Lesson 1 of 8 · 13 min

Present value and discount (zero-coupon) bonds

A cash flow received later is worth less today, and a zero-coupon bond's price is simply its principal discounted back at the market rate.

In short

Compounding and discounting are one equation: $FV_t = PV(1+r)^t$ , so $PV = FV_t/(1+r)^t$ .
Fixed-income cash flows follow three patterns: discount, periodic interest (coupon) and level payment.
A discount (zero-coupon) bond pays only its principal at maturity. Its whole return is the gap FV − PV.
Price and yield move in opposite directions. If the yield does not change, the price drifts toward par as maturity approaches.
With a negative yield the price is above par and falls (amortizes) to par over time.
More frequent compounding at the same stated rate lowers the PV. Continuous compounding gives the lowest PV: $PV = FV e^{-rt}$ .
The effective annual rate $(1 + R_s/m)^m - 1$ rises with compounding frequency, by ever smaller steps, toward $e^{R_s} - 1$ .

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