calculate the price of a bond, where F is the face value, c is the coupon rate, N is the number of years to maturity, and i is the interest rate. F=$10,000, c=7%, N- is infinity (bond never matures), i=6%
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calculate the price of a bond, where F is the face value, c is the coupon rate, N is the number of years to maturity, and i is the interest rate. F=$10,000, c=7%, N- is infinity (bond never matures), i=6%
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- How 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.)This is the entire question! Just answer A,B,C (Don't worry about the numbers for A&B) and answer the rest of the question. Complete the following table by identifying the appropriate corresponding variables used in the equation. Unknown Variable Name A (Bond Semi coupon annul payment, annual coupon payment,Bonds market price) B (Bond's semi coupon, annual coupon payment,par value) $1,000 C Semiannual required return Based on this equation and the data, it is (unreasonable,reasonal) to expect that Oliver’s potential bond investment is currently exhibiting an intrinsic value less than $1,000. Now, consider the situation in which Oliver wants to earn a return of 6.75%, but the bond being considered for purchase offers a coupon rate of 8.75%. Again, assume that the bond pays semiannual interest payments and has three years to maturity. If you round the bond’s intrinsic value to the nearest whole dollar, then its intrinsic value…Question 3. A fixed rate bond with notional 1 pays annual coupons of c at times T1, T2, . . . , Tn where Ti+1 = Ti + 1 and notional 1 at time Tn. a) Write down the bond price BFXD c (t) at time t ≤ T0 in terms of ZCBs. b) Suppose t = T0 = 0. The yield of the bond is defined as the value Y such that B FXD c (0) = Xn i=1 c (1 + Y ) i + 1 (1 + Y ) n , that is, the rate at which IRR discounting gives the bond price. By summing a geometric series, show that BFXD c (0) = 1 if and only if Y = c. c) By writing a swap as the difference between a fixed rate bond and a floating rate bond, show that BFXD c (0) = 1 if and only if c = y0[0, Tn]. Remark 1. This exercise shows that the T-year spot swap rate is the bond coupon such that a T-maturity bond has price par, that is 100% of notional.
- Explain 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 $1,000.00Which of the following statements regarding bonds and their terms is FALSE? *** OA. When we calculate a bond's yield to maturity by solving the formula, Coupon Coupon Coupon + Face Price of an n-period bond = (1 + )" + + + MA (1+)¹ (1+)² the yield we compute will be a rate per coupon interval. OB. The internal rate of return (IRR) of an investment in a zero-coupon 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. OC. The yield to maturity of a bond is the discount rate that sets the future value (FV) of the promised bond payments equal to the current market price of the bond. OD. Financial professionals also use the term spot interest rates to refer to the default - free zero- coupon yields.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?…
- Suppose that y is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that y is expressed with simply com- pounding, that interest is paid annually on the bond, and that y follows the process dy = a(y0 −y)dt + oydWt, where a, y0, and o are positive constants and dWt is a Wiener process. (a) What is the process followed by the bond price? (b) What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?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.For a bond that is currently selling for par value (i.e., $1000). which one of the following relationships is correct (note: assume that all factors, other than the one mentioned, remain constant)? O 1) if the coupon rate increases, the bond price will remain the same. 2) if the coupon rate increases, the bond price will decrease. 3) if the yield to maturity decreases, the bond price will decrease. O 4) if the term to maturity increases, the bond price will remain the same. O 5) if the yield to maturity increases, the bond price will remain the same.
- Suppose the current, zero-coupon, yield curve for risk-free bonds is as follows: (Click on the following icon in order to copy its contents into a spreadsheet.) Maturity (years) 1 4.45% 2 4.80% Yield to Maturity a. What is the price per $100 face value of a 3-year, zero-coupon, risk-free bond? b. What is the price per $100 face value of a 4-year, zero-coupon, risk-free bond? c. What is the risk-free interest rate for a 3-year maturity? Note: Assume annual compounding. a. What is the price per $100 face value of a 3-year, zero-coupon, risk-free bond? The price is $ (Round to the nearest cent.) b. What is the price per $100 face value of a 4-year, zero-coupon, risk-free bond? The price is $. (Round to the nearest cent.) c. What is the risk-free interest rate for a 3-year maturity? The risk-free rate is %. (Round to two decimal places.) C--- 3 5.06% 4 5.25% 5 5.38%Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000. Maturity (Years) 1 2 3 4 5 Show Transcribed Text B) How could you construct a 1-year forward loan beginning in year 3? (Face Value) C) How could you construct a 1-year forward loan beginning in year 4? (Face Value) Required A Required B Complete this question by entering your answers in the tabs below. Face value Rate of synthetic loan → Show Transcribed Text Price $ 970.93 898.39 836.92 How could you construct a 1-year forward loan beginning in year 3? Note: Round your Rate of synthetic loan answer to 2 decimal places. Required A 776.20 685.42 Required B Face value Rate of synthetic loan Required C 7.85 % Required C How could you construct a 1-year forward loan beginning in year 4? Note: Round your Rate of synthetic loan answer to 2 decimal places. Ċ 13.29 %Assume that the risk free rate is equal to 0.04. The corporate bond rate for a risky bond is 0.11. Assume a recovery rate of 0.33. All rates in this problem are stated as decimals. Using the precise calculation formula, calculate λ , the probability of default. Round your answer to three decimal places, and state as a decimal. Please answer fast i give you upvote.