Question

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 40. The timeline shows a cash flow of $ 19.32 each from Period 1 to Period 39. In Period 40, the cash flow is $ 19.32 plus $ 1,000.

PeriodPeriod

00

11

22

nothing

3939

4040

Cash FlowsCash Flows

nothing

$ 19.32$19.32

$ 19.32$19.32

nothing

$ 19.32

$ 19.32 plus $ 1,000$19.32+$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

2020

years.  ​(Round to the nearest​ integer.)

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

The coupon rate is

​(Round to two decimal​ places.)

Answer 1

a. The bond makes payments every 6 months (semiannually) of US$ 19.32. There are 40 such periods meaning that the maturity of the bond in years = 40/2 = 20 Years

b.Coupon rate is defined as the coupon payment in 1 year divided by the par value or face value of the bond. In 1 year, the bond holder receives 2 payments from the bond, each of US$ 19.32 - so total payment in the year = 38.64. Now look at the last period when the payment of US$19.32 is supplemented by US$1,000 - this is the original face value or the par value of the bond. Hence coupon rate = annual coupon/par value, which in our case is 38.64/1000 % = 3.864%

c. Face value of the bond is US$1,000 which is the final payment received by the bond holder