of the first year at 10% APR?
5. How long does it take to triple your investment at 6% per year?
a. 7.2 years
b. 10.2 years
c. 12.9 years
d. 14.6 years
e. 18.9 years
6. Which of followings is NOT the characteristics of a perpetuity?
a. A perpetuity continues for a fixed time period.
b. Value of a perpetuity can be calculated as “PMT/i”
c. In a perpetuity, returns are earned in the form of a series of cash flows.
d. A perpetuity is a constant infinite stream of identical cash flows.
e. Real estate and preferred stock are effectively perpetuities.
7. If an investment of $87,250 is earning 5% interest rate compounded annually, how long will it take for this investment to reach a value of $99,750 if no additional withdrawals or no deposits are being made during the period?
a. 2.47 years
b. 2.52 years
c. 2.74 years
d. 2.61 years
e. 2.83 years
8. If a security of $17,200 is worth $20,390 three years in the future and assuming that no withdrawals or deposits are made, what is the implied interest rate that the investor expects to earn on the security?
9. Keanu’s financial planner suggested once he crosses a threshold of $4,991,331 in savings, he will have enough money for retirement. Keanu has nothing saved for his retirement yet, so he has to start depositing $85,000 in retirement fund at a fixed rate of 12.00% at the end of each year. How long will it take for Keanu to retire?
a. 15.64 years
b. 18.40 years
c. 23.00 years
d. 24.84 years
e. Keanu will not be able to retire
10. You’ve decided to buy a house that is valued at $1 million. You have $500,000 as a down payment on the house and you take out a mortgage for the rest. Your bank is offering you a 30-year standard mortgage at a fixed nominal rate of 9% or a 15-year mortgage at a fixed nominal rate of 9%. How much larger must your monthly payment would be?
11. You’ve decided to buy a house that is valued at $1 million. You have $500,000 as a down payment on the house and you take out a mortgage for the rest. Your bank is offering you a 30-year standard mortgage at a fixed nominal rate of 9% or a 15-year mortgage at a fixed nominal rate of 9%. How much more interest will you pay if you took out a 30-year mortgage instead of a 15-year mortgage?
12. How long will it take for you to pay off $1,000 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?
a. 10 years
b. 12 years
c. 15 years
d. 17 years
e. You may not be able to pay off the debt
13. Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.
a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
14. Which of the following statements is CORRECT?
a. The cash flows for an ordinary annuity all occur at the beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, then the series is an annuity.
c. The cash flows for an annuity due must all occur at the ends of the periods.
d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.
e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.
15. You have 2 options to buy a membership. One is to pay $5,000 upfront today and the other one is to pay
$500 each year starting today. If the prevailing discount rate is 8%, how many years do you remain as a member before the $500 annual payment becomes more expensive than the one-time membership?
a. 14.5 years
b. 17.5 years
c. 18.5 years
d. 19.5 years
e. 21.5 years
16. You observed an upward-sloping normal yield curve. Which of following statement is the MOST correct?
a. Pure expectation theory must be correct.
b. There is a positive maturity risk premium.
c. If the pure expectation theory is correct, future (short-term) rates are expected to be higher than current (short-term) rates.
d. Inflation must be expected to change in the future.
e. Default risk premium or liquidity premium must be increasing in the future.
17. Charles Townsend Agency issues 15-year, AA-rated bonds. What is the yield on these bonds? Disregard cross-product terms, i.e., if average is necessary, use the arithmetic average.
Relationship between bond ratings and DRP
Rating Default Risk Premium
U.S. Treasury –
Real risk-free rate (r*) = 2.8% (expected to remain constant)
Inflation rate = 5%/yr for each of next five years, 4% thereafter
MRP = 0.1*(t – 1)%, t is the security’s maturity, LP = 0.55%
18. The yield on a one-year Treasury security is 5.84%, and two-year Treasury security has a 7.88% yield. Suppose the securities do not have a maturity risk premium, what is the market’s estimate of the one-year Treasury rate one year from now?
