Question

In: Finance

there are two bonds on the market:(a)​One-year $100 zero selling for $95.2381(b)​Two-year 8% coupon...

there are two bonds on the market:


(a)One-year $100 zero selling for $95.2381

(b)Two-year 8% coupon $1000 par bond selling for $1000

(1) Assume that the pure expectations theory for the term structure of interest rates holds and no liquidity premium exists. Find implied 1 year rate 1 year from now? show formulas


(2) for the same bonds, assume a liquidity premium of 0.5% for the 2-year long rate (i2t), what is the implied 1-year rate 1 years from now?


(3) your company plans to issue two-year coupon bonds but the current one-year rate suddenly increase to 10% and the two-year long rate becomes 9%, what coupon rate that you need to sell at par?

Solutions

Expert Solution

there are two bonds on the market: (a)​One-year $100 zero selling for $95.2381 (b)​Two-year 8% coupon $1000 par bond selling for $1000

(1) Assume that the pure expectations theory for the term structure of interest rates holds and no liquidity premium exists. Find implied 1 year rate 1 year from now? show formulas

a. 1 year yield = Sale price = Face Value / (1+ Interest)

95.2381 = 100 / (1 + Interest)

1 + Interest = 1.05

Interest = 1 year yield = 5%

b. 2 year yield = 8% because when the bond is selling at par, the coupon rate equals the yield to maturity

Thus implied 1 year rate 1 year from now: (1 + 1 year yield) * (1 + 1 year rate 1 year from now) = (1 + 2 year yield)^2

(1 + 0.05) * (1 + 1 year rate 1 year from now) = (1 + 0.08)^2

(1 + 1 year rate 1 year from now) = 1.1664 / 1.05

(1 + 1 year rate 1 year from now) = 1.1109

1 year rate 1 year from now = 11.09%

(2) for the same bonds, assume a liquidity premium of 0.5% for the 2-year long rate (i2t), what is the implied 1-year rate 1 years from now?

implied 1 year rate 1 year from now: (1 + 1 year yield) * (1 + 1 year rate 1 year from now) = (1 + 2 year yield)^2

(1 + 0.05) * (1 + 1 year rate 1 year from now + liquidity premium) = (1 + 0.08)^2

(1 + 1 year rate 1 year from now + 0.50%) = 1.1664 / 1.05

(1 + 1 year rate 1 year from now) = 1.1109 - 1.005

1 year rate 1 year from now = 10.59%

3. Assume Face Value = 1000%

Computation of Coupon Rate:

Face Value = Year 1 coupon / (1 + 1 year yield)] + [(Year 2 coupon + Face Value) / (1 + 2 year yield)^2]

1000 = 1000 * Coupon Rate / 1.10 + [(1000 * Coupon rate + 1000) / (1 + 9)^2]

