Question

1. A 3.375%, 10-year bond with semi-annual coupon payments and a face value of $10,000 has just been sold at par.
2. 1. What are the cash flows to the bond?
   2. What is the (annual) required return on the bond?
   3. If a 10-year zero-coupon bond were marketed at the same required return as in part b), what would be the price of a $10,000 face value bond?
   4. Immediately after issuance, if the required return increases by 0.50% per year, compounded semi-annually, what will be the new price of the coupon bond? (Note: this is a one-time increase of 0.50%, not a continuing series of increases.)
   5. What would happen to the price of the 10-year zero-coupon bond with a face value of $10,000 given this change in interest rate?
   6. What is the percentage change in the coupon bond, given the change in interest rates?
   7. What is the percentage change in the zero-coupon bond, given the change in interest rates?
   8. What causes the difference in the answers to part f) and part g)?

Answer 1

The cash flows to the bond will be interest semiannually of $ 10000 * 3.375% *0.5 = $168.8 and the pricipal payment after 10 years of $10000

b)

The annual required return on the bond is the yield to maturity . here the price of the bond is same as the par value ie the coupon rate is same as the ytm.

Annual required return on the bond = 3.375%

c) Price of the zero coupon bond = face value / ( 1 +r)^n

= 10000 / 1.03375 ^10

= $7,175.38

d)

Price of the bond = par value / ( 1 +ytm/2)^n*2 + coupon [ 1 - 1/ ( 1+ ytm/2)^n*2 ] / ytm /2

= 10000 / 1.019375^20 + 168.8 [ 1 - 1 / 1.019375 ^20 ] / 0.019375

= 6812.72 + 168.8 *16.4505

   = 6812.72 + 2776.84

= $9,589.56