he University of California has two bonds outstanding. Both issues have the same credit rating, a face value of $1,000 and a coupon rate of 6%. Coupons are paid twice a year. Bond A matures in 1 year, while bond B matures in 30 years.

The market interest rate for similar bonds is 12%.
What is the price of bond B?

To find the price of Bond B, which matures in 30 years, we need to use the present value formula for bonds, similar to what we did for Bond A but accounting for the longer maturity period. Here are the steps:

1. **Calculate the semi-annual coupon payment:**
   \[
   \text{Coupon Payment} = \frac{6\%}{2} \times \$1,000 = 3\% \times \$1,000 = \$30
   \]

2. **Determine the number of semi-annual periods:**
   \[
   \text{Number of periods} = 30 \text{ years} \times 2 = 60 \text{ periods}
   \]

3. **Calculate the semi-annual market interest rate:**
   \[
   \text{Semi-annual market rate} = \frac{12\%}{2} = 6\%
   \]

4. **Find the present value of the coupon payments:**
   The present value of an annuity formula is:
   \[
   PV_{\text{coupons}} = C \times \left(1 - (1 + r)^{-n}\right) / r
   \]
   Where:
   - $C$ is the semi-annual coupon payment ($30)
   - $r$ is the semi-annual market interest rate (0.06)
   - $n$ is the number of periods (60)

   Substituting these values in:
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - (1 + 0.06)^{-60}\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - \frac{1}{(1.06)^{60}}\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - \frac{1}{10.2867}\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - 0.0972\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times 0.9028 / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times 15.0467
   \]
   \[
   PV_{\text{coupons}} = \$451.40
   \]

5. **Find the present value of the face value:**
   The present value of a lump sum formula is:
   \[
   PV_{\text{face value}} = F / (1 + r)^n
   \]
   Where:
   - $F$ is the face value ($1,000)
   - $r$ is the semi-annual market interest rate (0.06)
   - $n$ is the number of periods (60)

   Substituting these values in:
   \[
   PV_{\text{face value}} = \$1,000 / (1.06)^{60}
   \]
   \[
   PV_{\text{face value}} = \$1,000 / 10.2867
   \]
   \[
   PV_{\text{face value}} = \$97.24
   \]

6. **Sum the present values to find the bond price:**
   \[
   \text{Bond Price} = PV_{\text{coupons}} + PV_{\text{face value}}
   \]
   \[
   \text{Bond Price} = \$451.40 + \$97.24
   \]
   \[
   \text{Bond Price} = \$548.64
   \]

Therefore, the price of Bond B is $ \$548.64 $.

Do you have any questions or need further details?

Here are some related questions:

1. How does the duration of a bond impact its price sensitivity to interest rate changes?
2. What is the difference between the current yield and the yield to maturity of a bond?
3. How do interest rate changes affect long-term bonds differently than short-term bonds?
4. What are the risks associated with holding long-term bonds?
5. How is the price of a zero-coupon bond calculated?
6. What factors can cause a bond’s credit rating to change?
7. How do callable bonds differ in valuation from non-callable bonds?
8. What impact does reinvestment risk have on long-term bond investments?

**Tip:** Longer-term bonds are generally more sensitive to interest rate changes than shorter-term bonds. This is because the present value of their distant future cash flows is more affected by changes in the discount rate.

Learn how to calculate the price of Bond B with a 30-year maturity using the present value formula. This problem involves bonds with a 6% coupon rate, maturing in 30 years, and a market interest rate of 12%. Discover step-by-step calculations for bond pricing. Suitable for college-level finance students.

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