A fixed rate bond with notional 1 pays annual coupons of c at times T1,T2,...,Tn whereTi+1 =Ti+1andnotional1attimeTn. a) Write down the bond price Bc^(FXD)(t) at time t ≤ T in terms of ZCBs.
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A fixed rate bond with notional 1 pays annual coupons of c at times T1,T2,...,Tn whereTi+1 =Ti+1andnotional1attimeTn.
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a) Write down the
bond price Bc^(FXD)(t) at time t ≤ T in terms of ZCBs.
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- TB TF Qu. 3-30 The yield to maturity on a bond is really... The yield to maturity on a bond is really its internal rate of return. True or False True FalseAcme Chemical, Inc. is a major manufacturer of chemical products for the agricultural ndustry, including pesticides, herbicides and other compounds. Due to a number of law suits elated to toxic wastes, Acme Chemical has recently experienced a market re-evaluation of its common stock. The firm also has a bond issue outstanding with 10 years to maturity and an annual coupon rate of 5 percent, with interest paid semi annually. The required nominal market annual interest rate on this bond has now risen to 10 percent due to the high risk level associated vith this firm. The bonds have a par or face value of $1,000. 1. Label each of the variables that you would use to determine the value of this bond in the market today: N (time periods until maturity) PMT (periodic interest payment) I per (periodic market interest rate) EV (future value to be received when the bond matures) = 2. Based on the variables that you have identified in Question #1, what is the market value. today (the present…(PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 825 1. A bond issued by Delta Corporation matures in 12 years. It has a 12.5 percent annual coupon rate and a face value of P10,000. The bond has a discount rate to maturity of 9.5 percent. What is the price of Omega's bond today?
- (PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 825 3. Assume that Greenwich and Pizza Hut have similar P100,000 par value bond issues outstanding. The bonds are equally risky. Pizza Hut bond has an annual coupon rate of 8 percent and matures 20 years from today, the nominal annual rate of return is 12%. Greenwich's bond has a coupon rate of 8 percent, with interest paid semiannually, matures in 20 years, and nominal required rate of return 12 percent on a semi-annual basis. What is the DIFFERENCE in current…(PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 825 2. Your sister has been offered a 5-year bond with a P1,000 par value and a 7 percent coupon rate. This bond's interest is paid semi-annually. If your sister is to earn a nominal rate of return of 9 percent, compounded semi-annually, how much should she pay for the bond?(PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 8251. Charlie Corporation is a chemical company. The company issued an outstanding bond with a P100,000 par value at 15-year maturity date. The coupon rate is 8%, and interest is paid quarterly. The required nominal interest rate on this borrowings has now increased to 16 percent . What is the current market value of the bond?
- This first table describes prevailing market interest rates. Market Data Yield 0.05 Required: Using the yield above and the information contained in the table below, please calculate the price and duration of the bond as well as all necessary steps. (Use cells A5 to B5 from the given information to complete this question.) Time Until Payment Payment Discounted Payment Weight Time × Weight 1.00 $30.00 2.00 $30.00 3.00 $30.00 4.00 $1,030.00 Price: DurationHow do investors calculate the net present value of a bond? If a bond's coupon payment is C, the interest rate is R, and the bond's coupon payment is made in each period for T years at which time the original principal, P, is repaid, then the bond's present discounted value (PDV) is C A. PDV = + (1 + R) (1 + R? (1 + R)T B. PDV = C(1 + R) + C(1 + R)2 - + C(1 + R)T + P(1 + R)T + C P OC. PDV = - + R R2 RT RT C D. PDV = P + C C (1 + R) (1+R)2 (1 + R)T C E. PDV = + + + + (1 + R) (1+ R)2 (1 + R)T (1 + R)T If the interest rate is 9 percent, what is the present value of a perpetuity that pays $50,000 each year, forever? The perpetuity's value is $ (Enter a numeric response rounded to two decimal places.)Calculating the risk premium on bonds The text presents a formula where (1+1) = (1-p)(1 +i+x) + p(0) where i is the nominal interest rate on a riskless bond x is the risk premium p is the probability of default (bankruptcy) If the probability of bankruptcy is zero, the rate of interest on the risky bond is When the nominal interest rate for a risky borrower is 8% and the nominal policy rate of interest is 3%, the probability of bankruptcy is %. (Round your response to two decimal places.) When the probability of bankruptcy is 6% and the nominal policy rate of interest is 4%, the nominal interest rate for a risky borrower is %. (Round your response to two decimal places.) When the probability of bankruptcy is 11% and the nominal policy rate of interest is 4%, the nominal interest rate for a risky borrower is %. (Round your response to two decimal places.) The formula assumes that payment upon default is zero. In fact, it is often positive. How would you change the formula in this case?…
- The following information about bonds A, B, C, and D are given. Assume that bond prices admit noarbitrage opportunities. What is the convexity of Bond D?Cash Flow at the end ofBond Price Year 1 Year 2 Year 3A 91 100 0 0B 86 0 100 0C 78 0 0 100D ? 5 5 105Explain what you see from the pricing calculations. How do the two bonds differ? Bond C Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 10%*$1,000 = $100 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 Bond Z Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 0%*$1,000 = $0.00 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 years Bond A Bond Z 4 $1,012.79 $693.04 3 $1,010.02 $759.57 2 $1,006.98 $832.49 1 $1,003.65 $912.41 0 $1,000.00 $1,000.00The forward rate f(t1,12) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a 14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond between t1 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) - 0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27: $82.9604 $96.0778 ✓(25 %) $96.2349 $82.1804