Question

~~~In Excel~~~~

Question 1. A US-Treasury bond with face value of $1,000 pays interest at an annual rate of 5%. Coupons are paid twice per year.

a. If this bond has 4 years to mature, what is the price of the bond if current yield to maturity is 4%? Calculate this by finding the value of coupons and principal separately. (12)

b. If the coupon were instead paid once per year, what would be the price of the bond?

~~~In Excel~~~~

Answer 1

1)

a.

Price of Bond

$ 1,036.63

Working:

Price of bond is the present value of cash flows from bond.

i.

Par Value

1,000

ii.

Semi annual coupon

1,000

x5% x 6/12

25

III.

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.02)^-8)/0.02

i

2%

=

7.3255

n

8

iv.

Present value of 1

=

(1+i)^-n

=

(1+0.02)^-8

=

0.8535

v.

Present Value of coupon

25

x

7.3255

=

183.14

Present Value of Par Value

1,000

x

0.8535

=

853.49

Current Price of Bond

1,036.63

b.

Price of Bond

$ 1,036.30

Working:

Price of bond is the present value of cash flows from bond.

i.

Par Value

1,000

ii.

Annual coupon

1,000

x5%

50

III.

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.04)^-4)/0.04

i

4%

=

3.6299

n

4

iv.

Present value of 1

=

(1+i)^-n

=

(1+0.04)^-4

=

0.8548

v.

Present Value of coupon

50

x

3.6299

=

181.49

Present Value of Par Value

1,000

x

0.8548

=

854.80

Current Price of Bond

1,036.30