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Exam 3 problems

Topic 10 – Bond valuation

  1. A 15%, 15-year bond is currently trading at $1,200. What is its current yield?
  2. Joe buys a 12% corporate bond with a current yield of 5%. How much did he pay for the bond?
  3. Find the price of a semiannual coupon bond given that the coupon rate = 9%, the face value = $1000, the required return = 10%, and there are 27 years remaining until maturity.
  4. A 5% coupon bond with semi-annual payments, maturing in 4 years, is purchased for $951.90. What is its yield to maturity? 
  5. An investor purchases an 8% coupon bond, annual payments, 10 years to maturity for $982.63. He sells the the bond 3 years later for $1,000. What is his yield on this bond?
  6. A 6% coupon bond, $10,000 par value, with semi-annual payments is purchased 3 years ago when it still has 14 years to maturity for a price of $10,172.15. The investor sells the bond today for $9,995.15. What is the realized yield on the bond?
  7. What is the price of a $10,000 par value bond, 6% coupon paid semi-annually, 10 years to maturity, when the required rate of return in the market is 4.5%?
  8. The $1,000 face value bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond's value today?
  9. Which of the following three bonds offers the highest current yield? Assume that the face value of all of the bonds is $1,000.
    1. A 9%, 18-year bond quoted at 908.
    2. An 18%, 12-year bond quoted at 1980.
    3. A 4%, 20-year bond quoted at 500.
  10. Using semiannual compounding, find the prices of the following bonds. Assume the face value is $1000 for each:
    1.  A 10%, 12-year bond priced to yield 9%
    2. A 6%, 8-year bond priced to yield 9.5%
    3. A 15%, 19-year bond priced to yield 10%
  11. Two bonds have face values of $1,000. One is a 6%, 12-year bond priced to yield 8%. The other is an 8%, 16-year bond priced to yield 4%. Which of these two has the lower price?
  12.  A 15-year bond has a coupon of 10% and is priced to yield 9%. Calculate the price per $1000 face value.
  13. A 12-year bond has an ANNUAL pay coupon of 7% and is priced to yield 10%. Calculate the price per $1,000 face value.
  14. A bond is currently selling in the market for $1,050. It has a coupon of 10% and a 20-year maturity. Calculate the promised yield on this bond.
  15. A bond is currently selling in the market for $1,750. It has a coupon of 8% and a 22-year maturity. Calculate the yield to maturity on this bond. Assume the face value is $1000.
  16. A zero-coupon bond that matures in 10 years is currently sells of $527.47 per $1,000 par value. Calculate the promised yield on this bond.
  17. A zero-coupon bond that matures in 14 years is currently selling for $256 per $1,000 par value. What is the promised yield?
  18. Assuming annual coupons, find the yield-to-maturity for each of the following bonds.
    1. An 8.5%, 20-year bond priced at $984.50.
    2. A 15%, 17-year bond priced at $1432.50.
    3. A 7%, 14-year bond priced at $379.80.
  19. You have an 8%, 20-year bond that is currently priced in the market at $900.
    1. Find current yield
    2. What is the yield to maturity?
  20. Complete the table below for zero-coupon bonds, all of which have face value of $1,000.
    Maturity  Price  YTM
     20 years
     400  
     15 years
      8%
       310.07  10%
  21. A 10%, 23-year bond has a face value of $1,200 and a call price of $1,250. (The bond’s first call date is in 5 years.)
    1. Find the current yield, YTM, and YTC on this issue, given that it is currently being priced in the market at $1,500. Which of these three yields is the highest? Which is the lowest? Which yield would you use to value this bond? Why?
    2. Repeat the 3 calculations above, given that the bond is being priced at $900. Now which yield is the highest? Which is the lowest? Which yield would you use to value this bond? Why?
