a 10 year bond pays 8% on a face value of $1000. If similar bonds are yeilding 10%, what is the market value of the bond. use annual analysis
The formula is:
PV of the principle, $1,000
Plus the PV of the interest
Are you using Present Value Tables?
PV of the principle comes from the PV of $1.
PV of the interest is one years' interest and the factor from he PV of annuity table.
Use the 10% column from the table for 10 periods.
To find the market value of the bond, we will need to calculate the present value of its future cash flows. In this case, the bond pays a fixed interest rate of 8% annually for 10 years on a face value of $1000.
To begin, let's calculate the annual interest payment. The bond pays 8% interest on the face value, which is $1000, so the annual interest payment will be 8% of $1000, which is $80.
Next, we need to calculate the present value factor for each year's cash flow. This is done by discounting the cash flow by the yield rate. The yield rate for similar bonds in the market is given as 10%.
Now, let's calculate the present value factor for each year using the formula:
Present Value Factor = 1 / (1 + yield rate)^number of years
Year 1: Present Value Factor = 1 / (1 + 10%)^1 = 1 / 1.10 = 0.9091
Year 2: Present Value Factor = 1 / (1 + 10%)^2 = 1 / 1.21 = 0.8264
Year 3: Present Value Factor = 1 / (1 + 10%)^3 = 1 / 1.331 = 0.7513
...
Year 10: Present Value Factor = 1 / (1 + 10%)^10 = 1 / 2.5937 = 0.3855
Now, let's calculate the present value of each year's cash flow by multiplying the annual interest payment by the respective present value factor:
Year 1 Present Value = $80 * 0.9091 = $72.73
Year 2 Present Value = $80 * 0.8264 = $66.11
Year 3 Present Value = $80 * 0.7513 = $60.10
...
Year 10 Present Value = $80 * 0.3855 = $30.84
Finally, to find the market value of the bond, we sum up all the present values of the cash flows:
Market Value = Present Value of Year 1 + Present Value of Year 2 + ... + Present Value of Year 10
Market Value = $72.73 + $66.11 + $60.10 + ... + $30.84
Adding up all the present values will give us the market value of the bond.