Ngata Corp. issued 19-year bonds 2 years ago at a coupon rate of 9.6 percent. The bonds make semiannual payments. If these bonds currently sell for 107 percent of par value, what is the YTM?
To calculate the Yield to Maturity (YTM) of a bond, we need to use the bond's price, coupon rate, time to maturity, and coupon payments.
In this case, we know that Ngata Corp. issued 19-year bonds with a coupon rate of 9.6 percent, and the bonds currently sell for 107% of par value.
First, let's calculate the bond's price. Since the bonds are selling for 107% of par value, this means they are priced at $1,070 for every $1,000 of par value.
Next, since the bonds make semiannual coupon payments, the number of periods until maturity is given by (19 years) × (2) = 38 periods.
To calculate the YTM, we need to use a financial calculator or a spreadsheet program like Excel. Alternatively, you can use the trial and error method to find the YTM by trying different discount rates until the calculated bond price matches the actual bond price.
Here's an example of using the trial and error method with a spreadsheet program:
1. Start by assuming a discount rate (YTM) of say 5%.
2. Calculate the present value of the bond's cash flows, including both coupon payments and the principal payment at maturity, using this discount rate of 5%.
3. If the sum of the present values of the cash flows is less than the current price of $1,070, try a higher discount rate.
4. If the sum of the present values of the cash flows is higher than the current price, try a lower discount rate.
5. Repeat steps 2-4 until you find a discount rate that makes the present value of the cash flows equal to the current price of $1,070.
Alternatively, you can use financial calculators or online tools that can directly calculate the YTM by inputting the bond information.
Remember, the YTM represents the interest rate that would make the present value of the bond's expected cash flows equal to its current market price.