Bond valuation

A bond is a debt security through which an investor lends money to a company, government or other issuer. In return, the issuer promises specified payments—commonly periodic interest and repayment of principal at maturity. Because many bonds trade after issuance, valuation determines the present price of those promised, but not always certain, cash flows.

When to use it

• To estimate a bond’s value when considering a purchase or sale.

• To assess the cost and attractiveness of raising capital through a bond issue.

Origins

Tradable public debt has a long history. The Republic of Venice used forms of funded government borrowing from the twelfth century, and early trading companies such as the Dutch East India Company issued debt securities. National governments increasingly financed themselves through bonds from the sixteenth century onward. Modern bond markets encompass sovereign, municipal and corporate obligations on an enormous scale, making the valuation and trading of fixed-income cash flows a central part of finance.

What it is

A bond’s value is the present value of its expected future cash flows, applying the time value of money. A conventional bond specifies a principal or face value, a coupon rate and a maturity date. Valuation has three stages:

1st. Estimate the expected cash flows: For a plain fixed-rate bond, the contractual coupons and principal are straightforward. Expected cash flows may differ from contractual amounts when default, restructuring, call provisions or conversion rights are possible. A highly rated sovereign and a repeat sovereign defaulter should not be valued as though the certainty of payment were identical.

1. Select an appropriate discount rate: Required yield reflects the time value of money and compensation for risks including credit, liquidity and optionality. If market yields rise from 2 to 3 per cent, an existing fixed coupon becomes less attractive and its price falls; when required yields fall, price rises. Evidence that an issuer is short of cash normally increases the required credit spread and depresses the bond’s value.

1. Calculate present value: Discount every expected coupon and principal payment at the appropriate rate for its timing and risk, then add the results.

Bonds may be held to maturity for their contractual payments, subject to default and embedded options, or traded in the secondary market. Their prices adjust continually to interest rates, inflation expectations, credit quality, liquidity, supply and demand, tax treatment and contractual features. Some influences belong to the issuer; others reflect the wider market.

How to use it

Consider Redwood Lane Ships, a listed company planning a $30 million bond issue to finance a shipbuilding facility in Maine. Each bond has:

• $1,000 face, or par, value: the principal on which the coupon is calculated and the amount repaid at maturity, assuming no default. It is not necessarily the market price.

• A five per cent annual coupon: Redwood Lane Ships pays $50 at the end of each year.

• A ten-year term: issued on 1st January 2015 and maturing on 1 January 2025.

Assume comparable issuers trade at a 5 per cent yield to maturity (YTM). YTM is the single discount rate that equates the present value of all promised coupons and principal with the bond’s market price, assuming the bond is held to maturity and payments occur as scheduled. Because the coupon rate equals the required yield in this example, the value is $1,000, or par.

If the required YTM falls to 3 per cent, the bond’s fixed 5 per cent coupon becomes more attractive and its price rises above par. If the required YTM increases to 7 per cent, the coupon is less attractive than current alternatives and the price falls below par. Price and yield therefore move in opposite directions.

Economic conditions change interest rates, while new information about the issuer can alter its credit spread. The bond price responds to both. If the issuer remains able to pay, required yield is otherwise unchanged and no embedded option intervenes, a premium or discount bond converges towards par as maturity approaches. Redwood Lane Ships’ ten-year bond valued at $1,170.60 with a 3 per cent YTM will therefore pull towards $1,000 over time. The figures below show the same bond with three years remaining.

Under the same conditions, a discount bond also moves towards par as maturity nears. Real securities take many forms, including Treasury Inflation-Protected Securities, zero-coupon, callable and convertible bonds. They differ in payment frequency, inflation adjustment, whether the issuer can redeem them early and whether the investor can convert the debt into equity. Financial institutions have created increasingly complex variants; the 2008 crisis demonstrated how severe the consequences can be when structure and underlying risk are poorly understood.

Top practical tip

Separate the contractual coupon from the market-required yield. Revalue every remaining cash flow when rates, credit or liquidity change, and compare bonds using yield-to-maturity, yield-to-call or yield-to-worst as appropriate to their terms.

Top pitfall

Do not assume a regular coupon makes a bond safe. Credit, interest-rate, inflation, liquidity, call and structural risks can produce large losses, as the collapse of mortgage-backed securities in 2008–2009 demonstrated.

Further reading

• Fisher, L. and Weil, R.L. (nineteen seventy-one). “Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies.” Journal of Business.
• Fabozzi, F.J. and Fabozzi, F.A. (twenty twenty-one). Bond Markets, Analysis, and Strategies. MIT Press.