Leggio Corporation issued 20-year, 7% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds has dropped to 6%. What is the new price of the bonds, given that they now have 19 years to maturity
To find the new price of the bonds, we can use the present value of a bond formula to calculate the price when the market interest rate is 6%. The present value of a bond formula is:
Price = (C * (1 - (1 + r)^-t) / r) + (F * (1 + r)^-t)
Where C = annual coupon payment, r = market interest rate, t = years to maturity, and F = face value.
In this case, the annual coupon payment is $1,000 * 7% = $70. With the market interest rate at 6%, r = 0.06. The bond now has 19 years to maturity, so t = 19. The face value is $1,000.
Price = ($70 * (1 - (1 + 0.06)^-19) / 0.06) + ($1,000 * (1 + 0.06)^-19)
First, calculate (1 + r)^-t:
(1 + 0.06)^-19 = 0.311804
Next, calculate the present value of the coupon payments:
($70 * (1 - 0.311804) / 0.06) = $70 * (0.688196 / 0.06) = $798.56
Now, calculate the present value of the face value:
($1,000 * 0.311804) = $311.80
Finally, add the present values to find the new price:
Price = $798.56 + $311.80 = $1,110.36
The new price of the bonds is $1,110.36.
To calculate the new price of the bonds, you can use the formula for calculating the present value of a bond:
P = C * [1 - (1 + r)^(-n)] / r + F * (1 + r)^(-n)
Where:
P = Price of the bond
C = Annual coupon payment
r = Market interest rate
n = Number of years to maturity
F = Face value of the bond
Given:
C = $1,000 * 7% = $70
r = 6%
n = 19
F = $1,000
We can now calculate the new price:
P = $70 * [1 - (1 + 6%)^(-19)] / 6% + $1,000 * (1 + 6%)^(-19)
P = $70 * [1 - (1.06)^(-19)] / 0.06 + $1,000 * (1.06)^(-19)
Using a calculator, the new price of the bonds is approximately $1,199.50.
To calculate the new price of the bonds, we need to use the bond pricing formula, which is based on the present value of future cash flows. Here are the steps to calculate the price of the bonds:
1. Determine the future cash flows: The bonds have a 20-year maturity, and they pay a 7% annual coupon rate. Since there are 19 years remaining until maturity, the bonds will make 19 coupon payments of $70 each ($1,000 * 7%).
2. Determine the market interest rate: The market interest rate has dropped to 6%. This will be used as the discount rate in the bond pricing formula.
3. Apply the bond pricing formula: The bond pricing formula is as follows:
Price = (C / (1 + r)) + (C / (1 + r)^2) + ... + (C / (1 + r)^n) + (F / (1 + r)^n)
Where:
- "C" represents the coupon payment,
- "r" represents the discount rate (market interest rate),
- "n" represents the number of periods remaining until maturity,
- "F" represents the face value of the bond.
In this case, C = $70, r = 6%, n = 19, and F = $1,000.
4. Plug in the values and calculate the price:
Price = (70 / (1 + 0.06)^1) + (70 / (1 + 0.06)^2) + ... + (70 / (1 + 0.06)^19) + (1000 / (1 + 0.06)^19)
Use a financial calculator or spreadsheet software to calculate the sum of the equation. The result will be the new price of the bonds.
By following these steps, you can calculate the new price of the bonds given the change in market interest rate.