19. Assume a scenario in which there is no maturity risk premium (MRP = 0) and the real risk-free rate is expected to remain constant, and the yield curve is likely to be normal for the next 10 years. Is inflation expected to increase, decrease, or stay the same over the next 10 years?
a. Stay the same
d. Increase at first and then decrease
e. None of above
20. Crockett Corporation’s 5-year bonds yield 6.65%, and 5-year T-bonds yield 4.75%. The real risk-free rate is r* = 3.60%, the default risk premium for Crockett’s bonds is DRP = 1.00% versus zero for T-bonds, the liquidity premium on Crockett’s bonds is LP = 0.90% versus zero for T bonds, 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 5-year bond yields?
21. Assume that interest rates on 20-year Treasury and corporate bonds are as follows:
T-bond = 7.72% AAA = 8.72% A = 9.64% BBB = 10.18%
The differences in these rates were probably caused primarily by:
a. Tax effects
b. Default risk differences
c. Maturity risk differences
d. Inflation differences
e. Real risk-free rate differences
22. If 0R1=5%, E(1R2)=4%, what is 0R2 according to the Expectations Hypothesis?
23. David Cone is concerned about the interest rate changes for his fixed income investment. He looked at the treasury yield curve on Wall Street Journal and observed a normal yield curve. Based on this observation, which of the following statements is correct?
a. Companies must have more investment opportunities now than they expected to have in the future
b. Future short-term interest rates are expected to be higher than current short-term interest rates assuming the pure expectation theory holds.
c. Maturity risk premium is positive
d. Inflation must be expected to increase in the future
e. Expectation theory must be correct
24. A bond trader observes the following information:
• The Treasury yield curve is downward sloping.
• Empirical data indicate that a positive maturity risk premium applies to both Treasury and corporate bonds.
• Empirical data also indicate that there is no liquidity premium for Treasury securities but that a positive liquidity premium is built into corporate bond yields.
On the basis of this information, which of the following statements is most CORRECT?
a. A 10-year corporate bond must have a higher yield than a 5-year Treasury bond.
b. A 10-year Treasury bond must have a higher yield than a 10-year corporate bond.
c. 5-year corporate bond must have a higher yield than a 10-year Treasury bond.
d. The corporate yield curve must be flat.
e. Since the Treasury yield curve is downward sloping, the corporate yield curve must also be downward sloping.
25. If the current one year CD rate is 5% and the best estimate of one year CD which will be available one year from today is 7%, what is the current two year CD rate with 1% liquidity premium?
26. In July 2009, Hungary successfully issued 1 billion euros in bonds. The transaction was managed by Citigroup. Who is the issuer and what is the category of bonds issued?
a. Citigroup, Corporate bonds
b. The bank of Budapest, Municipal bonds
c. The Hungarian government, Foreign government bonds
d. The New York Citibank, Sinking bonds
e. The Hungarian government, T-bonds
27. Roen is planning to invest in five-year 15% annual coupon bonds with a face value of $1,000 each. Calculate number to fill the blanks in the table and identify which one is the premium bond if the market is at equilibrium.
Bond Discount Rate Bond Value Current Yield
Bond A (1) $1,189.54 12.61%
Bond B 15.00% (2) 15.00%
Bond C 16.40% $954.58 (3)
a. 9.00%, $988.76, 14.47%, bond A
b. 10.00%, $1,000.00, 15.71%, bond A
c. 11.00%, $1,100.00, 15.92%, bond B
d. 12.24%, $1,000.00, 16.00%, bond B
e. 10.00%, $1,250.00, 16.12%, bond C
28. Assume that a $1 million par value, semiannual coupon U.S. Treasury note with five years to maturity has a coupon rate of 6%. The YTM of the bond is 11.00%. What is the value of the T-note?
29. Duff Brewing Co. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000 and their current market price is $1,190.35. However, Duff Brewing Co. may call the bonds in 8 years at a call price of $1,060. What are the YTM and YTC, respectively? Also, if Duff Brewing Co. issues new bonds today, what coupon rate must the bonds to be issued at par?
