Determine the market price on 28 February 2020 of a 10%, R4895 security, with interest payable on 28 February and 31 August. The security is redeemable on 28 February 2030 at R99% and the investor wants to earn a yield rate of 12.18% per year, compounded twice per year. (Give your answer rounded to 2 decimal places. If you think the answer is R1012.3456, type in 1012.35)

To determine the market price of the security, we need to calculate the present value of its future cash flows, which consist of periodic coupon payments and the redemption value.

### Given information:
- **Coupon rate**: 10% per year (R4895 security)
- **Coupon payments**: 5% of the face value every 6 months (since interest is payable semiannually)
- **Redemption value**: 99% of face value at maturity on 28 February 2030
- **Yield rate**: 12.18% compounded semiannually
- **Time to maturity**: 10 years from 28 February 2020 to 28 February 2030
- **Coupon periods**: 2 per year (since interest is compounded semiannually)

Let’s calculate the market price step by step.

### Step 1: Define the variables
- Face value (denoted \( F \)): R100
- Coupon payment every 6 months \( C = 5\% \times 100 = 5 \) per half-year
- Number of periods: \( n = 2 \times 10 = 20 \) (10 years × 2 payments per year)
- Redemption value \( R = 99\% \times 100 = 99 \)
- Semiannual yield \( i = \frac{12.18\%}{2} = 6.09\% \text{ per period} \)

### Step 2: Calculate the present value of the coupon payments
The present value of the coupon payments is given by the formula for the present value of an annuity:

\[
PV_{\text{coupons}} = C \times \frac{1 - (1 + i)^{-n}}{i}
\]

Substituting the values:

\[
PV_{\text{coupons}} = 5 \times \frac{1 - (1 + 0.0609)^{-20}}{0.0609}
\]

### Step 3: Calculate the present value of the redemption value
The present value of the redemption value is given by the formula:

\[
PV_{\text{redemption}} = \frac{R}{(1 + i)^n}
\]

Substituting the values:

\[
PV_{\text{redemption}} = \frac{99}{(1 + 0.0609)^{20}}
\]

### Step 4: Calculate the market price
The market price is the sum of the present value of the coupons and the present value of the redemption value:

\[
P = PV_{\text{coupons}} + PV_{\text{redemption}}
\]

Let's compute this value.

### Calculation

1. \( (1 + 0.0609)^{-20} = 0.311756 \)
2. \( 1 - 0.311756 = 0.688244 \)
3. \( \frac{0.688244}{0.0609} = 11.302 \)
4. \( PV_{\text{coupons}} = 5 \times 11.302 = 56.51 \)

For the redemption value:

1. \( (1 + 0.0609)^{20} = 3.207 \)
2. \( \frac{99}{3.207} = 30.87 \)

Now, summing these:

\[
P = 56.51 + 30.87 = 87.38
\]

Thus, the **market price** of the security on 28 February 2020 is **87.38**.

---

Would you like more details on any of the steps? 

Here are five related questions:
1. How would the market price change if the yield rate were 10%?
2. What happens to the market price if the bond is redeemed at 100% instead of 99%?
3. How does compounding frequency affect bond pricing?
4. What is the relationship between bond prices and interest rates?
5. How can the present value of the bond's cash flows be derived for quarterly payments?

**Tip:** The higher the yield rate relative to the coupon rate, the lower the bond price, and vice versa.

Learn how to calculate the market price of a 10% R4895 bond, redeemable in 2030, using present value formulas. This step-by-step guide covers bond pricing, yield calculations, and annuity principles. Suitable for finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation