Bond Valuation Calculation

Explanation

Present value of interest payments at 10%: $500 x 15.3725 = $7,686

Present value of principal payment at 10%: $10,000 x .2314 = 2,314

$7,686 + 2,314 = 10,000

To calculate the value of a bond, you need to determine the present value of its future cash flows. In this case, you have a 15-year bond that pays $500 every 6 months, and the face value is $10,000. The required rate of return is 10%.

Step 1: Determine the number of periods Since the bond pays $500 every 6 months for 15 years, there will be 30 periods (15 years * 2 payments per year).

Step 2: Calculate the periodic interest rate The required rate of return is 10% annually, which means the periodic interest rate is 10% divided by 2 (since there are 2 payments per year). Therefore, the periodic interest rate is 5% (0.10/2).

Step 3: Calculate the present value of each cash flow To calculate the present value of each cash flow, we'll use the formula for the present value of an ordinary annuity:

PV = C × [(1 - (1 + r)^(-n)) / r]

Where: PV = Present value C = Cash flow r = Periodic interest rate n = Number of periods

First, let's calculate the present value of each $500 payment. Using the formula, we have:

PV1 = $500 × [(1 - (1 + 0.05)^(-30)) / 0.05]

Calculating this, we get PV1 ≈ $6,652.84.

Step 4: Calculate the present value of the face value To calculate the present value of the face value, we can simply discount it back to the present using the formula:

PV2 = $10,000 / (1 + r)^n

Plugging in the values, we have:

PV2 = $10,000 / (1 + 0.05)^30

Calculating this, we get PV2 ≈ $3,783.51.

Step 5: Calculate the total bond value To find the total bond value, we need to sum up the present values of the cash flows:

Total bond value = PV1 + PV2 = $6,652.84 + $3,783.51 ≈ $10,436.35

Therefore, the value of the bond is approximately $10,436.35.

None of the provided answers A, B, or C match the calculated value. The correct answer is D (none of these answers A).