Unformatted text preview: Corporate Finance: The Core (Berk/DeMarzo) Chapter 8  Valuing Bonds 8.1 Bond Cash Flows, Prices, and Yields 1) Which of the following statements is false? A) Bonds are a securities sold by governments and corporations to raise money from investors today in exchange for promised future payments. B) By convention the coupon rate is expressed as an effective annual rate. C) Bonds typically make two types of payments to their holders. D) The time remaining until the repayment date is known as the term of the bond. 2) Which of the following formulas is incorrect? 1/ n A) ⎛ face value ⎞ Yield to maturity for an nperiod zerocoupon bond = ⎜ − 1⎟ ⎝ price ⎠ B) Coupon Coupon + Face Coupon + + ... + Price of an nperiod bond = 1 (1 + YTM )2 (1 + YTM )n (1 + YTM ) C) Price of an nperiod bond = Coupon × D) Coupon =
1 YTM ⎛ 1 ⎜1 − ⎜ (1 + YTM )n ⎝ ⎞ Face Value ⎟ + ⎟ (1 + YTM )n ⎠ Coupon rate x Face Value number of coupon payments per year 3) Which of the following statements is false? A) The IRR of an investment in a zerocoupon bond is the rate of return that investors will earn on their money if they buy a default free bond at its current price and hold it to maturity. B) The yield to maturity of a bond is the discount rate that sets the future value of the promised bond payments equal to the current market price of the bond. C) Financial professionals also use the term spot interest rates to refer to the defaultfree zerocoupon yields. D) When we calculate a bondʹs yield to maturity by solving the formula, Price of an nperiod bond = Coupon Coupon Coupon + Face + + ... + , the yield we compute will be a rate per coupon 1 (1 + YTM )2 (1 + YTM ) (1 + YTM )n interval. 4) Consider a zerocoupon bond with a $1000 face value and 10 years left until maturity. If the bond is currently trading for $459, then the yield to maturity on this bond is closest to: A) 7.5% B) 10.4% C) 9.7% D) 8.1% Use the table for the question(s) below. The following table summarizes prices of various defaultfree zerocoupon bonds (expressed as a percentage of face value): Maturity (years) 1 2 3 4 5 Price (per $100 face value) 94.52 89.68 85.40 81.65 78.35 5) The yield to maturity for the two year zerocoupon bond is closest to: A) 6.0% B) 5.8% C) 5.6% D) 5.5% 6) Based upon the information provided in the table above, you can conclude A) that the yield curve is flat. B) nothing about the shape of the yield curve. C) that the yield curve is downward sloping. D) that the yield curve is upward sloping. Use the table for the question(s) below. The following table summarizes prices of various defaultfree zerocoupon bonds (expressed as a percentage of face value): Maturity (years) 1 2 3 4 5 Price (per $100 face value) 94.52 89.68 85.40 81.65 78.35 WS1) Compute the yield to maturity for each of the five zerocoupon bonds. Answer: Maturity (years) 1 2 3 4 Price (per $100 face value) 94.52 89.68 85.40 81.65 Yield to maturity 5.8% 5.6% 5.4% 5.2% 5 78.35 5.0% Each yield to maturity above is calculated using the formula: YTM = (100/price)(1/n)  1 8.2 Dynamic Behavior of Bond Prices 7) Which of the following statements is false? A) When a bond is trading at a discount, the price drop when a coupon is paid will be larger than the price increase between coupons, so the bondʹs discount will tend to decline as time passes. B) When a bond trades at a price equal to its face value, it is said to trade at par. C) As interest rates and bond yield rise, bond prices will fall. D) Ultimately, the prices of all bonds approach the bondʹs face value when the bonds mature and their last coupon are paid. 8) Which of the following statements is false? A) A bond trades at par when its coupon rate is equal to its yield to maturity. B) The clean price of a bond is adjusted for accrued interest. C) The price of the bond will drop by the amount of the coupon immediately after the coupon is paid. D) If a coupon bondʹs yield to maturity exceeds its coupon rate, the present value of its cash flows at the yield to maturity will be greater than its face value. 9) Which of the following formulas is incorrect? A) Invoice price = dirty price B) Clean price = dirty price  accrued interest C) days since last coupon payment Accrued interest = coupon amount × 360 D) Cash price = clean price + accrued interest 10) Which of the following statements is false? A) Prices of bonds with lower durations are more sensitive to interest rate changes. B) When a bond is trading at a discount, the price increase between coupons will exceed the drop when a coupon is paid, so the bond’s price will rise and its discount will decline as time passes. C) Coupon bonds may trade at a discount, at a premium, or at par. D) The sensitivity of a bondʹs price changes in interest rates is the bondʹs duration. WS2) Consider a zero coupon bond with 20 years to maturity. The amount that the price of the bond will change if its yield to maturity decreases from 7% to 5% is closest to: A) $120 B) $53 C) $53 D) $673 Answer: A Explanation: A) FV = 1000 I = 7 PMT = 0 N = 20 Compute PV = 258.42 FV = 1000 I = 5 PMT = 0 N = 20 Compute PV = 376.89 chg = (376.89  258.42) = 118.47 Consider the following four bonds that pay annual coupons: Bond A B C D Years to maturity Coupon YTM 1 0% 5% 5 6% 7% 10 10% 9% 20 0% 8% 11) Which of the four bonds is the most sensitive to