You estimate that a 1-year zero-coupon bond (face value = $1000) has a probability of default equal to 26%. In the event of default, you estimate the bond issuer will bay $563. The current risk-free rate is 5%. How much should you pay for this bond?
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- The Expectations theory suggests that under certain conditions all bonds outstanding, especially Treasury bonds, must have identical total returns over a 1-year holding period, independently of their final maturity. suppose that today’s interest rate on a 2-year default free zero-coupon Treasury bond that pays $100 at maturity (0i0,2) is 6%. What is today’s price of such a bond (that is, what would you pay to purchase such a bond)?A bond has a Macaulay duration of 12.00 and is priced to yield 10.0%. If interest rates go up so that the yield goes to 10.5%, what will be the percentage change in the price of the bond? Now, if the yield on this bond goes down to 9.5%, what will be the bond's percentage change in price? Comment on your findings.Consider a bond that has a current value of $1,081.11, a face value of $1,000.00, a coupon rate of 10% and five years remaining to maturity.a. What is the bond’s yield-to-maturity today?b. If the bond’s yield does not change, what is its value one year from today? Please solve both parts
- Suppose the current zero-coupon yield curve for risk-free bonds is as follows:Maturity (years) 1 2 3 4 5YTM 4.14% 4.55% 4.78% 4.99% 5.37% What is the price per $100 face value of a three-year, zero-coupon, risk-free bond? What is the price per $100 face value of a four-year, zero-coupon, risk-free bond? What is the risk-free interest rate for a four-year maturity?• When the bond’s coupon rate is less than the bondholder’s required return, the bond’s intrinsic value will be less than its par value, and the bond will trade at . For example, assume Oliver wants to earn a return of 10.50% and is offered the opportunity to purchase a $1,000 par value bond that pays a 8.75% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond’s intrinsic value: Intrinsic ValueIntrinsic Value = = A(1+C)1+A(1+C)2+A(1+C)3+A(1+C)4+A(1+C)5+A(1+C)6+B(1+C)6A1+C1+A1+C2+A1+C3+A1+C4+A1+C5+A1+C6+B1+C6 Complete the following table by identifying the appropriate corresponding variables used in the equation. Unknown Variable Name Variable Value A B $1,000 C Semiannual required return Based on this equation and the data, it is to expect that Oliver’s potential bond investment is currently exhibiting an intrinsic value less than…Suppose a 1 dollar bond with 1 year maturity has a 1 dollar face value and is trading at a 33 percent discount. What is the market value of the bond? The contractual interest rate is 8 percent. What is the effective nominal yield on the bond? Now suppose a bond with 1 year maturity has a face value of d dollars (including principal and interest). There is a probability of 33 percent that the bond issuer (borrower) will default completely. Otherwise, the issuer will pay in full. What is the market value v of the bond? The contractual interest rate is 8 percent. What is the effective nominal yield on the bond? Suppose the default probability increases to 50 percent. What is the market value v′ of the bond now? At a contractual interest rate of 8 percent, what is the effective nominal yield on the bond now? Consider an investor. There are two bonds. One pays v′ with 100 percent certainty. The other bond pays d with a 50 percent chance, and zero otherwise. Which bond, if any, will the…
- Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $89.75, while a 2-year zero sells at $79.88. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 10% per year. Required: What is the yield to maturity of the 2-year zero? What is the yield to maturity of the 2-year coupon bond? What is the forward rate for the second year? If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year? Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?A bond that pays interest semiannually has a price of $981.73 and a semiannual coupon payment of $27.75. If the par value is $1,000, what is the current yield?Suppose that your firm issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%. For questions e-g, assume that this bond DOES NOT pay any coupon a) What was its price when it was issued? b) For this zero-coupon bond, suppose it is actually sold for $500, what should the YTM be?
- The bond J is a bond with a coupon rate of 4%. The bond K is a bond with a coupon rate of 10%. Both bonds have a maturity of 8 years, make semi - annual payments, and have a yield to maturity of 9%. If interest rates suddenly increase by 2%, what is the percentage change in the price of these bonds? And if the rates suddenly decrease by 2%? What does this problem teach you about the interest rate risk of low - coupon bonds?Assume the zero-coupon yields on default-free securities are as summarized in the following table: Maturity(Years) 1 2 3 4 5 YTM for this bond 6.20% 6.80% 7.00% 7.30% 7.60% What is the price of a three-year, default-free security with a face value of $1,000 and an annual coupon rate of 7%? What is the yield to maturity for this bond?Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 12% per year.a. What is the yield to maturity of the 2-year zero?b. What is the yield to maturity of the 2-year coupon bond?c. What is the forward rate for the second year?d. According to the expectations hypothesis, what are (i) the expected price of the coupon bond at the end of the first year and (ii) the expected holding-period return on the coupon bond over the first year?e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
