From the course: Applied Fixed Income

PV of a zero-coupon bond

From the course: Applied Fixed Income

Start my 1-month free trial Buy for my team

PV of a zero-coupon bond

“

- [Instructor] To price a zero-coupon bond, we simply go back to our trusty PV formula. We know that a zero-coupon bond will mature at 100 or whatever par value is, so we simply use that as a fee. Then as there are no coupon payments, we don't need to worry about discounting any other cash flows, so we simply have to discount the one cash flow, which is the FV, the future value. To do that, we use the formula PV, the present value or the price of the zero, is equal to FV multiplied by 1 over 1 + YTM raised to the power of N. Where YTM is the yield to maturity, and N is the number of periods or years to maturity. Let's look at a simple example of a five year zero-coupon bond that has a YTM of 4%. Subbing in the numbers for YTM, we get a PV of 82.19. Now, if we know the price, which is also the same as the present value, we can work backwards to solve for yield to maturity using the same formula and just rearranging the terms. The formula now becomes yield to maturity is equal to the future value divided by the present value raised to the power of 1 over N. Then, subtract one from the result to get your yield to maturity, YTM, in percentage terms. Using our earlier example, if we know the PV is 82.19 and FV is 100 and N is 5, we can solve for YTM, which gives us, not surprisingly, 4%.

Contents