Question

1. A six-year Eurobond pays coupons annually. Suppose the annual coupon is 8 percent, the face value of the bond is $1,000, and the current yield to maturity (R) is 8.5 percent. Compute the

a. Price of the bond

b. Duration of the bond.        

c. Modified duration of the bond

Answer 1

a)

we are given,

time to maturity(t) = 6

ytm(r) = 8.5%

Coupon rate = 8% or $80

face value = 1000

Present value of bond = ?

We can calculate the present value of the bond by the following formula,

PV = Value of coupon payment ( ∑C/(1+r)^t​ ) + face value​ (F/(1+r)^t​)

where:

C = coupon payments

r = yield to maturity

F=face value of the bond

t=number of periods

PV = 80/(1+0.085)^1 + 80/(1+0.085)^2 + 80/(1+0.085)^3 + .....80/(1+0.085)^6 + 1000/(1+0.085)^6

We can also calculate PV using a financial calculator or by using excel

we get the present value of the bond as $977.2

b) Duration of bond

We can calculate the duration of the bond by the following formula,

Duration = PV of cash flows/Face value

PV of cash flows = Period no. * Cash flow * discount factor

We can calculate the PV of cash flows in excel

Year	Cash flows	Discount factor	Present value of cash flow
1	80	0.922	73.733
2	80	0.849	135.913
3	80	0.783	187.898
4	80	0.722	230.904
5	80	0.665	266.018
6	1080	0.613	3971.884
		Sum	4866.350

Duration = 4688.35/1000 = 4.688

Hence the duration of the bond is 4.688

c) Modified duration

It tells us about the change in the value of a bond with a change in the interest rates.

Modified duration = Duration/(1+r) = 4.688/1.085 = 4.32

Hence the modified duration is 4.32.

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