Zero-Coupon Bond Yield To Maturity (YTM)

Updated: Mar 7, 2021

How do I find the YTM of a zero-coupon bond? A zero-coupon bond pays no coupons and instead, the profit made from investing in a zero-coupon bond is a result of the difference between the purchase price and par value. In other words, a zero-coupon bond does not many regular payments, it essentially only makes one and it is the par value of the bond.




There are two ways:

1) Use a financial calculator

2) Use a formula for zero-coupon bond yield





1) Find the YTM of a zero-coupon bond using a financial calculator



Example:

You buy a zero-coupon bond with a par value of $100 for $97. The bond matures in 2 years and 6 months.


How to Solve YTM

Enter the Following into your financial calculator


Enter 2.5 then push N

Enter -97 then push PV

Enter 0 then push PMT

Enter 100 then push FV

push CPT (top left of BAII PLUS)

push I/Y

The Answer = 1.22582%

The YTM of the zero-coupon bond is 1.22582%


Check:

$100/(1.0122582^2.5)=$97


2) Find the YTM of a zero-coupon bond using a formula

Formula:

YTM +1 = (par value / purchase price) ^ (1/n)



Test

(100/97)^(1/2.5) = YTM+1

1.0122582 = YTM+1

1.22582% = YTM


The Answer = 1.22582%

The YTM of the zero-coupon bond is 1.22582%


Dealing with periods of less than a year?

In order to calculate the YTM of a bond maturing at a period other than a round year or half-year simply add the fraction of a year to n.


For example, if a bond matures in 725 days we could simply divide 725/365 to find our n value. In this case, it would be 1.98630