a one percent increase in the YTM? A) Bond A B) Bond B C) Bond C D) Bond D 12) Which of the four bonds is the least sensitive to a one percent increase in the YTM? A) Bond A B) Bond B C) Bond C D) Bond D WS3) Consider a corporate bond with a $1000 face value, 8% coupon with semiannual coupon payments, 7 years until maturity, and a YTM of 9%. It has been 57 days since the last coupon payment was made and there are 182 days in the current coupon period. The dirty (cash) price for this bond is closest to: A) $949.70 B) $961.40 C) $936.40 D) $948.90 Answer: B Explanation: A) B) Dirty price = Clean price + accrued interest Clean Price: FV = 1000 PMT = 40 (80 / 2) I = 4.5 (9 / 2) N = 14 (7 × 2) Compute PV = 948.89 Accrued Interest = coupon × (days since last payment/days in current coupon period) = 40 × (57 / 182) = 12.53 So, dirty price = 948.89 + 12.53 = 961.42 C) D) 13) Consider a corporate bond with a $1000 face value, 10% coupon with semiannual coupon payments, 5 years until maturity, and currently is selling for (has a cash price of) $1,113.80. The next coupon payment will be made in 63 days and there are 182 days in the current coupon period. The clean price for this bond is closest to: A) $1146.50 B) $1065.70 C) $1113.80 D) $1081.10 Use the table for the question(s) below. Consider the following four bonds that pay annual coupons: Bond A B C D Years to maturity Coupon 1 0% 5 6% 10 10% 20 0% YTM 5% 7% 9% 8% WS4) Assume that the YTM increases by 1% for each of the four bonds listed. Rank the bonds based upon the sensitivity of their prices from least to most sensitive. A) A‐B‐C‐D B) A‐C‐B‐D C) B‐A‐C‐D D) B‐C‐D‐A Answer: Years to Price0 Price1 Bond maturity Coupon YTM $ Chg % Chg Rank A 1 0% 5% $952.38 $943.40 ($8.98) 0.94% 1 B 5 6% 7% $959.00 $920.15 ($38.85) 4.05% 2 C 10 10% 9% $1,064.18 $1,000.00 ($64.18) 6.03% 3 D 20 0% 8% $214.55 $178.43 ($36.12) 16.83% 4 8.3 The Yield Curve and Bond Arbitrage 14) Which of the following statements is false? A) We can use the law of one price to compute the price of a coupon bond from the prices of zerocoupon bonds. B) The plot of the yields of coupon bonds of different maturities is called the couponpaying yield curve. C) It is possible to replicate the cash flows of a coupon bond using zerocoupon bonds. D) Because the coupon bond provides cash flows at different points in time, the yield to maturity of a coupon bond is the simple average of the yields of the zerocoupon bonds of equal and shorter maturities. Use the table for the question(s) below. Consider the following zerocoupon yields on default free securities: Maturity (years) 1 2 3 4 5 ZeroCoupon YTM 5.80% 5.50% 5.20% 5.00% 4.80% 15) The price today of a 3 year default free security with a face value of $1000 and an annual coupon rate of 6% is closest to: A) $1000 B) $1021 C) $1013 D) $1005 16) The YTM of a 3 year default free security with a face value of $1000 and an annual coupon rate of 6% is closest to: A) 5.5% B) 5.8% C) 5.5% D) 5.2% 17) A 4 year default free security with a face value of $1000 and an annual coupon rate of 5.25% will trade A) at a premium. B) at par. C) at a discount. D) There is insufficient information to provided to answer this question. 8.4 Corporate Bonds 18) A corporate bond which receives a BBB rating from Standard and Poorʹs is considered A) a junk bond. B) an investment grade bond. C) a defaulted bond. D) a highyield bond. 19) Which of the following statements is false? A) Because the cash flows promised by the bond are the most that bondholders can hope to receive, the cash flows that a purchaser of a bond with credit risk expects to receive may be less than that amount. B) By consulting bond ratings, investors can assess the creditworthiness of a particular bond issue. C) Because the yield to maturity for a bond is calculated using the promised cash flows, the yield of bond’s with credit risk will be lower than that of otherwise identical defaultfree bonds. D) A higher yield to maturity does not necessarily imply that a bondʹs expected return is higher. Use the table for the question(s) below. Consider the following yields to maturity on various oneyear zerocoupon securities: Security Treasury AAA corporate BBB corporate B Corporate Yield (%) 4.6 4.8 5.6 6.2 WS5) The credit spread of the BBB corporate bond is closest to: A) 1.0% B) 5.6% C) 1.6% D) 0.8% Answer: A Explanation: A) = 5.6%  4.6% (BBB Yield  risk free yield) = 1.0% B) C) D) 20) The credit spread of the B corporate bond is closest to: A) 1.6% B) 0.8% C) 1.0% D) 1.4% Use the information for the question(s) below. Luther Industries needs to raise $25 million to fund a new office complex. The company plans on issuing tenyear bonds with a face value of $1000 and a coupon rate of 7.0% (annual payments). The following table summarizes the YTM for similar tenyear corporate bonds of various credit ratings: Rating YTM AAA 6.70% AA 6.80% A 7.00% BBB 7.40% BB 8.00% 21) What rating must Luther receive on these bonds if they want the bonds to be issued at par? A) A B) B C) BBB D) AA 22) Suppose that when these bonds were issued, Luther received a price of $972.42 for each bond. What is the likely rating that Lutherʹs bonds received? A) AA B) BBB C) B D) A ...
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 Spring '09
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