← All techniques

Finance · level 1

Zero-coupon yield

Price and yield are the same fact stated two ways. For a zero the algebra is one root; for a coupon bond you interpolate, but the intuition is identical: yield up, price down.

Worked example: A 10-year zero-coupon bond with $1,000 face trades at $463.19. Yield to maturity?

price$463.19
face$1,000
years10
YTM8%

Step by step

  1. 1

    YTM of a zero

    (F / P)^(1/n) − 1 = (1000 / 463.19)^(1/10) − 1 = 8%

  2. 2

    Sanity

    The discount is 53.7% over 10 years — about 5.4 points a year simple, so the compound yield is a little higher.

  3. 3

    Spot rate

    Zero yields are the spot rates that build the yield curve; coupon bonds are portfolios of zeros.

A 10-year zero-coupon bond with $1,000 face trades at $463.19. Yield to maturity? = 8

The theory behind it

Intuition

Finance is time and risk applied to cash: move every cash flow to the same date at a rate that reflects its risk, then compare.

Common pitfalls

  • ×Discounting a nominal flow at a real rate (or vice versa).
  • ×Mixing enterprise-value and equity-value numbers in the same ratio.

In the interview

Valuation, WACC, LBO and accretion rounds — where a wrong bridge is a wrong answer.