9-64 Calculate the duration of a two-year corporate bond paying 6 percent interest annually,selling at par.Principal of $20,000,000 is due at the end of two years.
A)2 years.
B)1.91 years.
C)1.94 years.
D)1.49 years.
E)1.75 years.

Question

Quizplus · Accepted Answer

To calculate the duration of a bond, you take the weighted average of the present value of all of its cash flows, divided by the bond's current market price. Since this bond is selling at par, its market price is equal to its face value of $20,000,000.

Using the formula for the present value of a bond with annual coupon payments, we can calculate the present value of each cash flow for this bond:

PV of each annual coupon payment = C / (1 + r)^t
Where:
C = the annual coupon payment (6% of $20,000,000, or $1,200,000)
r = the required rate of return (unknown)
t = the number of years until payment (1 or 2)

PV of the face value payment = $20,000,000 / (1 + r)^2

To calculate the required rate of return (r) for this bond, we can use the following formula:

Bond price = PV of coupon payments + PV of face value payment
$20,000,000 = ($1,200,000 / (1 + r)^1) + ($20,000,000 / (1 + r)^2)
Solving for r using a financial calculator or spreadsheet gives us a required rate of return of 5.830%.

Now we can calculate the duration using the following formula:

Duration = (PV of coupon payment at t=1 x 1 year) + (PV of coupon payment at t=2 x 2 years) + (PV of face value payment x 2 years)
Duration = ($1,200,000 / (1 + 0.0583)^1 x 1 year) + ($1,200,000 / (1 + 0.0583)^2 x 2 years) + ($20,000,000 / (1 + 0.0583)^2 x 2 years)
Duration = 1.939 years, or approximately 1.94 years

Therefore, the best choice is C) 1.94 years.

9-64 Calculate the Duration of a Two-Year Corporate Bond Paying