Valuing Bonds and Preference Shares

A bond is a promise: fixed payments of interest on fixed dates, and the return of the principal at the end. Because the amounts and dates are known, the value of a bond is a matter of arithmetic rather than judgement. It is the present value of the promised cash flows, discounted at the return that investors now require on bonds of that risk and term.

If that required return is higher than the bond’s interest rate, the bond must sell below its nominal value, so that the buyer earns the extra return as a gain; if it is lower, the bond sells above. This is why bond prices move opposite to interest rates.

The same idea values preference shares, and with one extra step a convertible bond, which is worth the higher of what it is as debt and what it is as shares.

This topic explains how to value irredeemable and redeemable bonds (including half-yearly interest, premiums and zero-coupon bonds), why bond prices move with yields and why longer bonds move more, the valuation of preference shares, and the valuation of a convertible bond, with worked examples. The next topic covers the efficient market hypothesis.

The terms and values of a convertible bond were tested in May Diet, 2026, Question 7 (15 marks). Read discounted cash flow valuation of a business first.

The principle

The value of a debt security is the present value of all future interest payments and of the repayment of principal, discounted at the pre-tax required return of investors. Tax is ignored because investors’ tax positions differ.

The amounts are known, not estimates, so a bond valuation is more exact than a share valuation. The uncertain element is the required yield, which is taken from the market yield on similar bonds (same issuer risk and term). By convention the value is stated per ₦100 or ₦1,000 nominal.

In Nigeria, Federal Government bond yields are the benchmark for the risk-free part of the required yield, and corporate bonds add a spread for credit risk (see the earlier topic on the cost of debt).

Irredeemable bonds

Interest for ever is a perpetuity: V = interest ÷ required yield. A 9% bond of ₦100 nominal with a required yield of 12% is worth 100 × 9% ÷ 12% = ₦75.00 (ex-interest). If interest is paid half-yearly, discount at the half-year rate: a 10% bond of ₦1,000 pays ₦50 every six months; with a required return of 8% a year (4% every six months), V = 50 ÷ 0.04 = ₦1,250. (If the 8% is an effective annual rate, the half-year rate is 1.08^0.5 − 1 = 3.92% and the value ₦1,274.5; use the basis given.)

Redeemable bonds

The value is the present value of the interest to maturity plus the present value of the redemption payment. A 14% bond of ₦1,000, with four years to redemption at par and a required yield of 11%, pays ₦140 a year:

The bond is worth about ₦1,093 (the unrounded figure is ₦1,093.07): above par, because it pays more than investors now require. Other cases:

• Redemption at a premium:
  for a ₦1,000 bond with interest of ₦80, redeemable in five years at 110% (₦1,100) and a required yield of 10%, the value is 80 × 3.791 + 1,100 × 0.621 = 303.3 + 683.1 = ₦986.3.
• Half-yearly interest:
  a ₦100 bond with a 12.5% coupon paid half-yearly (₦6.25 each), three years to redemption at par, and a required return of 16% a year (8% each half-year): six periods; V = 6.25 × 4.623 + 100 × 0.630 = 28.9 + 63.0 = ₦91.91.
• Zero-coupon bond:
  no interest; the value is the redemption value discounted: ₦100 redeemable in four years at 14% is 100 ÷ 1.14⁴ = ₦59.21.
  The whole return is the gain between the price and the redemption.

The yield that investors actually earn if they buy at a price and hold to redemption is the redemption yield or yield to maturity, the internal rate of return of the cash flows (the earlier topic on the cost of debt shows the method). Valuation and yield are the same calculation in opposite directions: given the yield, find the price; given the price, find the yield.

Price, yield and maturity

The same 14% ₦1,000 bond has different values as the required yield changes, and the effect is bigger the longer the time to redemption:

At a yield equal to the coupon the bond is worth its nominal value (par). Below the coupon it is worth more, above it, less. A rise in yield from 14% to 17% cuts the four-year bond by 8.2% but the ten-year bond by 14.0%.

Holders of long bonds face greater interest rate risk, which is why long bonds yield more than short ones in a normal market, and why a company that expects rates to rise would prefer to hold short bonds. Bond prices also fall if the issuer’s credit risk rises, since the required yield includes a premium for default risk.

Preference shares

A preference share pays a fixed dividend, so it is valued like a bond but with dividends in place of interest. Irredeemable: V = dividend ÷ required return. An 11% preference share of ₦100 with a required return of 14% is worth 11 ÷ 0.14 = ₦78.57. Redeemable: the present value of the dividends plus the redemption value: with five years to redemption at ₦105 and a required return of 13%, V = 11 × 3.517 + 105 × 0.543 = 38.7 + 57.0 = ₦95.68.

The required return on a preference share is above that on a bond of the same company, because its holders rank after lenders and the dividend may be missed. It is below the return on ordinary shares, whose holders rank last.

Valuing a convertible bond

The market value of a convertible bond is the higher of:

1. its value as a straight bond redeemed at maturity (the floor); and
2. the present value of the interest until conversion plus the present value of the expected value of the shares into which it can be converted (the conversion value).

A ₦1,000 bond pays 5% (₦50) a year, is convertible in three years into 200 shares, and redeemable at par otherwise. The share price is ₦4.50, expected to grow at 8% a year; investors require 12%. The expected share price in three years is 4.50 × 1.08³ = ₦5.67, and the conversion value 200 × 5.67 = ₦1,133.7.

• As a straight bond:
  50 × 2.402 + 1,000 × 0.712 = 120.1 + 711.8 = ₦831.9.
• If converted:
  120.1 + 1,133.7 × 0.712 = 120.1 + 806.9 = ₦927.1.

The bond is worth the higher figure, about ₦927, because holders will convert (the conversion value of ₦1,133.7 exceeds the redemption value of ₦1,000). If the conversion value had been below the redemption value, holders would take the cash and the straight value would apply. When the answer is obvious from the cash flows, as here, only the higher need be calculated.

The result also depends on the market’s present view: where the share price is already above the conversion price, the bond trades like the shares.

The ideas in more depth

Why the price of a bond moves opposite to the yield

The cash flows are fixed. If investors can now earn more elsewhere, the only way the bond can offer the higher return is for its price to fall, so that the same payments are a larger percentage of what is paid.

A bond that was issued at par at 14% is worth less when market yields reach 17% for the same reason that an old fixed rent is worth less when new tenants pay more.

Why a convertible has a floor

A convertible can never be worth less than the same bond without the option to convert, since the option has no negative value. As the shares rise, the conversion value grows and the bond comes to be priced by it; as they fall, the straight value limits the loss. The investor accepts a lower coupon than on a straight bond in return for this option.

Sources and references

• Bonds in Nigeria are issued under the Investments and Securities Act 2025 and the rules of the Securities and Exchange Commission; Federal Government bonds are traded on the FMDQ platform with half-yearly coupons; prices are quoted per ₦100 nominal. International Financial Reporting Standard (IFRS) 9 covers the measurement of financial instruments and International Accounting Standard (IAS) 32 the split of a convertible.

These points are stated as at 5 November 2026.

Worked examples

1. Interest. ₦9.
2. Value.
   9 ÷ 0.12 = ₦75.00.

1. Discount factor.
   1 ÷ 1.14⁴ = 0.592.
2. Value. ₦59.21.

1. Value.
   11 ÷ 0.14 = ₦78.57.

How to answer in the exam

• List the cash flows by year, using the ex-interest basis.
• Discount at the pre-tax required yield and show the factors.
• For a convertible, calculate the straight value and the conversion value and take the higher.
• Comment on how value changes with yield and maturity.

Common mistakes in the exam

• Using the after-tax rate to discount.
• Discounting half-yearly flows at the annual rate.
• Forgetting the redemption payment or the premium on it.
• Including the interest just paid (cum-interest).
• Taking the lower of the straight and conversion values for a convertible.
• Using the coupon rate instead of the required yield as the discount rate.

Quick revision

• Bond value = present value of interest and redemption at the required yield.
• Irredeemable: interest ÷ yield; zero-coupon: redemption discounted.
• Higher yield, lower price; longer maturity, bigger move.
• Convertible = higher of straight value and conversion route.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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