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.
What is the discount rate you used in your work? What is the annual interest in dollars paid by the Heinz bond?
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? What is the present value of the principal of the Heinz bond?
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 determine the present value (PV) of the bond's future cash flows, which includes both the annual interest payments and the principal repayment.
Step 1: Calculate the annual interest payment. The coupon rate is 8%, and the face value of the bond is $1,000. So, the annual interest payment is 8% of $1,000, which equals $80.
Step 2: Determine the discount rate. The question mentions that newly issued 5-year bonds with similar characteristics are yielding 4%. This can be used as the discount rate since it represents the market rate for bonds with similar risk profiles and maturities.
Step 3: Calculate the present value of the yearly bond interest. Since the interest payments are fixed at $80 per year for 5 years, we can calculate the present value using the formula for the present value of an ordinary annuity:
PV = (Annual Interest Payment) / (1 + Discount Rate) + (Annual Interest Payment) / (1 + Discount Rate)^2 + ... + (Annual Interest Payment) / (1 + Discount Rate)^n
Using this formula, the present value of the yearly bond interest is:
PV = $80 / (1 + 0.04) + $80 / (1 + 0.04)^2 + $80 / (1 + 0.04)^3 + $80 / (1 + 0.04)^4 + $80 / (1 + 0.04)^5
Calculating this expression will give us the present value of the yearly bond interest.
Step 4: Calculate the present value of the principal. The principal amount is $1,000, which will be received at the end of the 5-year maturity period. Since this payment is a single lump sum in the future, we can calculate the present value using the formula for the present value of a single sum:
PV = Principal / (1 + Discount Rate)^n
Using this formula, the present value of the principal is:
PV = $1,000 / (1 + 0.04)^5
Calculating this expression will give us the present value of the principal.
Step 5: Compute the total present value of the Heinz bond. This can be obtained by summing the present value of the yearly bond interest and the present value of the principal.
Total Present Value = Present Value of Yearly Bond Interest + Present Value of Principal
Calculating this expression will give us the total present value of the Heinz bond, which represents the market price of the bond.
To determine the discount rate used in the calculations, we can refer to the given information in the question, which states that newly issued 5-year bonds with similar characteristics are yielding 4%. Therefore, the discount rate used is 4%.
The annual interest paid by the Heinz bond is calculated in Step 1 and is found to be $80.
The present value of the yearly bond interest cannot be computed as an annuity because the interest payments are fixed at $80 per year for 5 years. An annuity refers to a series of equal payments occurring at regular intervals. In this case, the interest payments are constant, but they are not considered an annuity since the payments themselves are not related to each other (i.e., there are no compounding effects, changing interest rates, etc.).
The present value of the principal is calculated in Step 4 using the given information, which is found to be the result of $1,000 / (1 + 0.04)^5.
Lastly, the total present value of the Heinz bond is calculated in Step 5 by summing the present value of the yearly bond interest and the present value of the principal. This represents the market price of the bond.
To calculate today's market price of the Heinz bond, we need to use the concept of present value. The formula to calculate the present value of the bond is:
PV = C × (1 - (1 / (1 + r)^n)) / r + F / (1 + r)^n
Where:
PV = Present Value
C = Annual coupon payment = Coupon rate × Face value = 0.08 × $1,000 = $80
r = Discount rate or yield = 0.04 (4%)
n = Number of periods or years until maturity = 5
F = Face value = $1,000
By substituting the values into the formula, we can calculate the present value of the Heinz bond:
PV = $80 × (1 - (1 / (1 + 0.04)^5)) / 0.04 + $1,000 / (1 + 0.04)^5
= $80 × (1 - (1 / 1.216653)) / 0.04 + $1,000 / 1.216653
= $80 × (1 - 0.821933) / 0.04 + $822.81
= $58.78 + $822.81
= $881.59
Therefore, today's market price of the Heinz bond is approximately $881.59.
Discount rate used in the calculation is 4% (0.04).
The annual interest paid by the Heinz bond is $80.
The present value of the yearly bond interest that the Heinz bond pays is the same as the annual interest, which is $80. Yes, the yearly bond interest can be computed as an annuity because it represents a fixed annual payment for a specific duration.
The present value of the principal of the Heinz bond is $1,000, which is the face value of the bond.
The total present value of the Heinz bond, which includes both the interest and principal, is the sum of the present value of the yearly bond interest and the present value of the principal. Therefore, the total present value is $881.59 + $1,000 = $1,881.59.