  22. Find the yield to maturity on a semiannual coupon bond given that the bond price = $1024, the coupon rate = 13%, the face value = $1000, and there are 19 years remaining until maturity.
  23. Find the yield to maturity on a semiannual coupon bond given that the bond price = $790, the coupon rate = 14%, the face value = $1000, and there are 4 years remaining until maturity.
  24. Find the yield to call on a semiannual coupon bond with a face value of $1000, a 10% coupon rate, 15 years remaining until maturity given that the bond price is $1175 and it can be called 5 years from now at a call price of $1100.
  25. A 30 year bond has an 8% coupon is callable in five years at a call price of $1,100. Today, the bond sells to yield 7%. Assume the face value is 1000.
    1. What is the yield-to call?
    2. What is the yield to call if the call price is only $1,050?
    3. What is the yield to call if the call price is $1,100, but the bond can be called in two years instead of five years?
  26. Assume that you pay $900 for a long-term bond that carries a 8% coupon. Over the course of the next 12 months, interest rates drop sharply. As a result, you sell the bond at a price of $1,200.
    1. Find the current yield that existed on this bond at the beginning of the year. What was it by the end of the 1-year holding period?
    2. Determine the holding period return on this investment.
  27. An investor is considering the purchase of a 10%, 20-year corporate bond that’s being priced to yield 10%. He thinks that in a year, this same bond will be priced in the market to yield 9%. Assume the face value is $1,000.
    1. Find the price of the bond today and in 1 year.
    2. Find the realized yield on this investment, assuming that the investor’s expectations hold true.
  28. A bond has Macaulay duration equal to 8.5 and a yield to maturity of 8%. What is the modified duration of this bond?
  29. A bond has Macaulay duration of 9.5 and is priced to yield 9%. If the interest rates go down so that the yield goes to 7.5%, what will be the percentage change in the price of the bond?
  30. A bond sold six months ago for $10, 015.25 and sells today for $10,293.75. What is the percentage change in price of this bond?
    1. Find the Macaulay duration and the modified duration of a 17-year, 12% corporate bond priced to yield 9%.
    2. According to the modified duration of this bond, how much of a price change would this bond incur if market yield rose to 10%?
    3. Calculate the price of this bond if rates do rise to 10%. How does this price change compare to that predicted by the modified duration? Explain the difference.
  31. Rank the following bonds in order of DESCENDING duration.
  32.  Bond      Maturity  Coupon  YTM
    Abbott
    10 years
     11% 8%
     Ballyhoo  5 years
    14%
     12%
    Costello  5 years  14%  8%
     Davidson  10 years
     14%  8%
     Elephant  10 years
     0%  8%
  33. A 30-year bond has a face value of $1,000 and has a call price of  $1,375 in 7 years.  The coupon rate is 13% and it is currently being priced in the market at $1,450.
    1. Find the current yield.
    2. Find the YTM.
    3. Find the YTC. 
    4. Which of these three yields is the highest? Which is the lowest? 
  34. A 17%, 32 year bond is currently trading at $2,200.  What is its current yield?
  35. A 13 year bond has a coupon of 8% and its priced to yield 7%.  Calculate the price per 1000 face value.
  36. A 11 year bond has an ANNUAL coupon of 12% and its prices to yield 10%.  Calculate the price per 1000 face value.
  37. A zero coupon bond that matures in 13 years is currently selling for $874.36 per 1000 par value.  What is its promised yield?
  38. A bond is currently selling in the market for $914.76.  It has a coupon of 12% and 18 year maturity.  Calculate the promised yield on this bond.
  39. Suppose the YTM of a bond is 10%.The interest rates rise 1%, and as a result, the bonds price drops 1.7%. What is the Macaulay Duration?