YTM YTC Coupon Rate
a. 6.09%, 5.47%, 6.09%
b. 7.09%, 6.47%, 7.09%
c. 8.09%, 7.47%, 7.47%
d. 8.92%, 8.82%, 8.82%
e. 9.23%, 9.32%, 9.32%
30. The following bond list is from the business section of a newspaper on January 1, 2005 (all are semi-annual bonds). Prices are stated relative to the par value of $100. Calculate what number should be in the blank and indicate which bond is not trading at discount.
Company Coupon Maturity Last Price Last Yield EST
Schubert, Inc. 8.125% 01-01-2015 $82.25 11.11% 6.20 10 72,070
Chapman, Inc. 9.625% 01-01-2035 $80.48 12.05% 7.15 30 65,275
Rust, Inc. 4.500% 01-01-2010 5.62% 1.37 5 59,277
Murphy & Co. 5.375% 01-01-2010 $101.02 5.14% 0.89 5 57,465
Pickman, Inc. 7.750% 01-01-
2015 $93.11 8.80% 3.89 10 56,305
Last Price & Last Yield: bond’s price and YTM at the end of trading.
EST Spread: bond’s spread above the relevant U.S. Treasury benchmark (percentage).
UST: relevant maturity of U.S. Treasury benchmark for each bond.
EST Volume: # of bonds traded during the day.
a. $88.27, Rust, Inc.
b. $95.23, Murhpy & Co.
c. $95.18, Murhpy & Co.
d. $100.40, Pickman, Inc.
e. $102.80, Schubert, Inc.
31. A 15-year bond with a face value of $1,000 currently sells for $850. Which of the following statements is CORRECT?
a. The bond’s coupon rate exceeds its current yield.
b. The bond’s current yield exceeds its yield to maturity.
c. The bond’s yield to maturity is greater than its coupon rate.
d. The bond’s current yield is equal to its coupon rate.
e. If the yield to maturity stays constant until the bond matures, the bond’s price will remain at $850.
32. McCue Inc.’s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. What is the difference between this bond’s YTM and its YTC?
33. Taussig Corp.’s bonds currently sell for $1,150. They have a 6.35% annual coupon rate and a 20-year maturity, but they can be called in 5 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds?
34. Limitless Energy, Inc. is considering to issue 8.8% semi-annual coupon bonds with 15 years to maturity. The bonds are selling at $965.75 with a par value of $1,000. What rate of return are investors expected to earn?
35. Consider a 10 year semi-annual coupon paying bond with a face value=$1,000 and a coupon rate=8%. What is the PV of the bond at 8% discount rate? If the market price of the bond is $1,050, would you buy the bond?
a. $909.09, Buy
b. $1010.10, Buy
c. $909.09, Don’t
d. $1000, Don’t
e. $1000.00, Buy
36. A tax-free muni yields 7.5% and the before-tax equivalent yield of a corporate bond is 10%, what is your tax bracket?
37. Which one has the lowest priority?
b. Secured bonds
c. Junior bonds
d. Senior debenture
e. Unsecured bonds
38. You are considering two investment opportunities with $900. One is to invest in a two year CD at 10% per annum. The other is to invest in a two year annual coupon paying bond with a coupon rate=8% and FV=$1,000. What is the YTM of the bond? Are you going to invest in the CD or not?
a. 12%, Yes
b. 13%, Yes
c. 12%, No
d. 14%, No
e. 14%, Yes
39. Warren holds a small portfolio of 4 stocks as below.
Stock Percentage of Portfolio Expected Return Standard Deviation
Artemis, Inc. 20% 8% 23%
Babish & Co. 30% 14% 27%
Cornell Industries 35% 12% 30%
Danforth Motors 15% 3% 32%
What is expected return of the portfolio?
40. Bill has below portfolio consists of two stocks; Blue Ocean, Inc. and Red Ocean Corp. He invested 75% in Blue Ocean, Inc. and the rest in Red Ocean Corp.
