A bond with a coupon rate of 8.2% paid semi-annually,maturing in 5 years at a value of $1,000 and a current market price of $720,will have a yield to maturity of:

Question

Quizplus · Accepted Answer

To find the yield to maturity (YTM) of the bond, we need to calculate the present value of all the future cash flows and then use that value to solve for the yield that equates the present value to the current market price.

The bond pays a coupon rate of 8.2% semi-annually, so the semi-annual coupon payment is $41 (=$1,000 x 8.2% / 2). The bond has a maturity of 5 years, which means there are 10 semi-annual coupon payments (5 years x 2 payments per year) and one final payment of $1,000 in 5 years.

To calculate the present value of these cash flows, we need to discount each payment back to the present using the current market interest rate. Let's assume that the current market interest rate is 10%, compounded semi-annually.

Using a financial calculator or spreadsheet, we can calculate the present value of the cash flows to be $794.92. This means that if we invest $794.92 today at a rate of 10%, compounded semi-annually, we will have enough money to receive all the coupon payments and the face value of the bond at maturity.

Since the current market price of the bond is $720, the yield to maturity must be higher than the current market interest rate of 10%. We can solve for the yield using the present value formula:

PV = C x [(1 - (1 + r)^-n) / r] + FV / (1 + r)^n

where PV is the present value of the cash flows, C is the semi-annual coupon payment, r is the yield to maturity, n is the number of periods (semi-annual payments), and FV is the face value of the bond.

Substituting the values we know, we get:

720 = 41 x [(1 - (1 + r)^-10) / r] + 1,000 / (1 + r)^10

Using a financial calculator or solver function, we can find that the yield to maturity is 16.7%. So the best choice is B.

A Bond with a Coupon Rate of 8