Question

Consider the following two bonds: a 5-year and a 10-year bond, each with a 7% coupon. Both bonds currently sell at par and coupon payments are made annually (i.e., one coupon payment per year).

(a) What is the current price of each bond?

Hint: answer does not require calculations; read description of bonds carefully to determine what price must be (10 points) Suppose you buy the 10-year bond. One year later, interest rates decrease to 5%.

(b) What will be the new price of the bond? (30 points)

(c) What rate of return would you have earned on the bond over the one-year period? (20 points)

(d) Which bond will have a higher rate of return over the year, the 5-year bond or the 10-year bond? Why? (5 points).

You don’t need calculations for this one and will not be given any points for a numerical answer; respond based on your understanding of interest rate risk (price sensitivity) in bonds.

Answer 1

a]	Current price of each bond is $1,000, as they sell at par.
b]	Price of a bond is the PV of the expected cash flows
	from the bond if, it is held till matruity.
	The expected cash flows are the maturitry value of
	$1,000 and the annual interest [annuity].
	Price of the bond one year later:
	5 Year bond:
	= 1000/1.05^4+70*(1.05^4-1)/(0.05*1.05^4) =	$   1,070.92
	10 Year bond:
	= 1000/1.05^9+70*(1.05^9-1)/(0.05*1.05^9) =	$   1,142.16
c]	Rate of return earned on the bonds over the past one
	year period.
	5 Year bond:
	= (70+1070.92-1000)/1000 =	14.09%
	10 Year bond:
	= (70+1142.16-1000)/1000 =	21.22%
d]	The 10 Year bond will have a higher rate of return over
	the year, as its price will rise more for a given decrease
	in market interest rates than in the case of the 5 Year
	bond. This is because as maturity of the bond increases
	it becomes more price sensitive.