Question

Consider a newly issued straight bond with par value of $1,000 and 3 years until maturity. It makes semi-annual coupon payments at a coupon rate of 12%. The bond sells at a yield to maturity of 14%.

a. List the cash flows of the bond.

b. Calculate the current value of these cash flows as if they were zero-coupon bonds. For example, in half a year, the bond is going to pay a coupon of $60. Treat this coupon payment as a zero-coupon bond with par value of $60 and find its present value.

c. Determine the price of the straight bond. Compare this result to the portfolio of zero-coupon bonds from b.

d. Determine the price of the bond on the day after the first coupon, assuming that the yield to maturity has not changed.

Repeat your calculations for a yield to maturity of 10%.

Answer 1

Part (a) and (b):

Cash flows of the bond and their current values are as follows:

Detailed calculation as follows:

Part (c):

Price of the bond is the sum of current values of cash flows. The amount is ascertained at $952.33 as above.

Part (d):

Price of the bond on the day after first coupon= $959.00 as flows:

At the YTM=10%, Cash flows are as follows:

Detailed calculation as follows:

Price of the bond is the sum of current values of cash flows. Price at YTM of 10% is ascertained at $1,050.76 as above.

Price of the bond on the day after first coupon with YTM of 10%= $1,043.29 as flows: