Bond and share valuation estimates what a financial security is worth today by discounting the cash flows investors expect to receive. The same present-value principle applies to bonds, preference shares and ordinary shares, but the cash-flow patterns and risks differ.
Bond valuation formula
A conventional coupon bond normally provides periodic interest and repayment of face value at maturity:
Bond value = Σ[C ÷ (1 + Kd)t] + [F ÷ (1 + Kd)n]
- C = coupon payment per period
- F = face or redemption value
- Kd = required return per period
- n = number of periods to maturity
Worked bond valuation example
A five-year bond has a face value of $1,000 and pays an 8% annual coupon. Investors require 10%.
Annual coupon = 8% × $1,000 = $80
Value = $80 × PV annuity factor (10%, 5) + $1,000 × PV factor (10%, 5)
Using factors of approximately 3.7908 and 0.6209:
Value = ($80 × 3.7908) + ($1,000 × 0.6209) ≈ $924.18
The bond sells below face value because its 8% coupon is lower than the 10% return currently required by investors.
Bond price and required return
- If coupon rate = required return, value is approximately equal to face value.
- If coupon rate > required return, the bond normally trades at a premium.
- If coupon rate < required return, the bond normally trades at a discount.
- When market yields rise, existing fixed-rate bond prices fall; when yields fall, prices rise.
Explore this relationship in bond valuation and changes in interest rates.
Zero-coupon and redeemable bonds
A zero-coupon bond has no periodic coupon, so its value is the present value of the redemption amount:
Zero-coupon bond value = F ÷ (1 + Kd)n
For bonds redeemable at a premium, use the actual redemption amount rather than face value. If coupons are paid semi-annually, divide the annual required return and coupon by two and double the number of periods.
Valuation of irredeemable preference shares
An irredeemable preference share pays a constant dividend indefinitely:
Preference share value = Annual preference dividend ÷ Required return
If the annual dividend is $9 and investors require 12%, value = $9 ÷ 0.12 = $75.
For redeemable preference shares, discount the dividends and redemption value over the remaining life. See valuation of preference shares.
Ordinary share valuation
Ordinary shares have no fixed maturity and dividends are uncertain. Their intrinsic value is the present value of expected dividends and any expected sale price.
Zero-growth dividend model
For a constant dividend forever:
P0 = D ÷ Ke
Gordon dividend growth model
If dividends are expected to grow at a constant rate indefinitely:
P0 = D1 ÷ (Ke − g)
- D1 = expected dividend next year
- Ke = required return on equity
- g = constant dividend growth rate
If the latest dividend is $4, expected growth is 5% and the required return is 12%:
D1 = $4 × 1.05 = $4.20
P0 = $4.20 ÷ (0.12 − 0.05) = $60
The constant-growth model requires Ke > g and is most suitable for a mature company with a sustainable dividend policy.
Multi-stage dividend valuation
A growing company may experience high growth for several years before moving to stable growth. A multi-stage model:
- forecasts dividends during the explicit high-growth period;
- calculates a terminal value when stable growth begins; and
- discounts every dividend and the terminal value to today.
This approach is more realistic than forcing one perpetual growth rate onto a changing business.
Choosing the required return
The discount rate should reflect the security’s risk, currency and cash-flow timing. Bond valuation considers current risk-free rates, maturity, liquidity, default risk and contractual features. Equity valuation may use the capital asset pricing model or another defensible cost-of-equity method.
Key valuation risks
| Risk | Valuation effect |
|---|---|
| Interest-rate risk | Higher required returns reduce present value, especially for long-duration securities. |
| Default or credit risk | A higher probability of missed payments increases the required return and reduces value. |
| Liquidity risk | Hard-to-trade securities normally require a return premium. |
| Growth-estimation risk | Small changes in Ke or g can materially change a dividend-growth valuation. |
| Call or conversion features | Embedded options change the expected cash-flow pattern and value. |
Common valuation mistakes
- using a historic coupon rate as the current required return;
- forgetting redemption value or using the wrong maturity;
- mixing annual cash flows with a semi-annual discount rate;
- using D0 instead of D1 in the Gordon model;
- assuming perpetual growth greater than or equal to the required return;
- ignoring default, liquidity, currency or call risk; and
- treating an estimated intrinsic value as a guaranteed market price.
Frequently asked questions
Why do bond prices fall when interest rates rise?
Existing coupons become less attractive relative to newly issued bonds, so the price falls until the expected return is competitive.
What is the difference between face value and market value?
Face value is the contractual amount normally repaid at maturity. Market value is the current price investors are willing to pay.
Can the Gordon model value every share?
No. It is unsuitable when dividends are absent, unstable, or expected growth is not sustainably lower than the required return.
What is intrinsic value?
It is an analyst’s present-value estimate based on expected cash flows and risk. Market price can differ because assumptions and investor expectations differ.
Which cash flows are used to value preference shares?
Use the contractual preference dividends and any redemption amount, discounted at the return required for their risk.
Continue learning: review the foundations of valuation, then follow the finance learning path.
Valuation of Bond and SharesIntroductionAsset can be real or financial, like shares and bonds are called financial assets, asset like plant and machinery are called real assets. Real assets can be valued easily but there is no easy way to predict the prices of share and bonds.
The unpredictable nature of the security prices is, in fact, a logical and necessary consequence efficient capital markets.
Concepts of ValueThere are many concepts of value that are used for different purposes,
- Book value-Assets are recorded at historical cost, and they are depreciated over years. Book value may include intangible assets at acquisition cost minus amortized value.
- Replacement value-Ignore the benefits of intangibles and utility of existing assets.
- Liquidation value-If company sold its assets it would be liquidation value.
- Going concern value
- Market value-Price which the asset or security is being sold or brought in the market.
Features of a BondA bond is a long-term debt instrument or securities issued by the government do not have any risk default.
The main features of a bond are
- Face value.
- Interest rate.
- Maturity.
- Redemption value.
- Market value.
(1).Bonds with maturity.
(2).Pure discount bonds.
(3).Perpetual bonds.
(1).Bonds with Maturity
Issue bonds that specify the interest rate and the maturity period.
- Value of bond with maturity
B0=INT X [(1/Kd)-(1/Kd(1+Kd)n] Bn/(1+Kd)n
Bond Value = Present value of interest + Present value of maturity value - Yield to Maturity
Kd= INT/ B0
(2).Pure Discount Bonds
Bonds do not carry an explicit rate of interest, it provides for the payment of a lump sum amount at a future date.
- B0 = M / (1+Kd)n
(3).Perpetual Bonds
Also called consols, has an indefinite life and therefore, it has no maturity value.
- B0 = INT / Kd
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