Zero coupon bond yield is calculated by using the present value equation and solving it for the discount rate. The resulting rate is the yield. It is both the discount rate that is revealed by the market situation and the return rate that investors expect from the bond. The zero coupon bond yield helps investors decide whether to invest in bonds.
A bond is a note that companies sell to raise money — investors trade the purchase price for a future stream of payments. Some bonds make payments, or coupons, periodically, but zero coupon bonds only have one payment at the time that they mature. The amount of the payment is called the par value or face value of the bond. Investors decide whether to invest in bonds on the basis of the bond’s yield, or the return on the market price. Essentially, a bond is a loan the investor gives to the company, and the yield is the interest rate the investor receives in return.
There are different concepts that share the name of yield. For example, current yield is the coupon payment divided by the market price of the bond. Since zero coupon bonds pay no coupons, they have no current yield. Generally, when investors talk about a bond’s yield, they are referring to its yield to maturity — this is a measure of the return that an investor would get if he reinvested each payment that the bond made. For most bonds, the measure is somewhat unrealistic because investors do not always reinvest coupons at the optimal rate; however, the zero coupon bond yield is more accurate since there is no assumption of reinvestment.
Generally, you calculate yield to maturity by writing out the present value formula for the bond using a variable, y, in place of the discount rate. Then, you plug in values for the yield and see if the present value matches the actual market price. You adjust the yield value if it does not. This process is called guess and check. Even the calculators that find yield to maturity use this method; they simply iterate it.
The zero coupon bond yield is easier to calculate because there are fewer components in the present value equation. It is given by Price = (Face value)/(1 + y)^{n}, where n is the number of periods before the bond matures. This means that you can solve the equation directly instead of using guess and check. The yield is thus given by y = (Face Value/Price)^{1/n} - 1.