You purchase a bond for $875. It pays $60 a year (semiannual coupon is 3%),
&the bond matures after 10 years. What is the yield to maturity?
To calculate the yield to maturity (YTM) of a bond, you need to use the formula and manipulate it to solve for the interest rate. The formula to calculate the YTM is as follows:
Bond Price = (Coupon Payment / (1+YTM)^1) + (Coupon Payment / (1+YTM)^2) + ... + (Coupon Payment + Face Value / (1+YTM)^n)
Where:
Bond Price = Price of the bond
Coupon Payment = The periodic payment the bond pays (in this case, $60)
YTM = Yield to Maturity (the interest rate we need to solve for)
n = Number of periods until maturity (in this case, 10 years)
To solve for YTM, you can use trial and error or use Excel to find the rate. Here's an example of how you can solve it using Excel:
1. Create a new Excel spreadsheet.
2. In cell A1, enter -875 (the negative sign represents the cash outflow of the initial investment in the bond).
3. In cells A2 to A21 (representing 20 periods), enter 60 (the semiannual coupon payment)
4. In cell A22, enter 1000 (the face value of the bond).
5. In cell A23, enter 0 (this is the cash inflow at maturity).
6. In cell B23 (or any empty cell), enter the following formula:
=BondPriceByYield(A1:A22, B1)
This formula uses the BondPriceByYield function in Excel to calculate the bond price given a certain yield.
7. To calculate the yield to maturity, we need to determine the rate that makes the bond price equal to zero. Use the Goal Seek feature in Excel:
a. Go to the Data tab and click on "What-If Analysis."
b. Select "Goal Seek."
c. Set the "Set Cell" to B23 (the cell containing the bond price formula).
d. Set the "To value" to 0.
e. Set the "By changing cell" to B1 (the yield to maturity cell).
f. Click "OK" to let Excel determine the yield to maturity that will make the bond price equal to zero.
After performing these steps, Excel will display the YTM (yield to maturity) in cell B1. In this case, the yield to maturity is approximately 6.23%.
Therefore, the yield to maturity for this bond is approximately 6.23%.