A bond has a $l000 par value, l0 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
c. Assuke that the yield to maturity remains constant for the next 3 years, what will the price be 3 years from today?
a. 7.11%
b. N = 10, PV = -985, PMT = 70, FV = 1000
YTM = 7.2157% = 7.22%
c. N = 7, I/YR = 7.2157, PMT = 70, FV = 1000
PV = $988.46
a. Its current yield can be calculated by dividing the annual coupon payment by the current market price:
Current Yield = (Annual Coupon Payment / Current Market Price) x 100%
The annual coupon payment is 7% of the $1000 par value, which is $70.
The current market price is $985.
Current Yield = (70 / 985) x 100% ≈ 7.11%
b. The yield to maturity (YTM) is the total return anticipated on a bond if held until it matures. It can be calculated using the current market price, the par value, the coupon rate, and the number of years to maturity. Since the bond's coupon rate is 7% and it sells at a discount, the yield to maturity will be higher than the coupon rate.
To calculate the YTM, we need to find the discount rate at which the present value of the bond's future cash flows (coupon payments and principal) equals its market price.
Unfortunately, without any more information about the bond's cash flows or market conditions, I cannot provide an exact calculation for the YTM.
c. Assuming the yield to maturity remains constant for the next 3 years, the price of the bond after 3 years would depend on the prevailing market conditions and interest rates at that time. If interest rates remain constant, the bond would likely continue to sell at a discount since its yield to maturity is higher than its coupon rate. However, if interest rates rise, the price of the bond would decrease further. Conversely, if interest rates decrease, the price of the bond would increase.
To determine the exact price of the bond 3 years from today, we would need information about future interest rates and market conditions. Without this information, I cannot provide a specific answer.
a. To calculate the current yield, we need to divide the annual coupon payment by the market price of the bond.
The annual coupon payment can be calculated by multiplying the coupon rate (7 percent) with the par value ($1000):
Annual coupon payment = 7% * $1000 = $70
The current yield is then calculated by dividing the annual coupon payment by the market price ($985):
Current yield = $70 / $985 = 0.0711 or 7.11%
b. To calculate the yield to maturity, we will use the present value formula and solve for the yield.
The present value of the bond can be calculated as the present value of the annual coupon payments plus the present value of the final par value:
Present value of the coupon payments = (Coupon payment / yield) * (1 - (1 + yield)^-number of years) / yield
Present value of the coupon payments = ($70 / yield) * (1 - (1 + yield)^-10) / yield
Present value of the par value = $1000 / (1 + yield)^10
The yield to maturity is the discount rate that makes the present value of the bond equal to its market price ($985). It can be calculated by using trial and error or using Excel's IRR function.
c. Assuming the yield to maturity remains constant for the next 3 years, the price of the bond 3 years from today can be calculated by finding the future value of the coupon payments and the final par value.
Future value of the coupon payments = Annual coupon payment * (1 + yield)^3 + Annual coupon payment * (1 + yield)^2 + Annual coupon payment * (1 + yield)
Future value of the coupon payments = $70 * (1 + yield)^3 + $70 * (1 + yield)^2 + $70 * (1 + yield)
Future value of the par value = $1000 * (1 + yield)^3
The price of the bond 3 years from today is the sum of the future value of the coupon payments and the future value of the par value.
To answer these questions, we need to understand the concepts of current yield, yield to maturity, and how bond prices change over time.
a. Current Yield:
The current yield is calculated by dividing the annual coupon (interest) payment by the price of the bond and expressing it as a percentage. In this case, the annual coupon payment is 7% of the $1,000 par value, which is $70. Therefore, the current yield is:
Current Yield = (Annual Coupon Payment / Bond Price) * 100%
Current Yield = ($70 / $985) * 100% ≈ 7.11%
b. Yield to Maturity:
The yield to maturity (YTM) is the total return anticipated on a bond if it is held until maturity. It considers both the coupon payments and any gain or loss from the difference between the purchase price and the par value at maturity. There is no direct formula to calculate YTM, but it can be solved using financial calculators or software. Alternatively, you can use trial and error by plugging in different interest rates until you find the one that matches the bond price ($985) most closely.
c. Price after 3 Years:
Assuming the yield to maturity remains constant, the bond price will be affected by changes in market interest rates. If interest rates decline, the price of the bond will increase, and if interest rates increase, the price of the bond will decrease.
Unfortunately, without the knowledge of the specific yield to maturity or the future interest rate environment, we cannot determine the price of the bond after 3 years.
Remember that bond prices move inversely to interest rates. When interest rates go down, bond prices tend to go up, and when interest rates increase, bond prices tend to go down.