Question 1180513: Nungesser Corporation’s outstanding bonds have a $1,000 par value, a 9% semiannual coupon, 8 years to maturity, and an 8.5%
YTM. What is the bond’s price?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the bond's price:
**1. Determine the Cash Flows:**
* **Coupon Payments:** The bond pays a 9% semiannual coupon, meaning it pays 4.5% of the par value every six months. In dollar terms, this is $1,000 * 0.045 = $45 every six months.
* **Face Value:** At maturity (8 years), the bondholder receives the par value of $1,000.
**2. Calculate the Present Value of the Cash Flows:**
We need to discount each of these cash flows back to their present value using the yield to maturity (YTM) as the discount rate. Since the coupon payments are semiannual, we need to use a semiannual discount rate and number of periods.
* **Semiannual YTM:** 8.5% per year / 2 = 4.25% per period
* **Number of Periods:** 8 years * 2 = 16 periods
Here's a breakdown of the present value calculation:
* **Present Value of Coupon Payments:** This is an annuity. We can use the present value of an annuity formula or discount each payment individually.
* **Present Value of Face Value:** This is a single sum received at maturity. We discount it back 16 periods.
**3. Use a Financial Calculator or Spreadsheet:**
The easiest way to do this is with a financial calculator or spreadsheet software like Excel. Here's how you might input the values:
* **N (Number of Periods):** 16
* **I/YR (Interest Rate per Year):** 4.25 (semiannual YTM)
* **PMT (Payment):** 45 (coupon payment)
* **FV (Future Value):** 1000 (par value)
* **CPT PV (Compute Present Value):** This will give you the bond price.
**4. Result:**
The bond's price will be approximately $1043.30. This means that an investor would be willing to pay $1043.30 for this bond today, given its coupon payments and yield to maturity.
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