Question

2 Assume that a bond will make payments every six months as shown on the following timeline​ (using six-month​ periods):

The timeline starts at Period 0 and ends at Period 50. The timeline shows a cash flow of $ 19.31 each from Period 1 to Period 49. In Period 50, the cash flow is $ 19.31 plus $ 1,000.

Period012nothing4950

Cash Flows nothing$ 19.31$ 19.31nothing$ 19.31$ 19.31 plus $ 1,000

a. What is the maturity of the bond​(in years)?

b. What is the coupon rate​(as a​percentage)?

c. What is the face​value?

a. What is the maturity of the bond​(in years)?

The maturity is

Nothing years.  ​(Round to the nearest​integer.)

b. What is the coupon rate​(as a​percentage)?

The coupon rate is

Nothing​%. ​(Round to two decimal​places.)

c. What is the face​value?

The face value is $

Nothing. ​(Round to the nearest​dollar.)

Answer 1

Solution.

a) Maturity of the Bond.

It is given that there will be total of 50 periodical Coupon Payments using six months period. So there will be 2 payments in a year , that is once in six months.

Total payments = 50

so Maturity of the bond = 50/2 = 25 Years.

c) Face value of the Bond.

The bond will be redeemed at the end of its maturity. Since Nothing is mentioned about the Redemption Proceedings, It is assumed that the Bond is redeemed at the face value. At the time of redemption , the total cash flow will be coupon amount + Redemption value.

It is given that the cash flow at Period 50 is $19.31 + $1000. So the Redemption value = Face value = $1000

b) Coupon Rate

Coupon Payment = $19.31

Face Value = $1000.

So the Coupon Rate = $19.31/1000

= 1.93%

Since the coupon Payment is made in every six months, the above Coupon Rate is for only six months.

Therefore Yearly coupon Rate = 1.93 * 2 = 3.86%