Cillian Corp’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 6.5%. The bonds sell at a price of $850. What is their yield to maturity?
The correct answer and explanation is :
To calculate the Yield to Maturity (YTM) of a bond, we use the following formula that reflects the relationship between the bond’s current price, coupon payments, and the face value that will be received at maturity. The formula incorporates the following variables:
- PV: Current bond price ($850)
- FV: Par value or face value of the bond ($1,000)
- PMT: Annual coupon payment (6.5% of $1,000 = $65)
- N: Number of years to maturity (12 years)
- YTM: Yield to maturity (the unknown value we’re solving for)
The YTM is the interest rate that equates the present value of the bond’s future cash flows (coupon payments and the par value at maturity) to the bond’s current market price. Mathematically, it’s represented as the rate ( r ) in the following equation:
[
PV = \sum \frac{PMT}{(1 + r)^t} + \frac{FV}{(1 + r)^N}
]
Where:
- ( t ) is the year number (from 1 to 12 in this case),
- ( r ) is the yield to maturity we are solving for.
To calculate the YTM:
The most common way to solve for the YTM is through trial and error or using a financial calculator or spreadsheet tool like Excel. The process involves testing different interest rates until the sum of the present value of the coupons and face value equals the bond price.
Using Excel’s RATE function:
In Excel, we can use the RATE function to calculate the YTM by inputting the following:
- N = 12 (years to maturity)
- PMT = 65 (coupon payment)
- PV = -850 (current price, negative because it’s a cash outflow)
- FV = 1000 (face value)
The Excel formula would look like this:
=RATE(12, 65, -850, 1000)This yields an approximate YTM of 8.52%.
Explanation:
The bond’s yield to maturity represents the annual return an investor can expect to earn if the bond is held to maturity, assuming that the coupons are reinvested at the same rate as the YTM. In this case, the bond is selling below its par value (at $850), indicating that the bond’s yield is higher than the coupon rate of 6.5%. The bondholder will receive the annual coupon payments, plus the $1,000 face value at maturity, and the yield to maturity reflects the return that equates the present value of these future payments to the current bond price.
Thus, the yield to maturity for Cillian Corp’s bond is approximately 8.52%.