Crossfade Co. issued 15-year bonds two years ago at a coupon rate of 6.9 percent. The bonds make semiannual payments.


Required:
If these bonds currently sell for 94 percent of par value, what is the YTM?

940=34.5(PIVIFAr%,n)1,000(PVIFr%,n)

1213

3655

To calculate the Yield to Maturity (YTM) of a bond, you need to use an iterative approach. The YTM is the rate of return that an investor would expect to receive if they hold the bond until maturity and reinvest all coupon payments at the YTM itself.

Here's how you can calculate the YTM:

1. Determine the current market price: The bonds are currently selling for 94 percent of par value. If the face value of the bond is $1,000, then the current market price would be 0.94 * $1,000 = $940.

2. Determine the future cash flows: Since the bonds make semiannual payments, there will be 15*2 = 30 coupon payments over the life of the bond. Each coupon payment will be equal to 0.069 * ($1,000 / 2) = $34.50.

3. Set up the equation: The YTM is the discount rate that makes the present value of all future cash flows equal to the current market price. You'll need to solve this equation using trial and error or by using financial calculators or software.

The equation can be written as follows:

$940 = ($34.50 / (1 + YTM/2)^1) + ($34.50 / (1 + YTM/2)^2) + ... + ($34.50 / (1 + YTM/2)^30) + ($1,000 / (1 + YTM/2)^30)

4. Solve the equation: Since this is a complex calculation, it's recommended to use a financial calculator or specialized software. Alternatively, you can use Excel or Google Sheets and utilize the IRR (Internal Rate of Return) function to solve for YTM.

By plugging in the cash flows and the current market price into the equation, you can then find the YTM.

Please note that due to the iterative nature of the calculation, you may need to adjust your initial guess for the YTM until you find the rate that satisfies the equation. The actual YTM calculation might be further complicated by any potential bond features such as call provisions or sinking funds.