Topic 11 – Investment companies

  1. A year ago Big Growth Fund was being quoted at a NAV of $20 and an offer price of $22.5. Today, it’s being quoted at $22.10 (NAV) and $24.10 (offer). What is the holding period return on this load fund, given that it was purchased a year ago and that its dividend and capital gains distributions over the year have totaled $1.06 per share?
  2. You have uncovered the following per-share information about a certain mutual fund. On the basis of this information, find the fund’s holding period return for 2006, 2007, and 2008. (In all 3 cases you buy the fund at the beginning of the each year and sell it at the end of each year.)
       2006      2007  2008
     Ending share prices:
         
     Offer  44.10  61.28  58.46
     NAV  42.00  58.36  55.68
     Dividend income
     2.15  2.86 2.54
     Capital gains distribution
     1.56  5.23 4.11
     Beginning share prices:
         
     Offer  54.44 44.10
    61.28
     NAV  51.85 42.00
     58.36
  3. You invested in the no-load Best Mutual Fund one year ago by purchasing 1,400 shares of the fund at an NAV of $22.00 per share. The fund distributed dividends of $1.80 and capital gains of $2.00. Today, the NAV is $25.
    1. What was your HPR?
    2. If The Best was a load fund with 3% front end load, what would be the HPR?
  4. One year ago, High Return Closed-End Fund had a NAV of $11 and was selling at a 19% discount. Today, its NAV is $11.90 and it is priced at a 5% premium. During the year, High Return paid dividends of $0.50 and had a capital gains distribution of $0.90. On the basis of the above information, calculate each of the following.
    1. High Return’s NAV-based holding period return for the year.
    2. High Return’s market-based holding period return for the year. Did the market premium/discount hurt or add value to the investor’s return? Explain.
    3. Repeat the market-based holding period return calculation, except this time assume the fund started the year at a 20% premium and ended it at a 5% discount. (Assume NAVs remain the same.) Is there any change in return? Why?
  5. What is the net asset value of an investment company with $20 million in assets, $950,000 in liabilities, and 1,500,000 shares outstanding?
  6. A mutual fund has net asset value of $26.60 and the fund sells it shares at an offer price of $27.42. What is the front and load?
  7. You are considering investing in the Ahlgrim high value, low risk mutual fund. The fund has two classes of shares. Use the following load and expense information to evaluate the best fund depending on your investment horizon. Assume the underlying portfolio earns 15% and that you invest $1,000.
    1. Which class of shares provides the highest return if your investment horizon is two years?
    2. Which class of shares is best if your horizon is 25 years?
    Load/fee  Class A
     Class Z
     Front-end 6%
     0%
     Back-end  0% 4% CDSC
     12b-1  0.2% 1.1%
     Mgmt fee
    0.6%
     0.6%
    Operating expense
     0.3%  0.3%

  8. The opportunity for you to invest in a high value, low risk mutual fund has presented itself.  The fund has two classes of shares.  Refer to the load and expense data in the table below to determine which fund is the best.
  9. Load/Fee  Class Ahlgrim
     Class Jagmin
     Front-end  8.25%  0%
     Back-end  0%  6%
     12b-1(annual)  0.34%  1.3%
     Management Fee
     0.55%  0.70%
     Operation/Administration Fee
     0.25%  0.35%
    Assume the portfolio earns 12% and the amount you invest is $1,000.
    1. Which class of shares, either Ahlgrim or Jagmin, provides the greatest return if your investment horizon is three years?
    2. If the investment horizon was expanded which class of shares would be best in 20 years?
    3. After making these calculations, determine which class of shares is better in the short-term (3 years) AND long-term (20 years).
  10. Last year ISU Fund was being quoted at a NAV of $12 and an offer price of $16.  Today it is quoted at $18 (NAV) and $20.75 (offer).  What is the HPR on this fund given it was purchased a year ago and its capital gain distributions and dividend total $3.95/share?
  11. What is the net asset value of an investment of an investment company with assets of $50 million, $4,750,000 in liabilities, and 3 million shares outstanding?
  12. You invest in a no-load ISU mutual fund 1 year ago by purchasing 3,000 shares of the fund at an NAV of $8 per share.  The fund distributed dividends and capital gains of $1.75.  Today the NAV is $11.25.
    1. What is the HPR?
    2. If ISU was a load fund, what is the HPR if it had 4% front end load?
Subpages (1): Solutions to problems 3
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