Question

Linville Corporation issued 12-year, par $1,000 bonds seven years ago at a coupon rate of 5 percent. If these bonds currently sell for 85 percent of par value, what is its yield to maturity (YTM)? 9.7 6.2% 12.5% 8.8%

Answer 1

The yield to maturity (YTM) of the bond is approximately 6.2%.

Step-by-step explanation:

The yield to maturity (YTM) of the bond can be calculated by determining the current price of the bond in relation to its future cash flows.

In this case, the bond was issued at a par value of $1,000 and currently sells for 85% of that value, or $850. The bond has 5% coupon rate, which means it pays $50 in interest annually for 12 years.

To calculate the YTM, we can use the present value formula. The bond has 5 remaining years until maturity, so we discount the future cash flows at the YTM rate until the bond reaches its par value of $1,000. By trial and error or using financial calculators, we find that the YTM for this bond is approximately 6.2%.

Answer 2

To find the yield to maturity (YTM) of Linville Corporation's bonds, one must consider the annual coupon payments, the face value upon maturity, and the bond's current price. YTM is an internal rate of return that accounts for all future cash flows discounted to the present value, representing interest payments and capital gains. The actual calculation requires using a financial calculator or spreadsheet to solve for the discount rate.

Step-by-step explanation:

To determine the yield to maturity (YTM) for Linville Corporation's bonds, we first need to consider the cash flows the bondholder receives and the current market price of the bond. The bondholder will receive annual coupon payments of 5% of the $1,000 face value, which equals $50 per year. Additionally, at the end of the bond term, the bondholder will receive the face value of the bond, which is $1,000. Given that the bonds are currently selling for 85% of par value, the purchase price is $850. We can then use these figures to calculate the YTM, which represents the internal rate of return on the bond investment, reflecting both the interest payments and any capital gains or losses.

Importantly, we should recognize that the YTM calculation is a bit more complex than a simple yield calculation. It involves finding the discount rate that equates the present value of all future cash flows from the bond (coupon payments and the par value at maturity) to the bond's current price. This is often done using a financial calculator or spreadsheet software because it requires solving for the interest rate in the present value formula, which is not straightforward algebraically.

Without performing the entire calculation step by step here, we understand that the YTM would be higher than the coupon rate of 5% since the bond is currently selling below par. The total return includes the periodic coupon payments plus the capital gain realized by the bond's increase in value from $850 to $1,000 over the remaining life of the bond. However, YTM would also consider the time value of money and the remaining interest payments when discounting the future cash flows.