Heinz Corporation bonds carry a coupon of 8% and will mature in 5 years at $1,000. Newly issued 5-year bonds with similar characteristics are yielding 4%. Calculate today's market price of the Heinz bond. Compute your answer, submit all your work, then answer the following questions.
14. What is the discount rate you used in your work?
15. What is the annual interest in dollars paid by the Heinz bond?
16. What is the pv of the yearly bond interest that the Heinz bond pays? Could this yearly bond interest be computed as an annuity? Why, or why not ?
17.What is the present value of the principal of the Heinz bond ?
18, What is the total present value of the Heinz bond- interest plus principal?
To calculate the market price of the Heinz bond, we need to discount the future cash flows (coupon payments and principal) at the market yield rate.
Step 1: Calculate the present value of the coupon payments.
Coupon rate = 8% (8% of $1,000)
Market yield rate = 4%
Number of years = 5
Using the formula for present value of a coupon bond:
PV of coupon payments = Coupon payment * [1 - (1 + r)^(-n)] / r
where r is the market yield rate and n is the number of years.
Coupon payment = 8% of $1,000 = $80
PV of coupon payments = $80 * [1 - (1 + 4%)^(-5)] / 4%
Step 2: Calculate the present value of the principal.
Principal value = $1,000
PV of principal = $1,000 / (1 + 4%)^5
Step 3: Calculate the total present value of the bond.
Total present value = PV of coupon payments + PV of principal
Now let's calculate these values and answer the questions:
14. The discount rate used in the work is the market yield rate, which is 4%.
15. The annual interest in dollars paid by the Heinz bond is $80.
16. The PV of the yearly bond interest that the Heinz bond pays can be computed as an annuity because it is a fixed payment made annually over the bond's life. An annuity is a series of equal cash flows at regular intervals.
17. The present value of the principal of the Heinz bond is calculated using the formula mentioned above.
18. The total present value of the Heinz bond is the sum of the present values of the coupon payments and the principal.
Now let's calculate the values:
Step 1: Calculate the present value of the coupon payments
PV of coupon payments = $80 * [1 - (1 + 4%)^(-5)] / 4% = $324.57
Step 2: Calculate the present value of the principal
PV of principal = $1,000 / (1 + 4%)^5 = $822.70
Step 3: Calculate the total present value of the bond
Total present value = $324.57 + $822.70 = $1,147.27
Therefore, the market price of the Heinz bond today is $1,147.27.
To calculate the market price of the Heinz bond, we need to find the present value of the bond's future cash flows.
Step 1: Calculate the annual cash flow
The bond has a coupon rate of 8% and a face value (maturity amount) of $1,000. This means it will pay interest of 8% * $1,000 = $80 annually.
Step 2: Determine the discount rate
The newly issued bonds with similar characteristics are yielding 4%. This represents the required rate of return or the discount rate for valuing the bond.
Step 3: Calculate the present value of the annual interest payments
To calculate the present value of the annual interest payments, we need to discount each payment back to the present value using the discount rate.
Using the formula for the present value of an annuity:
PV = C * [1 - (1 + r)^(-n)] / r
Where PV is the present value, C is the cash flow (annual interest payment), r is the discount rate, and n is the number of periods (years).
In this case, C = $80, r = 4%, and n = 5.
PV = $80 * [1 - (1 + 0.04)^(-5)] / 0.04
PV ≈ $80 * [1 - (1.04)^(-5)] / 0.04
PV ≈ $80 * [1 - 0.8209] / 0.04
PV ≈ $80 * 0.1791 / 0.04
PV ≈ $80 * 4.4775
PV ≈ $358.2
So the present value of the yearly bond interest that the Heinz bond pays is approximately $358.2.
Step 4: Calculate the present value of the principal
Since the bond will mature in 5 years at $1,000, we can discount the future value back to the present value using the same discount rate.
Using the formula for the present value of a single future amount:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods (years).
In this case, FV = $1,000, r = 4%, and n = 5.
PV = $1,000 / (1 + 0.04)^5
PV ≈ $1,000 / (1.04)^5
PV ≈ $1,000 / 1.2167
PV ≈ $822.5
So the present value of the principal of the Heinz bond is approximately $822.5.
Step 5: Calculate the total present value of the Heinz bond
To find the total present value of the Heinz bond, we need to sum the present values of the interest payments and the principal.
Total Present Value = Present Value of Interest + Present Value of Principal
Total Present Value ≈ $358.2 + $822.5
Total Present Value ≈ $1,180.7
Therefore, the market price of the Heinz bond today is approximately $1,180.7.
Now let's answer the additional questions:
14. The discount rate used in the calculations is 4%.
15. The annual interest paid by the Heinz bond is $80.
16. The present value of the yearly bond interest can be computed as an annuity because the interest is a fixed amount paid annually over a specified period of time. Since the bond interest payments are consistent and occur at regular intervals (annually), it can be considered an annuity.
17. The present value of the principal of the Heinz bond is $822.5.
18. The total present value of the Heinz bond (interest plus principal) is $1,180.7.