Question

a) Describe the key feature of a zero-coupon bond. (1 mark)

b) “The price of a zero coupon bond should be equal to its face value.” True or false? Explain.

c) “The yield to maturity of a discount bond is greater than its coupon rate.” True or false? Explain.

d) You just purchased a 10-year semi-annual coupon bond with a par value of $1,000 and a coupon rate of 8%. The nominal yield to maturity is 7% per annum. Calculate the market price of the bond.

e) Three years later, immediately after receiving the sixth coupon payment, you sell the bond to your best friend. Your best friend’s nominal yield to maturity is 9% per annum. Calculate the price paid by your best friend.

Answer 1

a. A zero-coupon bond is a debt security which does not make coupon payments. There are purchased at a discount to their face value. These bonds normally appeal to issuers interested in conserving their cash flows over the life of the bonds. They also appear attractive to investors who wish to protect themselves against the reinvestment rate risk. The imputed interest on a zero coupon bond is automatically reinvested at a rate equal to its yield to maturity.

b. False.

The price of a zero coupon bond is always lower than its face value, as the price represents the present value of the bond, the discount rate being the yield to maturity of the bond.

For example, if you purchase a 10 year zero coupon bond with a face value of $ 1,000, with yield to maturity of 8 %, the price would be $ 1,000 * ( 1 / 1.08) ¹⁰ = $ 463.19

c. True.

When the yield to maturity on a bond exceeds the coupon rate, bonds are priced at a discount to their face value. A basic feature of a bond is that its price varies inversely with yield. As the required yield increases, the present value of the cash flows ( coupons + maturity proceeds) decreases. Therefore, the price decreases.

d. n = 10 x 2 = 20

i = 7 % x 1/2 or 3.5 %

Semiannual coupon = $ 1,000 x 8 % x 1/2 = $ 40.

PVIFA _{3.5%, n=20} = [ { 1 - ( 1 / 1.035)²⁰} / 0.035 ] = 14.2124

PVIF_{3.5%, n=20} = ( 1/1.035)²⁰ = 0.5026

Market price of the bond = $ 40 x 14.2124 + $ 1,000 x 0.5026 = 1,071.10

e. n = 7 x 2 = 14.

i = 9 % x 1/2 = 4.5 %

PVIFA_{4.5%, n=14} = 10.2228

PVIF_{4.5%, n=14} = 0.5400

Price paid by your best friend = $ 40 x 10.2228 + $ 1,000 x 0.5400 = $ 948.91