Pls show calculations.

1) Consider an 8% coupon bond selling for $953.10 with three years until maturity making annual coupon payments. The interest rates in the next three years will be, with certainty,r₁= 8%,r₂= 10%, andr₃= 12%. Calculate the bond's (a) yield to maturity and (b) realized compound yield

a) ....

b) ....

2) Consider two bonds, a 3-year bond paying an annual coupon of 12%, and a 20-year bond, also with an annual coupon of 12%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 15%.

a.What is the new price of the 3-year bond?

.......

b.What is the new price of the 20-year bond?

.......

c.Do longer or shorter maturity bonds appear to be more sensitive to changes in interest rates?

.......

3) A newly issued 10-year maturity, 8% coupon bond making annual coupon payments is sold to the public at a price of $963. What will be an investor's taxable income from the bond over the coming year? The bond will not be sold at the end of the year. The bond is treated as an original issue discount bond.

Taxable income: ....

4) The yield to maturity on 1-year zero-coupon bonds is currently 7.5%; the YTM on 2-year zeros is 8.5%. The Treasury plans to issue a 2-year maturitycouponbond, paying coupons once per year with a coupon rate of 10%. The face value of the bond is $100.

a.At what price will the bond sell?

.....

b.What will the yield to maturity on the bond be?

.....

c.If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year?

......

d.Recalculate your answer to (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1.5%

.....

5) Prices of zero-coupon bonds reveal the following pattern of forward rates:

Year Forward rate

1 6%

2 8%

3 9%

In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000.

a.What is the price of the coupon bond?

.....

b.What is the yield to maturity of the coupon bond?

......

c.Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond?

.....

d.If you forecast that the yield curve in 1 year will be flat at 8.0%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period?

....

6)

a.Find the duration of a 4% coupon bond making annual coupon payments if it has three years until maturity and has a yield to maturity of 4%. Note: The face value of the bond is $1,000.

4% YTM ...... years

b.What is the duration if the yield to maturity is 6%? Note: The face value of the bond is $1,000.

6% YTM ..... years

7)Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2.9 million per year to beneficiaries. The yield to maturity on all bonds is 14.5%.

a.If the duration of 5-year maturity bonds with coupon rates of 13.6% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 5% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?

5 year-bond ........ million

20 yea-bond ........ million

b.What will be the par value of your holdings in the 20-year coupon bond?

Par value ...... milion

8) A 30-year maturity bond making annual coupon payments with a coupon rate of 6% has duration of 14.59 years and convexity of 294.57. The bond currently sells at a yield to maturity of 6%.

a.Find the price of the bond if its yield to maturity falls to 5%

.....

b.What price would be predicted by the duration rule?

......

c.What price would be predicted by the duration-with-convexity rule?

.......

d-1.What is the percent error for each rule?

Duration rule duration with convexity rule

percentage error ...% ....%

d-2.What do you conclude about the accuracy of the two rules?

• The duration-with-convexity rule provides more accurate approximations to the true change in price.
• The duration rule provides more accurate approximations to the true change in price.

e-1.Find the price of the bond if its yield to maturity increases to 7%

......

e-2.What price would be predicted by the duration rule?

.....

e-3.What price would be predicted by the duration-with-convexity rule?

....

e-4.What is the percent error for each rule?

Duration Duration with convexity

percentage error ....% ....%

e-5.Are your conclusions about the accuracy of the two rules consistent with parts (a) - (d)?

• Yes
• No