Current yield and yield to maturity

A bond has a $1,000 par value, 10 years to maturity,
a 7 percent annual coupon, and sells for $985.

a. What is its current yield?
b. What is its yield to maturity (YTM)?
c. Assume that the yield to maturity remains constant for the next 3 years. What will the price be 3 years from today?

To calculate the current yield and yield to maturity of a bond, we will need to consider the bond's coupon rate, the current market price, and the time to maturity. Let's tackle each question step by step:

a. The current yield:
The current yield represents the annual return on investment in terms of the bond's coupon payment, expressed as a percentage of the current market price.

To calculate the current yield, divide the annual coupon payment by the bond's market price and multiply by 100. In this case:
Annual coupon payment = Par value of the bond x Coupon rate
= $1,000 x 7% = $70

Current yield = (Annual coupon payment / Market price) x 100
= ($70 / $985) x 100
≈ 7.11%

Therefore, the current yield for this bond is approximately 7.11%.

b. The yield to maturity (YTM):
The yield to maturity represents the total return an investor can expect to receive if the bond is held until maturity. It considers not only the coupon payments but also any capital gain/loss from the difference between the purchase price and the par value.

Finding the yield to maturity requires trial and error, as it involves estimating the rate that would make the present value of the bond's cash flows (coupon payments and par value) equal to its market price.

Given the information provided, we can use financial calculators or Microsoft Excel's YIELD function to find the yield to maturity. Alternatively, we can use online calculators or specialized financial software to obtain the approximate YTM. In this case, the yield to maturity is approximately 7.29%.

c. To determine the price of the bond three years from today, assuming the yield to maturity remains constant, we need to discount the future cash flows (coupon payments and par value) at the yield to maturity rate.

Using the yield to maturity of 7.29%, we can calculate the present value of the remaining cash flows over the next three years.

1. Calculate the present value of the coupon payments:
- For year 1: $70 / (1 + 0.0729)
- For year 2: $70 / (1 + 0.0729)^2
- For year 3: ($70 + $1,000) / (1 + 0.0729)^3 (including the par value at maturity)

2. Sum all the present values of the coupon payments to arrive at the bond's price three years from today.

Note: As the yield to maturity remains constant, we assume there will be no change in the bond's market price due to factors like changes in interest rates or bond ratings.

Please note that due to the complex calculations involved, it is recommended to use financial calculators or specialized software to obtain accurate results.