169k views
1 vote
In 2009, you purchased a $1,000 par value corporate bond with an interest rate of 10.25 percent. Today, comparable bonds are paying 7.75 percent.

What is the approximate dollar price for which you could sell your bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

2 Answers

5 votes

Final answer:

To calculate the approximate dollar price for which you could sell your bond, you need to consider the difference between the bond's interest rate and the market interest rate. Since the bond's interest rate is higher than the current market rate, it will be less attractive to investors.

Step-by-step explanation:

To calculate the approximate dollar price for which you could sell your bond, you need to consider the difference between the bond's interest rate and the market interest rate. Since the bond's interest rate is higher than the current market rate, it will be less attractive to investors. To determine the selling price, you can compare the cash flows from the bond and a comparable bond paying the lower interest rate. Let's calculate:

Calculate the present value of the bond's cash flows at the market interest rate of 7.75%:

The bond will pay $1,080 at the end of the first year.

Using the formula: PV = CF / (1+r)^n, where CF is the cash flow, r is the discount rate, and n is the number of periods, the present value of the cash flow is:

PV = $1,080 / (1+0.0775)^1 = $1,002.57

The approximate dollar price for which you could sell your bond is $1,002.57.

User Ashish Ramani
by
9.2k points
2 votes

To determine the approximate dollar price for which you could sell your bond, you would need to calculate its current market value. The market value of a bond is determined by discounting the future cash flows (i.e. the coupon payments and the final principal payment) at the prevailing market interest rate.

The bond you purchased in 2009 has a par value of $1,000 and an interest rate of 10.25 percent. This means that it pays a coupon of $102.50 per year ($1,000 x 10.25%), which is paid semi-annually in two equal installments of $51.25 each. The bond has a maturity of 10 years, which means that it will pay back the par value of $1,000 at the end of the 10-year period.

To calculate the market value of the bond, we need to discount each of these cash flows at the current market interest rate of 7.75 percent. We will assume that the next coupon payment is due in six months from now.

The present value of the six-month coupon payment of $51.25 is:

PV(Coupon) = $51.25 / (1 + 7.75%/2)^1 = $49.92

The present value of the second six-month coupon payment of $51.25 is:

PV(Coupon) = $51.25 / (1 + 7.75%/2)^2 = $48.63

The present value of the remaining eight semi-annual coupon payments is:

PV(Coupons) = $51.25 * [(1 - 1/(1 + 7.75%/2)^16) / (7.75%/2)] = $685.69

The present value of the principal payment of $1,000 at the end of 10 years is:

PV(Principal) = $1,000 / (1 + 7.75%/2)^20 = $476.28

The market value of the bond is the sum of the present values of all the cash flows:

Market Value = PV(Coupon) + PV(Coupon) + PV(Coupons) + PV(Principal)

= $49.92 + $48.63 + $685.69 + $476.28

= $1,260.52

Therefore, the approximate dollar price for which you could sell your bond today is $1,260.52.

User Renne Rocha
by
8.5k points

No related questions found