# Bond Valuation

> Pricing, yields, duration & interest rate risk

**Track:** Valuation  
**Read time:** 12 min

**Canonical:** http://localhost:3000/topics/bond-valuation

**Markdown:** http://localhost:3000/topics/bond-valuation/md

Bonds are the purest application of time value of money: a bond is nothing but a schedule of promised cash flows, and its price is the present value of those promises. Yet the bond market dwarfs the stock market globally, funds every government and most corporations, and sets the interest rates that echo through every other valuation.

This guide explains how bonds are priced, what yield to maturity really means, why prices fall when rates rise, and how duration quantifies that sensitivity. Understanding bonds is not optional in corporate finance — it defines the cost of debt that feeds WACC and every DCF.

## What Is a Bond?

A bond is a loan packaged as a tradable security. The issuer borrows a face value (par, typically $1,000) and promises to pay periodic coupons — interest — for the bond’s life, then repay the principal at maturity. A 10-year, 5% annual-coupon bond promises ten $50 payments and $1,000 at the end.

Key terms define the promise: maturity date, coupon rate, payment frequency, and any embedded options such as call features that let the issuer repay early. Credit quality varies enormously — from government bonds considered nearly risk-free to high-yield "junk" bonds — and that quality is embedded in the yield investors demand.

- Face value (par): the principal repaid at maturity, usually $1,000.
- Coupon: periodic interest payment = coupon rate × face value.
- Maturity: when the principal is repaid; terms range from 1 to 30+ years.
- Issuer credit quality determines the yield spread over government bonds.

## Bond Pricing — Discounting the Promises

A bond’s fair price is the present value of all promised cash flows, discounted at the market yield required for bonds of that risk and maturity. The price is simply the PV of an annuity (the coupons) plus the PV of a single sum (the face value).

The relationship between price and yield produces three states. When the required yield equals the coupon rate, the bond trades at par. When the required yield rises above the coupon, the bond trades below par (a discount) — its fixed coupons are below market, so only a cheaper entry price restores fair returns. When the required yield falls below the coupon, the bond trades at a premium.

**Formula** — C = coupon, F = face value, y = yield per period

```
Price = Σ_{t=1}^{n} C / (1 + y)^{t} + F / (1 + y)^{n}
```

> **Pricing a 5% bond**
>
> A 10-year bond pays 5% annual coupons ($50) with face value $1,000. If the market yield is 6%: price = 50 × [1 − 1.06^−10]/0.06 + 1,000/1.06^10 = $926.40. The bond sells at a discount because its coupons are below the market rate. At a 4% yield the same bond would price at $1,081.11 — a premium.

## Yield to Maturity — The Bond’s True Rate

Yield to maturity (YTM) is the single discount rate that makes the present value of all promised payments equal today’s market price. It is the bond’s internal rate of return: the annualized return you earn if you buy at the current price and hold to maturity, receiving every payment and reinvesting coupons at the same rate.

Because YTM solves a polynomial, it is found numerically — the same bisection used in IRR calculators. YTM lets investors compare bonds with different coupons, maturities, and prices on one scale. Note the assumption: reinvesting coupons at the YTM is optimistic in falling-rate environments, which is why realized returns can differ.

**Formula** — YTM is the rate that equates price and PV

```
Price = Σ C / (1 + YTM)^{t} + F / (1 + YTM)^{n}   →   solve for YTM
```

## Interest Rate Risk & Duration

Bond prices and interest rates move in opposite directions — the see-saw law. When market yields rise, existing fixed coupons look less attractive, so prices fall; when yields fall, prices rise. The longer the cash flows are pushed into the future, the bigger the swing: long-maturity, low-coupon bonds are the most rate-sensitive.

Duration measures that sensitivity precisely. Macaulay duration is the weighted average time to receive the bond’s cash flows; modified duration converts it into the approximate percentage price change for a 1% yield move: ΔP/P ≈ −D × Δy. A bond with modified duration 7 loses roughly 7% of its price if yields rise one percentage point. Duration is why "safe" government bonds can deliver brutal losses in rate shocks — as 2022 demonstrated worldwide.

**Formula** — Modified duration as price sensitivity

```
ΔP / P ≈ − D_{mod} × Δy
```

> **The 2022 lesson**
>
> A 10-year Treasury with modified duration around 8 lost roughly 15–18% in 2022 as yields rose about 2.5 points — worse than many stock portfolios that year. Duration math predicted it exactly: −8 × 2.5% ≈ −20% before convexity. Investors who "knew" bonds were safe learned that duration is risk too.

## Credit Risk & Ratings

Beyond interest rate risk sits credit risk — the chance the issuer fails to pay. Rating agencies (Moody’s, S&P, Fitch) grade issuers from AAA down through investment grade (BBB−/Baa3 and above) to high yield and default. Lower ratings demand higher yields: the spread over government bonds compensates for expected losses and risk aversion.

Spreads widen sharply in recessions and panic phases, causing high-yield bond prices to fall even when Treasury rates are unchanged. Corporate treasurers watch their own credit spreads because they set the cost of new debt — which flows directly into WACC and the hurdle rates used throughout capital budgeting.

## Why Bonds Matter in Corporate Finance

Bond mathematics is embedded in every corner of this hub. The yield on a company’s bonds is the direct estimate of its pre-tax cost of debt for WACC. Duration thinking appears in managing pension obligations and in valuing any fixed-payment stream, from leases to structured settlements.

For analysts, bonds also provide the risk-free benchmark that anchors CAPM: the 10-year government yield is the r_f in every equity expected-return calculation. In short, you cannot do corporate finance without bonds — they are the floor from which all other returns are measured.

## Key takeaways

- A bond price is the PV of coupons (annuity) plus PV of face value (single sum).
- Yield up → price down; bonds trade at par, discount, or premium depending on coupon vs yield.
- YTM is the bond’s IRR — the return if held to maturity with coupons reinvested.
- Duration converts yield moves into price moves: ΔP/P ≈ −D × Δy.
- Corporate bond yields set the cost of debt in WACC and anchor CAPM’s risk-free rate.

## Contact

Email: [webrank0001@gmail.com](mailto:webrank0001@gmail.com)
Contact form: http://localhost:3000/contact