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Consider a bond paying a coupon rate of 10% per year semi-annually when the market interest rate is only 4% per half-year. The bond has three years until maturity.

a. Find the bond’s price today and six months from now after the next coupon is paid.

b. What is the total rate of return on the bond?

Short Answer

Expert verified

a. $1,052.42 and $1,044.52

b. 4.00% per six months

Step by step solution

01

Calculation of current Bond price and six months after the next coupon is paid

a. The bond pays $50 every six months.

Current price: Coupon x Annuity factor (r, T ) + Par value x PV factor(r, T )

= [$50 x annuity factor (4%, 6)]+[1000 x PV factor (4%, 6)]

= $1,052.42

Assuming the market interest rate remains 4% per half year, price six months from now:

[$50 x annuity factor (4%, 5)]+[1000 x PV factor (4%, 5)]

= $1,044.52

02

Calculation of total rate of return

b. The formula for calculating total rate of return = income received from security + final value – initial value / initial value

$ 50 + ($ 1044.42 - $ 1052.42) / $ 1052.42

= $ 50 + (- $7.90) / $ 1052.42

= 0.0400

= 4.00% per six months

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Most popular questions from this chapter

You are managing a portfolio of $1 million. Your target duration is ten years, and you can choose from two bonds: a zero-coupon bond with a maturity of 5 years and an infinity, each yielding 5%.

An a. How much of each bond will you hold in your portfolio?

b. How will these fractions change next year if the target duration is nine years?

a. Explain the impact on the offering yield of adding a call feature to a proposed bond issue.

b. Explain the impact on the bond’s expected life of adding a call feature to a proposed bond issue.

c. Describe one advantage and one disadvantage of including callable bonds in a portfolio.

Rank the interest rate sensitivity of the following pairs of bonds.

a. Bond A is an 8% coupon, 20-year maturity bond selling at par value.

Bond B is an 8% coupon, 20-year maturity bond selling below par value.

b. Bond A is a 20-year, non-callable coupon bond with a coupon rate of 8%, selling at par.

Bond B is a 20-year, callable bond with a coupon rate of 9%, also selling at par.

The following multiple-choice problems are based on questions that appeared in past CFA examinations.

a. A bond with a call feature:

(1) Is attractive because the immediate receipt of principal plus premium produces a high return.

(2) Is more apt to be called when interest rates are high because the interest saving will be greater.

(3) Will usually have a higher yield to maturity than a similar non-callable bond.

(4) None of the above.

b. In which one of the following cases is the bond selling at a discount?

(1) Coupon rate is greater than current yield, which is greater than yield to maturity.

(2) Coupon rate, current yield, and yield to maturity are all the same.

(3) Coupon rate is less than current yield, which is less than yield to maturity.

(4) Coupon rate is less than current yield, which is greater than yield to maturity.

c. Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be:

(1) Higher

(2) Lower

(3) The same

(4) Par

d. Which of the following statements is true?

(1) The expectations hypothesis indicates a flat yield curve if anticipated future short term rates exceed current short-term rates.

(2) The basic conclusion of the expectations hypothesis is that the long-term rate is equal to the anticipated short-term rate.

(3) The liquidity hypothesis indicates that, all other things being equal, longer maturities will have higher yields.

(4) The liquidity preference theory states that a rising yield curve necessarily implies that the market anticipates increases in interest rates

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds.

a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position?

b. What must be the face value of the two zeros to fund the plan?

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