Question

a) Suppose the following zero-coupon bonds are trading at the prices shown below per $150 face value. Determine the corresponding yield to maturity for each bond.

Maturity	1 year	2 years	3 years	4 years
Price	$86.45	$82.25	$77.58	$73.42

b) Assume that it is January 15th, 2010 and the U.S. Treasury has just issued securities with January 15th, 2018 maturity, $1000 par value and a 4% coupon rate with semiannual coupons. Since the original maturity is only 8 years, these would be called “notes” as opposed to “bonds”. The first coupon payment will be paid on July 15th, 2010. What cash flows will you receive if you hold this note until maturity?

c) Consider three 25-year bonds with annual coupon payments. One bond has a 4% coupon rate, one has a 2% coupon rate, and one has a 1% coupon rate. If the yield to maturity of each bond is 3%, what is the price of each bond per $150 face value? Which bond trades at a premium, which trades at a discount, and which trades at par?

d) Why Bond Prices Change?

Answer 1

part (A) to (C) are solved in images

(D) Bond prices change due to change in Yield to maturity. Bond prices are inversely proportional to YTM, as YTM increases bond prices decrease and as YTM decreases, Bond prices increase.

YTM is the IRR required by the investor before investing in fixed income securities. YTM is different for different types of bonds. The more the risk in the fixed income instruments, the more will be the desired return required by the investor to compensate the risk in the instrument, and therefore less will be the price of the instrument.

Note: You can take the help of a financial calculator or excel to calculate YTM of a bond in part (B).