A firm's bond's have a maturity of 10 years with a $1,000 face value, an 8 percent semiannual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their yield to maturity and their yield to call? What return should investors expect to earn on this bond?
To find the yield to maturity (YTM) and the yield to call (YTC) for the bond, we can use the following formulas:
- YTM: The rate of return an investor would receive if they hold the bond until maturity.
- YTC: The rate of return an investor would receive if the bond is called before maturity.
Let's break down the steps to calculate each of them:
1. Yield to Maturity (YTM):
YTM is the annualized rate of return based on the bond's current price and future cash flows (coupon payments and face value at maturity).
To calculate YTM, we need to find the discount rate that equates the present value of all future cash flows to the bond's current price.
In this case, since the bond pays a semiannual coupon, we need to adjust the formula a bit.
Here's how to calculate YTM step by step:
Step 1: Calculate the number of periods until maturity:
Since the bond has a 10-year maturity and pays a semiannual coupon, the number of periods until maturity is 10 years * 2 = 20 periods.
Step 2: Calculate the periodic coupon payment:
The bond has an 8 percent semiannual coupon on a $1,000 face value. This means each coupon payment would be 8% * $1,000 / 2 = $40.
Step 3: Calculate the present value of the coupon payments:
To calculate the present value of the 20 coupon payments, we discount each cash flow back to the present using the YTM as the discount rate.
Step 4: Calculate the present value of the face value at maturity:
The face value of the bond is $1,000, which will be received at the 20th period.
Step 5: Calculate the YTM using trial and error or Excel's YIELD function:
By finding the discount rate that makes the present value of all future cash flows equal to the bond's current price of $1,100, you can determine the YTM.
2. Yield to Call (YTC):
The YTC will be the rate of return an investor would earn if the bond is called at the callable price.
Here's how to calculate YTC step by step:
Step 1: Calculate the number of periods until the call date:
The bond is callable in 5 years, which means there are 5 years * 2 = 10 periods until the call date.
Step 2: Calculate the present value of the coupon payments and the call price:
Repeat the steps from calculating the YTM, but this time calculate the present value until the call date and include the callable price of $1,050 in the present value calculation.
Step 3: Calculate the YTC using trial and error or Excel's YIELD function:
By finding the discount rate that makes the present value of all future cash flows (including the callable price) equal to the bond's current price of $1,100, you can determine the YTC.
3. Investors' expected return on the bond:
To calculate the return investors should expect to earn on this bond, consider whether the bond will mature or be called.
- If the bond matures, the return will be equal to the YTM.
- If the bond is called, the return will be equal to the YTC.
- To determine which return is more likely, compare the YTM and YTC. If the YTM is higher than the YTC, it is more likely the bond will mature rather than be called.
By following these steps, you can calculate the YTM, YTC, and expected return for this bond.