Table of Contents |
As with all financial securities, the true value of a bond can be calculated from the net present value of all the expected cash flows. If a bondholder holds a bond to maturity, they will receive interim interest payments at the coupon rate and the face value at maturity.
Consider the cash flows on a timeline. If we are going to receive these coupon payments and the face value at maturity, what is the interest rate at which the present value equals the price of the bond today?
We can determine this by directly solving the following equation:
In this formula, the variables are equivalent to:
Suppose a bond has a face value of $1,000, with a coupon rate of 8%, and five years left to maturity. The coupon payments are semi-annual and the bond is currently trading at $1,000, meaning it is trading at par. What is the yield of maturity?
Face Value: | $1,000 |
Annual Coupon Rate: | 8% |
Years to Maturity: | 5 |
Coupon Payments per Year: | 2 |
Current Bond Price: | $1,000 |
Yield to Maturity: | 8.00% |
The yield to maturity, or the internal rate of return, would be 8%, which is the same as the coupon rate. This is due to the fact that the bond is currently selling at par.
Suppose a bond has the same information as above, but now the bond is currently selling at $940. What is the yield of maturity? Do you think it will be 8%, higher than 8%, or lower than 8%?
Face Value: | $1,000 |
Annual Coupon Rate: | 8% |
Years to Maturity: | 5 |
Coupon Payments per Year: | 2 |
Current Bond Price: | $940 |
Yield to Maturity: | 9.54% |
The yield to maturity would actually be 9.54%. It is higher than the coupon rate because the current price is low at $940. If we are going to still get the face value at maturity in the same coupon payments, the net present value of this bond is worth more to us. We can say that this bond is selling at a discount.
Suppose we have the same bond as above, but the price today is $1,090. The bond is selling at a premium. What is the yield of maturity?
Face Value: | $1,000 |
Annual Coupon Rate: | 8% |
Years to Maturity: | 5 |
Coupon Payments per Year: | 2 |
Current Bond Price: | $1,090 |
Yield to Maturity: | 5.90% |
The yield to maturity would actually be 5.90%. It is lower than the coupon rate because the the bond is selling at a premium. Since we have to pay so much for it, the yield of maturity will be less.
Source: THIS TUTORIAL HAS BEEN ADAPTED FROM "BOUNDLESS FINANCE" PROVIDED BY LUMEN LEARNING BOUNDLESS COURSES. ACCESS FOR FREE AT LUMEN LEARNING BOUNDLESS COURSES. LICENSED UNDER CREATIVE COMMONS ATTRIBUTION-SHAREALIKE 4.0 INTERNATIONAL.