Question

Valuing Bonds                                                 

Q1.   Suppose a 20-year, $1000 par value bond with an annual fixed 5% coupon rate (coupons paid semiannually, as are most bonds) is trading for a price of $1065.48.

a.   What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?

b.   If this bond’s yield to maturity or YTM changes to 4% APR, what will the bond’s new price?  What is this bond’s new price if the YTM changes to 5%?

Q2.   Understanding what maturity risk means for bonds is very important.  Complete the following table by calculating the new bond prices and then the % price change that results for the two bonds given below.  For example, in the table if YTMs go up 1 percentage point (also known as 100 basis points or bp) on the short-term bond, that means that the YTM would go from 3% to 4%.  Then calculate the new price at a YTM of 4% and then calculate the % change in price from today's price of $1,000 to the new price.

Short term bond:  Face value of $1,000 with a fixed annual coupon rate of 3% with semi-annual payments, and a maturity in 2 years.  Assume that today's YTM on a 2 year bond is 3% so therefore today's price is $1,000.

Long term bond:  Face value of $1,000 with a fixed annual coupon rate of 3% with semi-annual payments, and a maturity in 30 years.  Assume that today's YTM on a 30 year bond is 3% so therefore today's price is $1,000.

	YTM goes down by 1.0% (100 basis pts)		YTM goes down by 0.5% (50 basis pts)		Today's Price	YTM goes up by 0.5% (50 basis pts)		YTM goes up by 1.0% (100 basis pts)
	New     $ Price	% change from Today	New   $ Price	% change from Today		New  $ Price	% change from Today	New  $ Price	% change from Today
Short Term Bond					$1,000
Long Term Bond					$1,000

this is all the data that was provided, as it is.

Answer 1

Q1)

a)

b)