1000 = 1000 * Coupon Rate / 1.10 + [(1000 * Coupon rate + 1000) / 1.881

1000 * 1.1 * 1.881 = 1881 * Coupon rate + 1100 * Coupon Rate + 1100

206.91 = 2981 * Coupon rate

Coupon Rate to issue at par = 6.94%

jeff jeffy answered 2 years ago
Next > < Previous

Related Solutions

2. Zero Coupon Bond B Company sold a $5,000,000, 8 year zero coupon (zero interest paid)...
2. Zero Coupon Bond B Company sold a $5,000,000, 8 year zero coupon (zero interest paid) bond on January 1, 2018 to yield an effective interest rate of 7% annual. Calculate the sale price of the bond. Prepare an 8 year amortization schedule. Make any required entry on December 31, 2021 and on Dec. 31, 2025.
The yield to maturity on one-year zero-coupon bonds is currently 7 percent; the YTM on two-year...
The yield to maturity on one-year zero-coupon bonds is currently 7 percent; the YTM on two-year zeroes is 8 percent. The federal government plans to issue a two-year-maturity coupon bond, paying coupons once per year with a coupon rate of 9 percent. The face value of the bond is $100. At what price will the bond sell? What will be the yield to maturity on the bond? If the expectations theory of the yield curve is correct, what is the...
Suppose that a six-month zero coupon bond is currently selling at $925.93 and a one-year zero...
Suppose that a six-month zero coupon bond is currently selling at $925.93 and a one-year zero coupon bond is selling at $797.19. (a.)Determine the annualized six-month spot rate and the annualized one-year spot rate. (b.)Determine the implied annualized six-month forward rate for six-months from now. (c.)Suppose the annualized yield-to-maturity on an eighteen-month zero-coupon bond was 7.00%and the spot yield on a two-year zero was 13.00%. Based on this information and your results from above, describe which theory (or theories) of...
Suppose the prices of one-year, two-year, and three-year zero coupon bonds each with a par value...
Suppose the prices of one-year, two-year, and three-year zero coupon bonds each with a par value of $100 are $90,$80, and $70, respectively. Determine the arbitrage-free price of the annuity
U.S. Treasury 30 year maturity, zero coupon bonds are currently selling in the marketplace with a...
U.S. Treasury 30 year maturity, zero coupon bonds are currently selling in the marketplace with a yield to maturity of 7.00%. Even though the bonds have a coupon rate of 0.00%, please assume semi–annual compounding, which is the bond market convention? If inflation increased unexpectedly, forcing the nominal required rate of return on these Treasury bonds to increase by 1.50% to 8.50%, by what dollar amount would the current market price of these bonds decrease? Enter your answer rounded to...
Assume the spot rates for one-, two-, and three-year zero coupon bonds are 2%, 3%, and...
Assume the spot rates for one-, two-, and three-year zero coupon bonds are 2%, 3%, and 4%. (a)Calculate P(1), P(2), and P(3).(b)Calculate the price of a three-year 8% coupon bond, with interest paid annually.(c)Calculate ?1,1, ?1,2, and ?2,1(d)Calculate F(1,1), F(1,2), and F(2,1).(e)If ?1,3= 5%, calculate P(4).
Currently, the term structure is as follows: One-year bonds yield 9.50%, two-year zero-coupon bonds yield 10.50%,...
Currently, the term structure is as follows: One-year bonds yield 9.50%, two-year zero-coupon bonds yield 10.50%, three-year and longer maturity zero-coupon bonds all yield 11.50%. You are choosing between one, two, and three-year maturity bonds all paying annual coupons of 10.50%. You strongly believe that at year-end the yield curve will be flat at 11.50%. a. Calculate the one year total rate of return for the three bonds. (Do not round intermediate calculations. Round your answers to 2 decimal places.)...
Currently, the term structure is as follows: One-year bonds yield 9.50%, two-year zero-coupon bonds yield 10.50%,...
Currently, the term structure is as follows: One-year bonds yield 9.50%, two-year zero-coupon bonds yield 10.50%, three-year and longer maturity zero-coupon bonds all yield 11.50%. You are choosing between one, two, and three-year maturity bonds all paying annual coupons of 10.50%. You strongly believe that at year-end the yield curve will be flat at 11.50%. a. Calculate the one year total rate of return for the three bonds. (Do not round intermediate calculations. Round your answers to 2 decimal places.)...
Currently, the term structure is as follows: One-year bonds yield 8.25%, two-year zero-coupon bonds yield 9.25%,...
Currently, the term structure is as follows: One-year bonds yield 8.25%, two-year zero-coupon bonds yield 9.25%, three-year and longer maturity zero-coupon bonds all yield 10.25%. You are choosing between one, two, and three-year maturity bonds all paying annual coupons of 9.25%. You strongly believe that at year-end the yield curve will be flat at 10.25%. a. Calculate the one year total rate of return for the three bonds. b. Which bond would you buy?
The price of a one-year zero-coupon bond is $943.396, the price of a two-year zero is...
The price of a one-year zero-coupon bond is $943.396, the price of a two-year zero is $873.439, and the price of a three-year zero-coupon bond is $793.832. The bonds (each) have a face value of $1,000. Assume annual compounding. a) Come the yield to maturity (YTM) on the one-year zero, the two-year zero, and the three-year zero. b) Compute the implied forward rates for year 2 and for year 3. c) Assume that the expectations hypothesis is correct. Based on...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT