How to calculate the price and yield of a zero-coupon bond
About this lesson
In this video, I will explain a zero-coupon bond and how to calculate its yield to maturity.
What a zero-coupon bond is
A zero-coupon bond pays no interest along the way. You buy it at a deep discount and receive the full face value at maturity. The difference is your return. US Treasury STRIPS and savings bonds work this way.
The price
Price = Face value ÷ (1 + y)T
Example: a 10-year zero with a $1,000 face value and a 5% yield:
1,000 ÷ 1.0510 = 1,000 ÷ 1.6289 = $613.91
In Excel: =PV(5%,10,0,1000) → −613.91
The yield to maturity
Turn the formula around:
y = (Face value ÷ Price)1/T − 1
Example: a 10-year zero costs $500:
(1,000 ÷ 500)1/10 − 1 = 20.1 − 1 = 7.18%
In Excel: =RRI(10,500,1000) → 7.18%
Key features
- No reinvestment risk: there are no coupons to reinvest, so the yield you lock in is the yield you earn if you hold to maturity.
- High interest-rate risk: all the cash comes at the end, so the price reacts strongly to yield changes. A zero’s duration equals its maturity.
- Taxes: in the US, the yearly increase in value is usually taxed each year, even though you receive no cash until maturity.