Question

A bond has a $1,000 par value, 15 years to maturity, and a 8% annual coupon and sells for $1,080.

What is its yield to maturity (YTM)?

Answer 1

Yield to Maturity (YTM) is the total return expected from a bond if held to maturity, factoring in all coupon payments and the redemption of face value. It is calculated by equating the present value of future cash flows with the bond's current price, considering the bond's coupon rate and market price. The calculation provided does not accurately represent YTM as it appears to describe a simple annual return.

Step-by-step explanation:

The calculation of Yield to Maturity (YTM) is a process used to determine the total return an investor will receive by holding a bond until it matures. The YTM takes into account all future coupon payments, as well as the difference between the bond's current market price and its face value. To calculate YTM, the formula involves finding the interest rate that equates the present value of these future cash flows (the coupon payments and the repayment of the principal) to the bond's current price.

An important note here is that a bond's coupon rate remains fixed as expressed in the bond's terms; however, the market yield can vary based on changes in market interest rates. This is why a bond might sell for more (premium) or less (discount) than its face value. Knowing this, here's a simplified step to consider:

1. Calculate the annual coupon payment by multiplying the bond's face value by its coupon rate. For instance, an 8% coupon rate on a $1,000 bond would yield $80 per year.
2. If the bond is sold for $1080, the investor will have paid more than the face value. This means the yield to maturity will be less than the coupon rate, since the investor is paying a premium for the bond.
3. The YTM is the rate that equates the present value of the bond's future coupon payments and the repayment of the face value at maturity, with the current market price of the bond.

Calculating the exact YTM involves a complex iteration process, which is usually done using financial calculators or spreadsheet tools. The provided calculation from the information snippets, ($(1080 - $964)/$964 = 12%), is not correct for YTM, as it seems to reflect the calculation of return over a single year, not over the bond's entire life.