Ngata Corp. issued 12-year bonds 2 years ago at a coupon rate of 8.4 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, the YTM is ? percent

7.67

To find the yield to maturity (YTM) of the bonds, we need to calculate the present value of the bond's cash flows and solve for the yield that equates the present value to the current market price.

Given information:
- Bonds were issued 2 years ago, so there are 10 years remaining until maturity (12 - 2 = 10).
- The coupon rate is 8.4%, which is paid semiannually.
- The bonds currently sell for 105% of the par value.

Step 1: Calculate the number of coupon payments
There will be 10 x 2 = 20 coupon payments remaining (since they are paid semiannually).

Step 2: Calculate the coupon payment amount
The coupon payment is the coupon rate multiplied by the face value (par value) of the bond. Assuming a face value of $100, the coupon payment amount is 8.4% * $100 / 2 = $4.20.

Step 3: Calculate the present value of the coupon payments
To calculate the present value of the coupon payments, we need to discount each semiannual payment using the YTM. The semiannual discount rate is YTM / 2.

Using the formula for the present value of an annuity, the present value of the coupon payments can be calculated as follows:

PV_coupon = [Coupon payment / (1 + (YTM/2))^1] + [Coupon payment / (1 + (YTM/2))^2] + ... + [Coupon payment / (1 + (YTM/2))^20]

Step 4: Calculate the present value of the bond's face value
The present value of the bond's face value is calculated by dividing the face value by (1 + (YTM/2))^20.

Step 5: Calculate the present value of the bond
The present value of the bond is the sum of the present value of the coupon payments and the present value of the face value.

Step 6: Solve for YTM
We need to find the YTM that makes the present value of the bond equal to the current market price (105% of the face value).

We can now use financial calculator software or an online financial calculator to find the YTM that satisfies the equation.

Note: The YTM will be expressed as a semiannual rate, which needs to be multiplied by 2 to obtain the annual YTM.

Keep in mind that YTM is an estimation and the actual yield an investor would receive may differ based on factors such as market prices and reinvestment rates.

To calculate the Yield to Maturity (YTM) of a bond, you need to follow these steps:

1. Determine the bond's present value: The bonds currently sell for 105 percent of par value, which means the present value is 105% of the par value.

2. Calculate the coupon payment: The coupon rate is given as 8.4 percent, and since the bonds make semiannual payments, you need to divide the coupon rate by 2 to get the semiannual coupon rate.

3. Determine the number of periods: The bonds were issued 2 years ago and have a 12-year maturity, making a total of 12 * 2 = 24 semiannual periods.

4. Set up the equation: The YTM is the discount rate that will make the present value of the bond's future cash flows equal to its current price. You can use a financial calculator or a spreadsheet formula like Excel's RATE function to find the YTM.

The formula would be:

Present Value = Coupon Payment * (1 - (1 + YTM/2)^(-2*number of periods)) / (YTM/2) + Par Value / (1 + YTM/2)^(2*number of periods)

In this case, the present value is given as 105% of the par value.

By solving this equation for the YTM, you can find the answer.