An AT&T bond has 10 years until maturity, a coupon rate of 8 percent, and sells for $1,050.
a. What is the current yield on the bond?
b. What is the yield to maturity?
To calculate the current yield and yield to maturity of an AT&T bond, you will need to use the formula and some information provided.
a. Calculating the current yield:
The current yield is the annual interest payment divided by the current market price of the bond, expressed as a percentage.
Given:
- Coupon Rate = 8% (annual interest payment as a percentage of the face value)
- Market Price = $1,050 (current selling price of the bond)
1. Calculate the annual interest payment:
Annual Interest Payment = Coupon Rate * Face Value
The face value of the bond is usually $1,000, since most bonds have a $1,000 face value.
Annual Interest Payment = 0.08 * $1,000 = $80
2. Calculate the current yield:
Current Yield = Annual Interest Payment / Market Price * 100%
Current Yield = $80 / $1,050 * 100% ≈ 7.62%
Therefore, the current yield on the bond is approximately 7.62%.
b. Calculating the yield to maturity:
The yield to maturity (YTM) is the total return anticipated on a bond if it is held until maturity. It is the internal rate of return (IRR) of the bond's future cash flows.
Given:
- Coupon Rate = 8% (annual interest payment as a percentage of the face value)
- Market Price = $1,050 (current selling price of the bond)
- Maturity = 10 years (time left until maturity)
To calculate the yield to maturity, you can either use a financial calculator or an Excel spreadsheet. However, I'll provide you with the steps to calculate it using Excel:
1. Open Excel and input the following information in a column:
- Year (starting from 0)
- Cash Flows (annual interest payment + face value repaid at maturity)
2. Calculate the cash flows for each year:
For each year, the cash flow will be the annual interest payment ($80) and the face value ($1,000) repaid at maturity, except for the last year, where the face value is repaid without the annual interest payment.
3. Use the "IRR" function in Excel to calculate the yield to maturity:
- Select a cell where you want the result to appear.
- In that cell, type "=IRR(Cash Flows Range)" and press Enter. Replace "Cash Flows Range" with the range of the cash flows you calculated.
The result will be the yield to maturity of the bond.
Please note that the yield to maturity is an estimate and assumes that all future coupon payments are reinvested at the same rate as the bond's yield.