Ngata Corp. issued 17-year bonds 2 years ago at a coupon rate of 9.8 percent. The bonds make semiannual payments. If these bonds currently sell for 102 percent of par value, what is the YTM?
10.5%
To calculate the Yield to Maturity (YTM) of a bond, we need to use the present value formula for calculating the price of a bond.
The YTM is the discount rate that will make the present value of the bond's cash flows equal to its current market price. In this case, the current market price is given as 102 percent of par value.
Let's break down the steps to find the YTM:
Step 1: Identify the relevant information:
- Coupon rate: 9.8% (annual coupon rate)
- Bond term: 17 years
- Bond's semiannual coupon payments
- Current market price: 102% (or 1.02 in decimal form) of par value
Step 2: Determine the cash flows:
Since this bond makes semiannual coupon payments, you will receive 34 coupon payments over the bond's 17-year life. The coupon payment is calculated by taking the coupon rate and dividing it by 2 since the payments are semiannual. To calculate the total cash flows, multiply the coupon payment by the number of periods.
Step 3: Calculate the present value of the cash flows:
Using the YTM as the discount rate, calculate the present value of each cash flow. For a bond with semiannual payments, divide the discount rate (YTM) by 2 since the payments are made semiannually.
Step 4: Calculate the sum of the present values:
Sum up the present values of all the cash flows to find the bond's present value.
Step 5: Solve for YTM:
Use trial and error or an Excel function, such as Goal Seek or the IRR function, to find the YTM that makes the present value of the cash flows equal to the current market price.
By following these steps, you should be able to calculate the YTM for the Ngata Corp. bonds.