Question.2998 - Your assignment for this week is to complete the following questions and problems from Chapter 5. Please submit your complete assignment in the course room by the due date. Chapter 5 Questions (5-2) “Short-term interest rates are more volatile than long-term interest rates, so short-term bond prices are more sensitive to interest rate changes than are long-term bond prices.” Is this statement true or false? Explain. (5-3) The rate of return on a bond held to its maturity date is called the bond’s yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond’s price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond’s price? Why or why not? (5-4) If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain. (5-5) A sinking fund can be set up in one of two ways. Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders. Chapter 5 Problems (5-1) Jackson Corporation’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds? (5-2) Wilson Wonders’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $850. What is their yield to maturity? (5-5) A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 9%. Assume that the liquidity premium on the corporate bond is 0.5%. What is the default risk premium on the corporate bond? (5-6) The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.3%. What is the maturity risk premium for the 2-year security? (5-7) Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5%. What is the price of the bonds? (5-8) Thatcher Corporation’s bonds will mature in 10 years. The bonds have a face value of $1,000 and an 8% coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds are callable in 5 years at a call price of $1,050. What is their yield to maturity? What is their yield to call? (5-10) The Brownstone Corporation’s bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. a. What is the yield to maturity at a current market price of (1) $829 or (2) $1,104? b. Would you pay $829 for one of these bonds if you thought that the appropriate rate of interest was 12%—that is, if rd = 12%? Explain your answer. (5-14) A bond that matures in 7 years sells for $1,020. The bond has a face value of $1,000 and a yield to maturity of 10.5883%. The bond pays coupons semiannually. What is the bond’s current yield? (5-18) The real risk-free rate is 2%. Inflation is expected to be 3% this year, 4% next year, and then 3.5% thereafter. The maturity risk premium is estimated to be 0.0005 × (t − 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security? (5-21) Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell? b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell? c. Suppose that 2 years after the issue date (as in part a) interest rates fell to 6%. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time?
Answer Below:
Your assignment for this week is to complete the following questions and problems from Chapter 5. Please submit your complete assignment in the course room by the due date. Chapter 5 Questions (5-2) “Short-term interest rates are more volatile than long-term interest rates, so short-term bond prices are more sensitive to interest rate changes than are long-term bond prices.” Is this statement true or false? Explain. Ans - Duration, which is measured in years, measures how much a bond will change after a change in interest rates. The longer the duration the greater the change is for a change in interest rates. Short term bonds maybe more sensitive to changes in short-term rates, but long term bonds are more sensitive generally to changes in rates, with longer term zero coupon bonds being the most sensitive. The reason is that bonds represent a series of cashflows (interest payments) over time plus a final payment at maturity. To find the value of the bond, you discount the cashflows by the applicable interest rate using the net present value formula. Since long bonds have more interest payments over time, there is a bigger change to the value when interest rates are changed. The answer to your question is false because short term bonds are valued on short-term rates and longer term bonds are based on long term rates. Changes in short term rates do not necessarily move in lockstep with changes in long-term rates. Longer term rates have more of an inflation expectation component. (5-3) The rate of return on a bond held to its maturity date is called the bond’s yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond’s price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond’s price? Why or why not? Ans - The market rates only effect the Bond's YTM to the next buyer. If you buy a bond and hold it for it's term then your YTM will not change. However, Market conditions play a role in the day to day value of the Bonds. For example if you buy a $1000 bond at 10% interest due in 10 years, and rates go up. Then the market value of your bond will go down. The amount it goes down is dependant on the Time Left until it matures and the market rates. A good financial calculator can be used to value a bond at any given time. I can also calculate the YTM among other things. (5-4) If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain. Ans –No it will not because the value of callable bond depends on first call (yield to call) not maturity. (5-5) A sinking fund can be set up in one of two ways. Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders. Ans - A sinking fund can be set up in one of two ways: (1) The corporation makes annual payments to the trustee, who invests the proceeds in securities (frequently government bonds) and uses the accumulated total to retire the bond issue at maturity. (2) The trustee uses the annual payments to retire a portion of the issue each year, either calling a given percentage of the issue by a lottery and paying a specified price per bond or buying bonds on the open market, whichever is cheaper. For the organization retiring debt, it has the benefit that the principal of the debt or at least part of it, will be available when due. For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk. However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds: ? The firm will choose to buy back discount bonds (selling below par) at their market price, ? while exercising its option to buy back premium bonds (selling above par) at par. Therefore, if interest rates fall and bond prices rise, a firm will benefit from the sinking fund provision that enables it to repurchase its bonds at below-market prices. In this case, the firm's gain is the bondholder's loss – thus callable bonds will typically be issued at a higher coupon rate, reflecting the value of the option. Chapter 5 Problems (5-1) Jackson Corporation’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds? Ans - :- Rate = 9% Nper =12 PMT = 1000x8%=-80 FV = -1,000 PV = ? Solve for PV PV = $928.39 Market Price of the bond = $928.39 (5-2) Wilson Wonders’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $850. What is their yield to maturity? Ans - USING A BOND YIELD CALCULATOR Current Price = $850 Par Value = $1000 Coupon Rate = 10% Years to Maturity = 12 Years CALCULATION RESULT Current Yield = 11.765 Yield to Maturity = 12.48 (5-5) A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 9%. Assume that the liquidity premium on the corporate bond is 0.5%. What is the default risk premium on the corporate bond? Ans - YTM-Liquidity-Risk free = default risk premium... YTM = 9% Liquidity = 0.5% Risk free = 6% 9%-0.5%-6% = 2.5% (5-6) The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.3%. What is the maturity risk premium for the 2-year security? Ans - K= K* + IP + DRP + LP + MRP KT-2 = 6.3% = 3% +3% + MRP; DRP=LP=0 MRP = 6.3%-6% MRP=0.3% (5-7) Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5%. What is the price of the bonds? Ans - FV =1,000, PMT= 50, N= 16, R= 4.25%, PV=? Present Value = $1,085.80 (5-8) Thatcher Corporation’s bonds will mature in 10 years. The bonds have a face value of $1,000 and an 8% coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds are callable in 5 years at a call price of $1,050. What is their yield to maturity? What is their yield to call? Ans - YTM = 6.62% (FV 1,000, PMT 40, N 20, PV 1,100) Yield to Call = 6.49% (FV 1,050, PMT 40, N 10, PV 1,100) (5-10) The Brownstone Corporation’s bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. a. What is the yield to maturity at a current market price of (1) $829 or (2) $1,104? b. Would you pay $829 for one of these bonds if you thought that the appropriate rate of interest was 12%—that is, if rd = 12%? Explain your answer. Ans - Redemption value= $1,000 Maturity= 4 years Price= $829.00 Therefore , yield= 14.52% =(90+(1000-829)/4)/(0.5*(1000+829)) Answer: 14.99% (5-14) A bond that matures in 7 years sells for $1,020. The bond has a face value of $1,000 and a yield to maturity of 10.5883%. The bond pays coupons semiannually. What is the bond’s current yield? Ans - CURRENT YIELD = ANNUAL COUPON - PV FV = 1000; PV = 1020; I/Y = 10.5583 + 2 = 5.2942; N = 14; CPT PMT PMT = $55 ANNUAL COUPON = 55x2 =110 CURRENT YIELD = 110 + 1020 = 10.78% (5-18) The real risk-free rate is 2%. Inflation is expected to be 3% this year, 4% next year, and then 3.5% thereafter. The maturity risk premium is estimated to be 0.0005 × (t − 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security? Ans - Equated inflation rate over 7 year, I = (1.03*1.04*1.035^5)^(1/7) -1 = 0.035 approx. Maturity risk premium, r(p) = 0.0005(t-1) = 0.0005*6 = 0.003 r(m) = r(f) + I + r(p) r(m) = 2 + 3.5 + 0.0030 = 5.503 % (5-21) Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell? b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell? c. Suppose that 2 years after the issue date (as in part a) interest rates fell to 6%. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time? Ans – a) Given: TTM = 10 years Par = $1,000 Coupon = 10% ($50 payments) r = 6% (after two years) Formula: Using Financial Functions on 12c: n = (10 x 2) - (2 x 2) = 16 i = 6% x .5 = 3 PMT = $100 x .5 = 50 FV = 1000 PV = solve PV = -$1,251.2220 b. Given: TTM = 10 years Par = $1,000 Coupon = 10% ($50 payments) r = 12% (after two years) Formula: Using Financial Functions on 12c: n = (10 x 2) - (2 x 2) = 16 i = 12% x .5 = 6 PMT = $100 x .5 = 50 FV = 1000 PV = solve PV = -$898.9410 Bond Price = $1,251.22 Bond Price = $898.94c. Suppose that the conditions in part a existed—that is, interest rates fell to 6 percent 2 years after the issue date. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the Ford Motor Company bonds over time? As time progresses, the price/value of the bond will slowly decrease. ?is table illustrates that: Using Financial Functions in 12c: (Assume i, PMT, and FV remain constant for following ?gures) n Price 20 $1,297.55 16 $1,251.22 12 $1,199.08 8 $1,140.39 4 $1,074.34 2 $1,038.27 ?erefore, the price decreases over time.More Articles From Accounting
.ico)
.ico)
.ico)
.ico)
