Question

Suppose a 2 year 5% (annual coupon) bonds are selling at par (that is, for $100 of face value, the price is equal to $100) and 1 year zero coupon bonds has a yield to maturity of 7%.

(a) What are the 1-year and 2-year interest rates, r1 and r2, respectively?
(b) What should be the price of a two year 8% coupon bond with a face value of $100?

(c) What are the Durations of 5% coupon bonds and 8% coupon bonds? Which one has longer duration? What is the implication about interest rate risk?

(Please give the specific numbers of part c.)

Answer 1

(a) r1 = 7% and r2 = 4.95%

Year	Cashflow	PVF	PV of Cashflow
1	$ 5	1/1.07 = 0.9346	$ 4.67
2	$ 105	(1+r)^(-2)	$ 105 / (1+r)^2
-	($5 Coupon + $100 Redemption)	Price of Bond	=$4.67 + ($105/(1+r)^2)

Price of Bond = $4.67 + ($105/(1+r)^2)

$100 = $4.67 + ($105/(1+r)^2)

$100 - $4.67 = $105/(1+r)^2

$95.33 = $105/(1+r)^2

(1+r)^2 = $105 / $95.33

1+r = 1.1014^(1/2)

r2 = 4.95%

(b)

Year	Cashflow	PVF	PV of Cashflow
1	$ 8	0.9346 (1/1.07)	$ 7.48
2	$ 108	0.9079 (1/1.0495^2)	$ 98.0537
-	($ 8 Coupon + $100 Redemption)	Price of Bond	$ 105.53

(c)

Duration = (Present value of a Future cash flows * Year of receipt ) /Price of Bond.

Year	PVF	Cash Flow	PV of Cash flow	Present value of a Cash flows * Year of Reciept
A	B	C	B*C	C*A
1	0.9346	5	4.67	4.67
2	0.9079	105	95.33	190.66
			100	195.33
Duration =	195.33 / 100	1.9533

Year	PVF	Cash Flow	PV of Cash flow	Present value of a Cash flows * Year of Reciept
A	B	C	B*C	C*A
1	0.9346	8	7.48	7.48
2	0.9079	108	98.05	196.11
			105.53	203.59
Duration =	195.33 / 100	1.9292