Tim Dimby calls his broker to discuss the possibility of purchasing a bond and L&O manufacturing. His broker quotes a price of $1,180. Tim is concerned that the bond may be overpriced based on the facts involved. The $1,000 par value bond pays 14% interest, and it has 25 years remaining until maturity. The current yield on similar bonds is 12%. Compute the new price of the bond and comment on whether you think it is overpriced in the marketplace.

To determine whether the bond is overpriced or fairly priced, we can calculate its theoretical price using the **present value (PV) of future cash flows** method. The bond price is calculated by adding the present value of the bond's interest payments (coupon payments) and the present value of the bond's face value (par value).

### Step 1: Bond Information
- **Par value (Face value)**: $1,000
- **Coupon rate**: 14%
- **Coupon payment**: 14% of $1,000 = $140 annually
- **Years to maturity**: 25 years
- **Current yield on similar bonds**: 12%

The formula for the price of a bond is:

\[
\text{Bond Price} = \left( \sum_{t=1}^{n} \frac{C}{(1+r)^t} \right) + \frac{F}{(1+r)^n}
\]

Where:
- $ C $ is the annual coupon payment ($140),
- $ r $ is the market interest rate (12% or 0.12),
- $ F $ is the face value of the bond ($1,000),
- $ n $ is the number of years to maturity (25).

### Step 2: Calculate Present Value of Coupon Payments
The coupon payments are an annuity, and we can calculate the present value of these payments using the following formula for the present value of an annuity:

\[
PV_{\text{coupons}} = C \times \left( 1 - \frac{1}{(1+r)^n} \right) \div r
\]

### Step 3: Calculate Present Value of Face Value
The face value is a lump sum payment at the end of the bond's life, so the present value of this payment is:

\[
PV_{\text{face}} = \frac{F}{(1+r)^n}
\]

Let me calculate the theoretical price of the bond using these formulas.The theoretical price of the bond, based on a 12% market yield, is approximately **$1,156.86**.

### Conclusion:
- The quoted price from the broker is **$1,180**, while the calculated fair price is **$1,156.86**.
- Since the broker's price is slightly higher than the calculated price, it suggests that the bond may be **slightly overpriced** in the marketplace by around **$23.14**.

Do you want further details, or have any questions?

Here are 5 related questions to expand your understanding:
1. What happens to bond prices when market interest rates increase?
2. How does the bond's time to maturity affect its sensitivity to interest rate changes?
3. What is the difference between current yield and yield to maturity (YTM)?
4. How do callable bonds affect pricing differently from non-callable bonds?
5. Can you explain the relationship between bond prices and inflation expectations?

**Tip:** Bond prices and interest rates have an inverse relationship — when rates go up, bond prices fall, and vice versa.

Calculate the price of a $1,000 par value bond with a 14% interest rate and 25 years to maturity, given a 12% market yield. Understand the bond pricing method, annuity formula, and present value of cash flows in this detailed example. Learn if Tim Dimby's bond is overpriced in the marketplace.

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