Market Condition Probability Blue Ocean, Inc. Red Ocean Corp.
Strong 0.20 38% 53%
Normal 0.35 23% 30%
Weak 0.45 -30% -38%
Based on the information, calculate expected rate of return of (1) Blue Ocean, Inc., (2) Red Ocean Corp., and (3) portfolio.
a. 1.80%, 2.78%, 1.54%
b. 2.15%, 4.00%, 2.61%
c. 3.69%, 4.19%, 3.15%
d. 4.19%, 5.16%, 3.82%
e. 5.16%, 5.49%, 4.42%
41. Below table describes historically realized returns on Towson, Inc.
2005 2006 2007 2008 2009
Stock Return 12.50% 8.50% 15.00% 21.00% 6.50%
Calculate (1) average realized return, and coefficient of variation. (Hint: standard deviation is 5.71%)
a. 12.70%, 0.48
b. 25.40%, 0.55
c. 31.75%, 0.69
d. 39.37%, 0.72
e. 40.18%, 0.84
42. Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to increase by 30%. What is the stock’s new required rate of return?
Initial beta 1.00
Risk free rate (rs) 6.20%
Market risk premium, RPM 6.00%
43 If you expect (=demand=require) 10% return on security A and 12% return on security B, what causes such a disparity?
a. real risk free rate
b. expected inflation rate
c. risk premium
d. A & B
e. B& C
44. Given that a (nominal) risk free rate is 2% and the market average return is expected to be 5%, what is the market risk premium (=slope of the SML)? Determine the required rate of return for a security with a beta of 1.5.
a. 3%, 6.5%
b. 5%, 9.5%
c. 3%, 9.5%
d. 5%, 6.5%
e. 3%, 10.5%
45. If US T-Bill has 4% return, what is the risk premium of an investment which has 7% required rate of return?
46. During the coming year, the market risk premium (rM − rRF), is expected to fall, while the risk-free rate, rRF, is expected to remain the same. Given this forecast, which of the following statements is CORRECT?
a. The required return will increase for stocks with a beta less than 1.0 and will decrease for stocks with a beta greater than 1.0.
b. The required return on all stocks will remain unchanged.
c. The required return will fall for all stocks, but it will fall more for stocks with higher betas.
d. The required return for all stocks will fall by the same amount.
e. The required return will fall for all stocks, but it will fall less for stocks with higher betas.
47. Which of the following statements best describes what you should expect if you randomly select stocks and add them to your portfolio?
a. Adding more such stocks will reduce the portfolio’s unsystematic, or diversifiable, risk.
b. Adding more such stocks will increase the portfolio’s expected rate of return.
c. Adding more such stocks will reduce the portfolio’s beta coefficient and thus its systematic risk.
d. Adding more such stocks will have no effect on the portfolio’s risk.
e. Adding more such stocks will reduce the portfolio’s market risk but not its unsystematic risk.
48. Which of the following statements is CORRECT? (Assume that the risk-free rate is a constant.)
a. If the market risk premium increases by 1%, 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.
b. The effect of a change in the market risk premium depends on the slope of the yield curve.
c. If the market risk premium increases by 1%, then the required return on all stocks will rise by 1%.
d. If the market risk premium increases by 1%, then the required return will increase by 1% for a stock that has a beta of 1.0.
e. The effect of a change in the market risk premium depends on the level of the risk-free rate.
49. Jill Angel holds a $200,000 portfolio consisting of the following stocks. The portfolio’s beta is 0.875.
Stock Investment Beta
A $ 50,000 0.50
B 50,000 0.80
C 50,000 1.00
D 50,000 1.20
If Jill replaces Stock A with another stock, E, which has a beta of 1.50, what will the portfolio’s new beta be?
50. Mikkelson Corporation’s stock had a required return of 11.75% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The risk-free rate and the firm’s beta remain unchanged. What is the company’s new required rate of return? (Hint: First calculate the beta, then find the required return.)
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