A $2,000,000 bond was issued on September 10 2015 with a 6 year maturity.  Coupon rate is 4.75% and the present YTM is 6.8% p.a. compounded half-yearly. Interest is paid semi annually. How much is the bond worth on 10 March 2018?

To determine the value of the bond on **March 10, 2018**, we need to use the **present value of future cash flows formula**. The value of the bond is the sum of the present values of the future coupon payments and the face value of the bond, discounted at the yield to maturity (YTM). Here's a step-by-step breakdown:

### Key Variables:
- **Face value of bond** (F): \$2,000,000
- **Coupon rate** (c): 4.75% per annum
- **Coupon payments frequency**: Semi-annual (every 6 months)
- **Present yield to maturity (YTM)**: 6.8% per annum compounded semi-annually
- **Time of bond issuance**: September 10, 2015
- **Maturity period**: 6 years
- **Date of valuation**: March 10, 2018

### Step 1: Calculate the number of periods (N)
The bond matures in 6 years, with semi-annual payments, so:
\[
N = 6 \times 2 = 12 \text{ semi-annual periods total.}
\]

By **March 10, 2018**, the bond has been outstanding for:
\[
\text{From September 10, 2015 to March 10, 2018} = 2.5 \text{ years} = 5 \text{ semi-annual periods}.
\]

Thus, the number of periods remaining:
\[
N_{\text{remaining}} = 12 - 5 = 7 \text{ semi-annual periods remaining}.
\]

### Step 2: Calculate the coupon payment (PMT)
The coupon rate is **4.75%** annually, but interest is paid semi-annually, so the coupon payment every 6 months is:
\[
PMT = \left(\frac{4.75\%}{2}\right) \times 2,000,000 = 0.02375 \times 2,000,000 = 47,500 \text{ per period}.
\]

### Step 3: Calculate the YTM per period
The YTM of 6.8% p.a. compounded semi-annually is divided by 2 for semi-annual compounding:
\[
YTM_{\text{semi-annual}} = \frac{6.8\%}{2} = 3.4\% = 0.034 \text{ per period}.
\]

### Step 4: Calculate the present value of coupon payments (PVC)
The present value of the coupon payments is the sum of the discounted coupon payments for the remaining periods:
\[
PVC = PMT \times \sum_{t=1}^{7} \frac{1}{(1 + YTM_{\text{semi-annual}})^t}
\]
This can be simplified using the formula for the present value of an annuity:
\[
PVC = PMT \times \frac{1 - (1 + YTM_{\text{semi-annual}})^{-N_{\text{remaining}}}}{YTM_{\text{semi-annual}}}
\]

### Step 5: Calculate the present value of the face value (PVF)
The present value of the face value, which will be paid at the end of the remaining 7 periods, is:
\[
PVF = \frac{F}{(1 + YTM_{\text{semi-annual}})^{N_{\text{remaining}}}} = \frac{2,000,000}{(1.034)^7}
\]

### Step 6: Bond price
The price of the bond is the sum of the present value of the coupon payments and the present value of the face value:
\[
\text{Bond Price} = PVC + PVF
\]

Now let's calculate it.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can still guide you through the remaining steps or clarify any questions you may have. Here's what you might consider:

1. Use a financial calculator to input the remaining formulas for **PVC** and **PVF**.
2. Do you need further explanations for bond valuation steps?
3. Would you like to explore how semi-annual compounding affects YTM in detail?
4. Are you familiar with the present value formula for annuities?
5. Would you like to explore different bond pricing scenarios under changing YTMs?

**Tip**: Understanding the impact of YTM on bond price can help you make better financial decisions when bond yields fluctuate.

A $2,000,000 bond was issued on September 10, 2015, with a 6-year maturity. Coupon rate is 4.75% and the present YTM is 6.8% p.a. compounded half-yearly. Interest is paid semi-annually. How much is the bond worth on 10 March 2018?

Learn how to calculate the value of a $2,000,000 bond with a 4.75% coupon rate and 6.8% YTM (compounded semi-annually). This detailed solution covers bond valuation principles, including the present value of future cash flows and time value of money. Suitable for finance professionals and college-level students.

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