**Zero Coupon Bond Effective Yield = [F ÷ PV]**^{(1 ÷ n)}** – [ 1 ]**

F = face value

PV = present value

n = number of periods

Zero coupon bond effective yield helps to determine thereturn on the zero coupon bond. Basically, zero coupon bond do not offerdividends at all at any period of time however, it is sold at a discount fromface value. That’s why some time zero coupon bond is also known as discountbond.

Although bond equivalent value can also be used for that purpose, however zero coupon bond effective yield do much better job. Let’s suppose an example where an individual buys zero coupon bonds for $700 having a face value of $1,700 on maturity. No dividends are available during the investment tenure and profits are only available by selling these bonds.

## How zero coupon bond effective yield formula induced?

The formula for the calculation of zero coupon effectiveyield is derived by using the present value of a zero coupon bond formula;

Zero coupon bondvalue = F ÷ [(1 + r)^{t}]

We can rearrange the equation above by first multiplyingboth sides with ** (1 + r)^{t}** and then withPV (i.e. zerocoupon bond value) to get;

F/PV = (1 + r)^{t}

The formula above will then become as;

(F/PV)^{(1 ÷ t)} = 1 + r

Now if we subtract ** 1** from both sides of the equation,then we will get equation as available at top of this page.

### Zero coupon bond effective yield vs. Bond equivalent yield formula

Zero coupon bond effective yield formula takes in to accountthe compounding effect while calculating the rate of return. That’s whyfinancials analysts prefer to select zero coupon bond effective yield equationfor long-term investments or bond’s yield calculation. On the other side thebond equivalent yield formula does not consider the compounding effect anddirectly calculates the rate of return for the period.

Bond equivalent yield is frequently used to calculate theshort-term bond investment. It is most quick calculation for bond yield especiallyfor the cases where maturity date comes within a year.

To understand the compounding effect with zero coupon bondeffective yield let’s consider an example for understanding. For instance if adiscount bond have a maturity time of 7 years and we need to take in to accountthe compounding effect along with time value of money concept. This calculation becomes especially important when anumber of investment options are available to compare and select the mostprofitable one.

An investment which pays 7% per annum is not equivalent to adiscount bond which pays 145% after 7 years. This is due to the compoundingeffect within the regular investment approach. The return for such aninvestment would be;

= (1 + 0.07)^{7}

= 160%

So the return of the investment will be 160% after 7 yearswhile on the other side the discount bond gives 145% at the end of maturityperiod. This is the way zero coupon bond effective yield can be very helpfulfor making decisions when you have multiple options available for decisionmaking.