Assume a company issues a P100,000 bond due in four years paying seven percent interest annually at year-end. The market rate for similar bonds is 11 percent. What is the present value of the face value of the bond?

To calculate the present value (PV) of the bond's face value, we use the present value formula for a lump sum amount, which discounts the bond's future value (FV) back to the present using the market interest rate.

The formula for the present value of a lump sum is:

\[
PV = \frac{FV}{(1 + r)^n}
\]

Where:
- \( FV \) is the future value of the bond (₱100,000 in this case),
- \( r \) is the market interest rate (11% or 0.11),
- \( n \) is the number of periods (4 years in this case).

### Step-by-step calculation:

\[
PV = \frac{100,000}{(1 + 0.11)^4}
\]

\[
PV = \frac{100,000}{(1.11)^4}
\]

Now, calculate \((1.11)^4\):

\[
(1.11)^4 = 1.5181
\]

Now, divide the future value by this factor:

\[
PV = \frac{100,000}{1.5181} = 65,858.18
\]

Thus, the present value of the face value of the bond is approximately **₱65,858.18**.

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Do you want more details or have any questions? Here are some related questions to expand on this topic:

1. How is the present value of interest payments calculated for this bond?
2. How would the present value change if the market rate increased to 12%?
3. What would be the impact of semi-annual interest payments on the bond valuation?
4. Can you explain the difference between nominal interest rate and market interest rate in bonds?
5. How does the time to maturity affect the present value of a bond?

**Tip:** When interest rates in the market rise, the present value of bonds falls, and when market rates fall, the present value rises.

Learn how to calculate the present value of a P100,000 bond due in four years with a 7% annual interest and an 11% market rate. This problem covers key concepts in bond valuation, including the present value formula and the time value of money. Suitable for college-level finance students or advanced high school learners.

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