Pricing and Yields · Bonds Explained

Start with one future payment

Suppose a hypothetical bond will pay $1,000 in one year and has no coupon. If the required annual return is 5%, its present value is $1,000 ÷ 1.05, or $952.38. A buyer paying that price earns 5% if the payment arrives in full on time.

If investors instead require 6%, the same payment is worth $1,000 ÷ 1.06, or $943.40. The contract has not changed. The price adjusts so that the unchanged payment offers the newly required return.

Extend the idea to coupons

A coupon bond is a series of payments. Discount each coupon and principal payment for its own time interval, then add their present values. Using a single yield provides a convenient summary. A fuller valuation can use a separate discount rate for each maturity.

For a two year bond paying $50 annually and $1,000 principal, a 5% annual yield produces $50 ÷ 1.05 plus $1,050 ÷ 1.05 squared, equal to $1,000. At a 6% yield, the same calculation gives approximately $981.67.

Distinguish cause from measurement

A quoted yield can rise because benchmark interest rates rise, credit quality deteriorates or liquidity becomes less attractive. These explanations have different implications even when the immediate price direction is similar.

Do not infer that every price fall is an opportunity. A lower price may reflect a lower probability of receiving the promised cash flows. Discounting payments assumes a particular cash flow scenario, which must be examined separately.

Keep the horizon visible

If you sell before maturity, the sale price contributes to your realised return. If you hold to maturity and the issuer pays, interim market fluctuations still affect opportunity cost and your ability to sell early. A plan that relies on never needing liquidity should be tested against realistic spending needs.

Try it yourself

What is the present value of a certain $1,000 payment in one year at a 4% annual discount rate?

Show the worked answer

It is $1,000 ÷ 1.04 = $961.54, rounded. A lower required return gives a higher present value for the same payment.

Further reading

Educational material. Examples are hypothetical and do not recommend a security or a personal allocation. Contract terms and market conventions vary.

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