a 15 year bond pays 11% on a face value of $1000. If similar bonds are currently yeilding 8%, what is the market value of the bond? use annual analysis
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a 10-year bond pays 5% on a face value of $1,000. if similar bonds are currently yielding 10%, what is the market value of the bond? use annual analysis.
To calculate the market value of the bond, we need to use the concept of present value and the formula for present value of an annuity.
In this case, the bond is paying 11% annually on a face value of $1000, and similar bonds are currently yielding 8%.
Step 1: Determine the annual interest payment:
The annual interest payment is 11% of $1000, which is 0.11 * $1000 = $110.
Step 2: Determine the number of years remaining until maturity:
Since it is a 15-year bond, the number of years remaining until maturity is 15 years.
Step 3: Determine the yield on similar bonds:
The yield on similar bonds is 8%.
Step 4: Calculate the present value of the bond using the present value of an annuity formula:
PV = (A/r) * (1 - (1+r)^-n)
Where:
PV = Present Value
A = Annual interest payment
r = Discount rate or yield
n = Number of years
Using this formula, we can calculate the market value of the bond:
PV = ($110/0.08) * (1 - (1+0.08)^-15)
PV = $1375 * (1 - 1.893849)
PV = $1375 * (-0.893849)
PV ≈ -$1229.34
Therefore, the market value of the bond is approximately -$1229.34, indicating that the bond is currently undervalued.
To calculate the market value of the bond, we need to determine the present value of the bond's future cash flows. In this case, the bond has a 15-year maturity period and pays an 11% interest rate on a face value of $1000.
To find the present value, we need to discount the future cash flows by the current market rate of 8%. This means that each annual interest payment is multiplied by the present value interest factor, which is calculated as (1 - (1 + r)^(-n)) / r, where r is the interest rate and n is the number of years.
Let's break down and calculate the present value of the bond's future cash flows:
1. Determine the annual interest payment using the face value and interest rate:
Annual interest payment = Face value * Interest rate
= $1000 * 11%
= $110
2. Calculate the present value interest factor using the market rate of 8% and the bond's maturity of 15 years:
Present value interest factor = (1 - (1 + r)^(-n)) / r
= (1 - (1 + 8%)^(-15)) / 8%
3. Multiply the annual interest payment by the present value interest factor to find the present value of the bond's future cash flows:
Present value of future cash flows = Annual interest payment * Present value interest factor
= $110 * Present value interest factor
Now, you can substitute the appropriate values into the equation to find the present value of the bond's future cash flows. The resulting value will be the market value of the bond.