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 A?

To find the price of Bond A, we will use the present value formula for bonds. Since Bond A has a face value of $1,000, a coupon rate of 6%, and it pays coupons semi-annually, the steps are as follows:

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

2. **Determine the number of semi-annual periods:**
   Since Bond A matures in 1 year and pays coupons semi-annually:
   \[
   \text{Number of periods} = 1 \text{ year} \times 2 = 2 \text{ periods}
   \]

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

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 (2)

   Substituting these values in:
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - (1 + 0.06)^{-2}\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - \frac{1}{(1.06)^2}\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - \frac{1}{1.1236}\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times \left(1 - 0.8900\right) / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times 0.1100 / 0.06
   \]
   \[
   PV_{\text{coupons}} = \$30 \times 1.8333
   \]
   \[
   PV_{\text{coupons}} = \$55.00
   \]

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 (2)

   Substituting these values in:
   \[
   PV_{\text{face value}} = \$1,000 / (1.06)^2
   \]
   \[
   PV_{\text{face value}} = \$1,000 / 1.1236
   \]
   \[
   PV_{\text{face value}} = \$890.00
   \]

6. **Sum the present values to find the bond price:**
   \[
   \text{Bond Price} = PV_{\text{coupons}} + PV_{\text{face value}}
   \]
   \[
   \text{Bond Price} = \$55.00 + \$890.00
   \]
   \[
   \text{Bond Price} = \$945.00
   \]

Therefore, the price of Bond A is $ \$945.00 $.

Do you have any questions or need further details?

Here are some related questions:

1. How does the market interest rate affect bond prices?
2. What would be the price of Bond A if the market interest rate was 10%?
3. How do you calculate the yield to maturity for a bond?
4. What factors influence a bond's credit rating?
5. What is the difference between a bond's coupon rate and its yield to maturity?
6. How does the time to maturity affect the price sensitivity of a bond?
7. What is the significance of semi-annual coupon payments in bond valuation?
8. How does inflation impact the real return on bonds?

**Tip:** When calculating bond prices, remember that as market interest rates increase, the present value of future cash flows decreases, leading to lower bond prices, and vice versa.

Learn how to calculate the price of Bond A using bond valuation techniques. This problem involves calculating coupon payments, determining present values, and applying market interest rates. Suitable for professionals and students of finance.

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